text:
Institutional Architecture
Gymnasium of the Louis de Cormontaigne High School in Metz
Metz, France
agence ENGASSER & associés
Institutional Architecture, Health + Wellness, Industrial Architecture, Institutional Interior Design, Lighting Design
Paris, France, 2018-03-01 -
Louis de Cormontaigne's new gymnasium is located on the tip of the island between the Moselle River on one side and the canal on the other, a bow-shaped structure across from the day school and the motorway, the location's major acoustic challenge. The building reproduces the orientation of the high school building and is perpendicular to the canal. It has also been designed according to the input of light with broad openings in Reglit glass on the north-by-northeast side to offer unified, ideal natural light. The south-by-southwest side has been designed as very opaque, like a mask—a large acoustic shield to counter the motorway noise. Work on the volumes and roofs, reproducing the shed-like appearance, also adds to the indoor staging and the design of the sports areas. Composed of a main all-purpose gym entirely clad in wood and a secondary gym for body-building, the new gym offers the best possible conditions for all sporting activities.
A Challenging Context
The new gymnasium is located on the site like a ship's bow, facing the Louis de Cormontaigne High School building, a three-story structure housing the classrooms between the Moselle River and the canal and facing the motorway, which is the site's main acoustic challenge. The decision to place the playing field between the two buildings creates a welcome distance between them. It makes it possible to suitably meet the need for working continuity with the present gymnasium and the entire high school having to continue to operate until the new complex is delivered.
The geometric composition reproduces the high school's orientation, perpendicular to the canal, with a slight concentric zone rotation up to the bridge, which itself is a part of the design. It incorporates the outdoor areas like full-fledged elements of the entire layout.
To limit the motorway noise, the southwest facade has been designed very opaque like a shield, a purposely elevated acoustic screen to both create a shed in the north and to protect it from the motorway noise. This facade is covered by cladding over insulation on the outside, then another wooden soundproofing layer on the inside. It thereby ensures both thermal and acoustic quality inside both sports halls.
Three Layers, Three Roofs
The sports halls call for imposing volumes that are often difficult to incorporate into an urban setting. Here, we have carved the building up into several layers. It includes a low, telluric foundation; this is the volume of the annexes. Above it three ledges form 3 layers that cut through the top of the big halls through which abundant natural light flows in.
This composition creates 3 ledges for 3 roofs:
The first roof caps the low volume of the annexes. It is landscaped because it is visible from the school building, the classrooms, and motorway. It is extended by a slight overhang of the roof between the annexes and the outdoor areas.
The second roof covers the large halls. A slight inflection translates the sectioning, a two-layer sealant placed onto a steel base.
The third roof serves as an acoustic screen facing the motorway. Its curve enables a third contribution from the north, partially vertical light, and completes the luminous scheme. It is clad in continuous metal between the roof and its vertical part.
Bright Spaces
With a view to visual and environmental comfort it is essential for gymnasiums to choose the best orientation in relation to the sun. In this case the gym's north/south position highlights the quality of natural light.
The vertical, abundant northern light provides the uniformity good for sports because it isn't too dazzling. The translucent Reglit glass of the northern facades provides generous, harmonious light in the main gym's remotest corners. The sheds make it possible to increase the light cone throughout the entire volume of the two gyms that avoids shadowy or overly bright areas. They also add to the indoor decor and the design of sports areas.
The soft, controlled southern light provides the gyms with added heat from the sun. This intentionally soft opening gives a direct view to the surrounding plant life and woodland, creating a warm, friendly undergrowth-like atmosphere.
The presence of a "hat" at the upper level makes it possible to avoid overheating from sunlight in the summer while still taking advantage of the winter sun.
The gyms thereby enjoy excellent lighting and add to the building's heating performance while providing a pleasant view.
Simple, Readable Functionality
The annexes' low volumes open onto the athletics track and outdoor football pitch. It revolves around the volume of the main gym by circling it on the northern and southeastern corners. A large glass facade in this low volume makes the foot traffic-friendly, pleasant and bright. Interaction with the outdoor areas is therefore clear-cut. This entire low volume is topped by a green roof to limit the volumes in rainwater retention, improve heating and offer a pleasant view from the classrooms which have an uninterrupted view of the new gym.
This base condenses the many access points, i.e. from the path along the embankment for outdoor users, from the high school's buildings and from the outdoor track and pitch.
The inside has been organised to enable several uses of the annexes and access points:
• The smaller gym has a dedicated changing room. It is located across from it and also opens onto the outdoor areas
• the main gym has two dedicated changing rooms, also accessible through the glass band
• the main access to the centre gives onto both gyms with a second access point into the main gym
• a secondary access point from the embankment for sporting associations and clubs (evenings and weekends)
• outdoor access to the service and storage rooms
The entry hall for the general public can easily be seen from the school and outdoor areas. It communicates with the entrances of the two gyms, the reception, the toilets, the changing rooms for teachers and the service areas. A friendly space that, weather-permitting, extends to the outdoor space. The changing rooms are walk-through in order to adhere to the ideal layout:
• dirty feet/clean feet
• street shoes/sports shoes
Location: Metz (57)
Client: Région Alsace-Champagne-Ardenne-Lorraine
Team: agence Engasser & associés
ID+ (engineer)
Programme: Reconstruction and extension of the gymnasium, two gyms and an outdoor field
Area: 2,000 m² SP - 1,850 m² SU
Budget: 2.9 M€ HT
Photographers: Mathieu Ducros
www.agenceengasser.com/
www.facebook.com/agenceengasser
twitter.com/AgenceEngasser
kyubes
Nancy Angama
nancy@v2com-newswire.com
Phone +33 (0) 6 60 68 84 33
The Louis de Cormontaigne High School in Metz
Low-resolution images ~ 4.39 MB
High-resolution images ~ 621 MB
Photo credit: ©Mathieu Ducros
Very High-resolution image : 19.2 x 12.8 @ 300dpi ~ 9.3 MB
Photo credit: ©aEa, agence Engasser+associés
Medium-resolution image : 10.0 x 5.0 @ 300dpi ~ 3.7 MB
Medium-resolution image : 10.34 x 5.72 @ 300dpi ~ 1.8 MB
Paris, France, 2018-01-12
The House of Sports in Bezons
Finland, 2019-07-17
Helsinki Central Library Oodi
ALA Architects
Bio 21 Nancy Millis Building
DesignInc
Dongcheng Qu, China, 2019-07-02
2019 AZ Awards Winner: UCCA Dune Art Museum
Suginami City, Japan, 2019-06-28
Tomioka Chamber of Commerce and Industry
Tezuka Architects
Chicago, United States, 2019-06-10
Rockford Public Schools K-5 Prototype School: Architecture as Community
CannonDesign
École Sainte-Anne - A new redesigned schoolyard
Taktik design
Edmonton, Canada, 2019-05-23
The iconic new Walterdale Bridge connects the city, nature, and people
EVOQ Architecture appointments ensure continuity of firm's legacy
EVOQ Architecture
Bishop's University Library Learning Commons: New Lighting and Interior Design
LumiGroup
Maison de la littérature (House of Literature)
Chevalier Morales Architectes


This report studies the Fiber Laser market. A fiber laser or fiber laser is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, thulium and holmium. They are related to doped fiber amplifiers, which provide light amplification without lasing. Fiber nonlinearities, such as stimulated Raman scattering or four-wave mixing can also provide gain and thus serve as gain media for a fiber laser.
In the coming years there is an increasing demand for Fiber Laser in the regions of North America and Europe that is expected to drive the market for more advanced Fiber Laser. Increasing of downstream industry fields expenditures, more-intense competition, launches in introducing new products, increasing of spending on general industry, retrofitting and renovation of old technology, increasing adoption of Fiber Laser will drive growth in China markets.
Globally, the production of CW fiber laser is concentrated, as the development and manufacturing technology is still high. IPG Photonics holds the lion's share of global fiber laser industry with its industry top technology status. Over the past years, the development of low power and small fiber laser has achieved remarkable market in China. The production volume of these low end fiber laser in China is growing quite fast. But the production value of these low end fiber laser is not high.
The consumption volume of Fiber Laser is related to downstream industries and global economy. As there will be many potential market for Fiber Laser, the prospect of Fiber Laser is still be full of hope.
The worldwide market for Fiber Laser is expected to grow at a CAGR of roughly 12.6% over the next five years, will reach 3420 million US$ in 2024, from 1680 million US$ in 2019, according to a new GIR (Global Info Research) study.
This report focuses on the Fiber Laser in global market, especially in North America, Europe and Asia-Pacific, South America, Middle East and Africa. This report categorizes the market based on manufacturers, regions, type and application.
Chapter 1, to describe Fiber Laser product scope, market overview, market opportunities, market driving force and market risks.
Chapter 2, to profile the top manufacturers of Fiber Laser, with price, sales, revenue and global market share of Fiber Laser in 2017 and 2018.
Chapter 3, the Fiber Laser competitive situation, sales, revenue and global market share of top manufacturers are analyzed emphatically by landscape contrast.
Chapter 4, the Fiber Laser breakdown data are shown at the regional level, to show the sales, revenue and growth by regions, from 2014 to 2019.
Chapter 12, Fiber Laser market forecast, by regions, type and application, with sales and revenue, from 2019 to 2024.
Chapter 13, 14 and 15, to describe Fiber Laser sales channel, distributors, customers, research findings and conclusion, appendix and data source.


text:
Modernizing without Westernizing: Social Structure and Economic Action in the Indian Financial Sector
Chen, G and Chittoor, R and Vissa, B (2015) Modernizing without Westernizing: Social Structure and Economic Action in the Indian Financial Sector. Academy of Management Journal, 58 (2). pp. 511-537.
To better understand whether the transition by Asian countries toward market economies mirrors the path taken in the West, we ask how embedded network ties between equity analysts and the chief executive officers (CEOs) of the firms that they follow in India influence the accuracy of analysts' earnings forecasts. We contrast traditional institutions of caste and regional language with contemporary institutions, such as universities, as the locus of such ties. We posit that CEOs from the postreform generation are more likely to transfer material private information via their school ties, while prereform-generation CEOs favor caste or language ties. Contrasting domestic business groups (BGs) with Western multinational corporations (MNCs) as organizational contexts, we argue that BGs legitimate the transfer of private information along particularistic ties, whereas MNCs mitigate such transfers. Our conceptual framework is supported by analyses that draw on a sample of 1,552 earnings forecasts issued between 2001 and 2010 by 296 equity analysts. Our findings suggest that the embeddedness perspective should be broadened to incorporate the influence of the larger historical social structures within which economic action is embedded, and to view BGs as carriers and repositories that blend modern management practices with particularistic behavioral patterns among top executives.
Chittoor, R UNSPECIFIED
Business Groups, MNC, BGs
https://doi.org/10.5465/amj.2012.1039

redpajama_set_name: RedPajamaCommonCrawl


Under the general direction of a Program & Project Supervisor, this Public Utilities Regulatory Analyst V (PURA V) will be assigned responsibility over issues related to video service and broadband infrastructure and usage with the highest scope of complexity, sensitivity and controversy. This position will be located within the Video Franchising and Broadband Deployment Group.
This PURA V serves as the Commission's lead technical and policy analyst responsible for a variety of the Group's most complex and sensitive analytical assignments regarding video franchising, broadband infrastructure and competition within California. The incumbent will also provide expert advice regarding advanced communications technologies, issues of convergence in the communications and broadband areas, and specifically work on ensuring the Commission's processes do not act as a barrier to video competition and broadband deployment in California. These issues will have significant attention from external stakeholders, including Executive and Legislative decision makers, service providers, local entities and the media. The analysis to be undertaken may use moderate to advanced statistical methods. The incumbent will be expected to present the findings and propose appropriate policy recommendations to Commission management and decision makers clearly and concisely either verbally or in writing.
The assignments will include being a senior or lead analyst to support the Video Franchise Group's assessment of video programming services, broadband infrastructure and subscribership levels, research in advanced technologies on which broadband and video services rely, the variety and availability of, and subscribership to, various video and broadband products in California, research surrounding the composition of services offered to consumers purchasing video programming and broadband products, and researching and providing support to other state agencies involved in supporting video programming service, broadband deployment and broadband-based programs. The incumbent will also work closely with Administrative Law Judges (ALJ) and Commissioners' offices. Topics particularly include regulatory, legislative and judicial actions at both the state and federal level to review and reshape broadband and video policy, policies regarding the deployment of facilities (such as access to utility support structures and rights of way) and policies regarding industry structures in support of competitive markets. Work will require high-level analyses to evaluate, for example, the state of the broadband and video marketplaces and types of policy recommendations which will effectively expand video service competition, broadband penetration and digital access in California, and eliminate the Digital Divide.
The incumbent is expected to work independently as a team leader, or part of a team, supporting ALJs and decision makers in major proceedings, conducting workshops and preparing reports, conducting research and studies on pending issues, and presenting findings and recommendations to management and Commission decision makers. The incumbent may also interact with consumers, local government and industry representatives. The PURA V's work expertise should cover a complex synthesis of economics, finance, telecommunications, cable, and information services law, the government, private, and non-profit marketplaces for video and broadband services and other advanced technology and technology applications, and the practical intersection of video service and broadband infrastructure. In addition, the incumbent may also be involved in other related projects and assignments as necessary.
This PURA will undertake work assignments and tasks to help the Legislature, Commissioners, other policymakers and the public understand, develop and/or evaluate various video service and broadband-related policy issues.
The Communication Division's Video Franchising/Broadband Deployment Group assists the Commission in implementing the requirements of AB 2987, the Digital Infrastructure and Video Competition Act of 2006 (DIVCA), and gathers, analyses and visualizes and reports on data regarding video and broadband deployment, quality, subscribership, and employment. The Group provides analysis and advice regarding policies, laws and regulations involving video and broadband services and supports other deployment, adoption and usage projects and programs.
If you are using education to meet the minimum qualifications for this position, you must submit a copy of your transcript or diploma. An official transcript will be required prior to appointment.
Applications will be screened and only the most qualified applicants will be selected to move forward in the selection process.Applicants must meet the Minimum Qualifications stated in the Classification Specification(s).
and many more! Visit www.calhr.ca.gov for a full list of available benefits!
Demonstrated ability to conduct independent research and analysis.
Demonstrated ability to conduct policy and data analysis and prepare clear and concise written work products and oral presentations.
Demonstrated ability to engage with others in a collaborative settings; work cooperatively with all levels of staff, management, decision-makers, stakeholders and government representatives and recommend policy outcomes.
Demonstrated ability to take initiative on work assignments, manage multiple tasks; prioritize work according to strict deadlines and exercise independent judgement.
Demonstrated ability to lead projects, work well in a team environment and establish and maintain cooperative and positive working relationships with others.
Knowledge of state and federal communications regulation and administrative proceedings including Rulemakings and Inquiries.
Knowledge of communications technologies and business plans and the impact of competition and regulation on innovation, technological development and investment.
Knowledge of cable television franchising at the state and local levels, including the California state-issued franchising scheme, and the interaction of state and federal policies, laws and regulations.
Knowledge of state and federal policies, laws and regulations relating to access to, and the use of, utility rights of way.
Knowledge of state and federal policies, laws and regulations relating to communications attachments to utility support structures (poles and conduits), including both access and safety issues.
To become "list eligible" for consideration, interested candidates must successfully pass a civil service exam.
**The Department of Human Resources currently administers the Public Utilities Regulatory Analyst V (PURA V) online examinations on a continuous basis.
A new report highlighting how cable ISPs can make smart cities become a reality offers city planners successful case studies and useful planning steps for how to make their communities digital leaders.
In an interview with NCTA, The Walter Kaitz Foundation's new executive director Michelle Ray shed light on how the Foundation came to be and how it continues to lead the charge for cultivating diverse talent and initiatives across the internet and television landscape.
Cox Communications has long been making a difference for families and individuals across its footprint through Connect2Compete–which now reaches over 400,000 people that Cox serves–and its dedication to broadband adoption over the past two decades.
In the latest video from CableLabs' Near Future series, light field displays are featured prominently and viewers get a peek into how people will interact with media in the future and how it will impact the future of education.


The Wine Collective's Wine Library is one of the largest sources of wine information in Australia, created to give our customers all the help they need to find the perfect wine for any occasion.
Learn about the hundreds of different grape varieties in our wine selection.
Travel to our finest wine regions – both in Australia and around the world.
Meet the dozens of local and international wine critics that write our wine reviews.


text:
1. The first Sunday edition of the Newark News in 1946 easily made the transition from the previous week's Sunday Call because it picked up most of the Sunday Call features and many of its key staff members.
Edward F Bataille, editor of the Sunday Call became a member of the editorial staff of the Newark News. Many Call editors and writers went over to the News including Josephine Lawrence, Edward Sothern Hipp, John E. Beer, long-time Call sports editor Gus Falzer, and Antoinette Gentile, the Call's society editor. Harry Dorer, the Call's chief photographer, took up similar duties at the News.
Copyright 1998 - 2021 Glenn G. Geisheimer


Automotive OEM is recruiting a Purchasing Administrator on a 12 month contract basis to provide administrative support to the procurement team.
The administrator will assist the Project Manager and wider team with programme implementation, data analysis and administrative activities supporting development of processes and documents including reporting key metrics.
You will be a positive and pro-active self-starter with excellent attention to detail and be confident to support the procurement team.
You must hold demonstrable relevant previous experience across data analysis & administration using Microsoft Office applications, in particular Excel.


text:
Review: Alienware's 38-inch Curved Gaming Monitor Is a Spectacular Viewing Experience
Advertiser Disclosure: At Slickdeals, we work hard to find the best deals. Some products in our articles are from partners who may provide us with compensation, but this doesn't change our opinions.
By Mike Jackson
I was never truly sold on the ultrawide movement. To me, they always felt like a full 4K monitor had been cut in half. But, at 37.5 inches from corner to corner, the massive Alienware 38 Curved Gaming Monitor has me well and truly on board.
The sheer size makes all the difference. The display area is taller than a decently sized 16:9 monitor (including my 27-inch Acer Predator), but the horizontal dimension reaches deep into your peripheral vision. Thus, for the first time, I genuinely feel like I'm getting double the width, rather than simply losing half the height.
It also has a killer specs list that makes it great not just for gaming but also as a productivity monitor. It's a true replacement for the traditional multi-monitor setup. But this luxury will cost you. With a regular retail price of $1,899.99, it's quite the investment. But for your money, you're getting one of the most cutting edge, awe-inspiring gaming monitors available today.
Shop at Dell
Alienware 38 Curved Gaming Monitor Technical Specifications
37.5-inch ultrawide display
3840 x 1600 resolution (21:9 aspect ratio)
2300R curved
IPS type display
95% DCI-P3 wide color gamut
VESA DisplayHDR 600 with local dimming
Nvidia G-Sync Ultimate
144Hz refresh rate
Up to 1ms gray to gray pixel response
ComfortView mode
1x DisplayPort, 2x HDMI 2.0
AlienFX RGB lighting
Yes, It's Really Wide
Credit: Slickdeals
The Alienware 38 Gaming Monitor has an impressive list of features, as you'd expect with a price tag that will bust through the $2,000 mark once taxes are added. But in the interest of not getting bogged down in the numbers, just have a glance at the list above. Yes, it's big. It's also bright, vibrant and fast.
With that established, I just want to talk about what it's like to use such a massive, expensive monitor. The short answer? It's amazing in just about every way.
Firstly, the obvious: Ultrawide monitors present clear benefits to productivity and multitasking since you have so much more space to play with. Video editing is a particular treat, as acute scrubbing becomes a breeze. And your video monitoring window is still large, even when tucked into a quarter of the screen.
Multitasking is awesome. When split down the middle, it feels like using two separate screens. But I've also been quite happy to slice it into thirds, with email, a word processor and web browser all comfortably sharing an even slice of the action.
I'm a compulsive second-screen user. While testing this monitor, though, my second screen went pretty much unused in all but one scenario: to display system monitoring apps while playing games in full screen on the big boy. That's the only reason why I'd keep a second screen available.
The Real Meat and Potatoes
Right, I got the boring stuff out of the way first. My excitement of reviewing this ridiculously large Alienware monitor wasn't just to talk about multitasking web browser windows.
This was a no-faffing around testing process. That means straight to DOOM Eternal the moment I got it set up. Hoo boy! If there's a better game to demonstrate the full capabilities of an ultrawide, HDR-capable, high-refresh rate monitor, I certainly can't think of it.
My slightly overclocked Geforce RTX 2080 graphics card can run the impressively optimized DOOM Eternal at over 100fps at its native resolution (3840 x 1600) on ultra settings, and it looks incredible. This massive screen brought the game's high-detail environments to the forefront, and with HDR activated, the spectacular highlights in its demonic, contrast-y worlds really pop.
It's a colorful game, too, putting every last bit of that P3 wide color gamut to good use. All of that, along with a silky smooth, G-Sync-locked frame rate over such a massive canvas is really a sight to behold.
On to Quake Champions next — a fast-paced multiplayer arena shooter to test the response and accuracy of this monitor against other humans. I know many competitive gamers prefer to play on smaller screens so they don't miss opponents in their peripheral vision. I get it. But I'm less about the try-hard life and more about immersion, and this screen delivers in spades.
Speaking of immersion, oh yes, I had to try the new Microsoft Flight Simulator. Of course, it's a total showstopper. Seeing the floating horizon stretching across this massive screen, those fluffy clouds hanging beautifully above a densely packed city, this game (sorry, 'simulator', don't @ me) is the reason to own a monitor like this, even if it does tank the frame rate on the most powerful PCs.
I touched down on the runway, and then I jumped swiftly over to Command & Conquer Remastered (Yes, Doom, Quake, MSFS and C&C. I know, I'm an old man). I expected the extra screen space to make an excellent canvas for commanding my massive armies of heavy tanks, but unfortunately C&C Remastered was my first (and only) disappointment. Since it doesn't fully support ultrawide screens, there was just a black bar of nothingness on the left side.
I'm highlighting this not because I expect many of you to play C&C, but because it demonstrates one of the main challenges of gaming on an ultrawide monitor: the inconsistent support for the 21:9 ratio.
This is obviously not something that's specific to this monitor. It affects all ultrawides. And of course, the issue extends to other media like YouTube videos or TV shows, the vast majority of which display in 16:9 with black borders on the sides. But, for gaming at least, it's a situation that has improved greatly in recent years. This is thanks both to an increase in official support in modern games, and the rise of reliable unofficial mods that can be used to patch most games that snubbed ultrawide support.
Signature Alienware Touches
Alienware's 'Lunar Light' aesthetic continues to be a winner in my book. It's just such a clean, modern look. It's edgy enough to be at home next to an RGB-happy gaming PC, yet subtle enough for a respectable office setting.
The AlienFX lighting is tasteful, illuminating the power button and an accent on the rear of the screen. There's also a down-firing light on the underside, which can be turned on or off with a simple brush of the hidden touch sensor below the Alienware logo. And all lighting can be customized to display the full RGB colors of your liking.
For a screen of this size, the stand does well to keep it sturdy without taking up too much space. It's obviously not ideal on a compact desk, but what do you expect from a 38-inch monitor? If space is a concern, a VESA mount will certainly improve things.
A Treasure Trove of Options
It wouldn't be a gaming monitor without a long list of gaming-oriented menu options for you to play with, although the results are a predictably mixed bag.
The usual options to display a timer, the frame rate or adjust the display alignment are all nice features, even if somewhat gimmicky.
I found the out-of-the-box picture to be pretty good, but there are also a load of picture preset modes to choose from, and surprisingly, they're not all bad. Standard mode offers a decent balance of neutral colors and slightly dimmed lighting that's easy on the eyes. I really like the 'RPG' mode, which seems to slightly boost saturation — something I tend to do on all my screens due to my preference for more vibrant colors.
The 'FPS' mode kills blacks and overall contrast, so that's a no-go for me. And the Sports mode, while certainly bright, is just too overbearing. Conversely, Dell's ComfortView mode is perfect for long periods of non-gaming screen time, since it cuts down on blue light emission to reduce eye strain.
The Overdrive Setting Isn't for Everyone
A Response Time setting, otherwise known as 'overdrive', is another feature I personally have mixed feelings about. It affects the screen's gray-to-gray response and input lag by blasting extra voltage at those little pixels. But anything above the standard 'Fast' setting introduces an issue where the pixels overshoot their target color value.
In practice, this manifests as a so-called corona artifact, where contrasting colors leave behind a trail of bright light. On the highest 'Extreme' setting, you get the best pixel response and lowest input lag, but it also induces poor image quality in motion, with blown out blacks and severe visual artifacts that, to me, are simply unacceptable.
Luckily, the medium setting, 'Super Fast', strikes a decent balance of reducing input lag below that of the standard setting, while only introducing slight visual artifacts that you'd have to be trying to see. This is likely the best setting, since it looks significantly better and I reckon you'd need to be a professional gamer to notice the couple of milliseconds of added lag it presents over 'Extreme.'
Dark Stabilizer and Local Dimming
On that note, Dell's Dark Stabilizer is also a feature that I didn't find particularly advantageous. It raises visibility in darker areas of the display to help gamers spot potentially hidden foes. Unfortunately, it does this by destroying the colors and contrast levels. Look, for goodness' sake, please don't spend $2,000 on a beautiful wide-color gamut monitor and turn on this feature.
Local dimming is another area of contention, since some have complained of this monitor's relatively low number of separate backlight zones. This, in theory, is detrimental in darker scenes, where a localized light source (like a small fire in a dark forest, for example) will cause a large vertical bar of bloom to appear as the backlight illuminates that entire section of the display, forcibly raising black levels to a murky gray.
But in use, I'd argue that local dimming is a non-issue. Ori and the Will of the Wisps is a dark game with a bright white character, and I didn't notice any such artifact. If you need a special benchmarking tool to demonstrate a flaw because it can't be tangibly demonstrated when in normal use, then I'd say it doesn't really make much of a difference.
Should You Buy the Alienware 38 Curved Gaming Monitor?
Absolutely you should. That is, if you can afford it without remortgaging the house, selling the dog and living on cup noodles for three years. Yes, it's expensive, but for your money you get one of the most spectacular-looking gaming monitors on the market.
And it's not just an excellent performer for gaming. Its wide color gamut is great for video and photo production, not to mention the obvious benefits of multitasking on a screen this large. It's also worth considering as a true alternative to having two high-end 16:9 monitors.
That said, $1,899.99 is a lot to ask, even for a monitor of this quality. Luckily, Dell is known for running frequent sales, and it's currently discounted to $1,449.99, at the time this review was published. In my opinion, if you can find this monitor for around $1,500, I'd say go ahead and grab it!
Shop Now at Dell
Make sure you don't miss out on the next Dell sale by setting a custom Deal Alert. We'll notify you as soon as a new discount pops up on our forums. Additionally, check in on all current sales on our Dell Coupons page.
Can't Find a PS5 or Series X In-Stock? Save Christmas With These 12 Gamer-Friendly Gift Ideas
Review: Google's Nest Thermostat Smartly Manages Your Home Environment So You Don't Have To
Our editors strive to ensure that the information in this article is accurate as of the date published, but please keep in mind that offers can change. We encourage you to verify all terms and conditions of any product before you apply.
Costco Coupon Book February 2023
5 Must-Watch Movies to Celebrate AAPI Heritage Month
14 Cheaper YETI Cooler Alternatives You May Not Know About
Is a Disney Plus Subscription Worth It?
How to Get Free Trials from the 21 Best Video Streaming Services
Stop Overpaying for Shows and Get on These Streaming Bundles
Where to Find Discounts on The Amazon Fire TV Stick 4K
Where to Find the Best Black Friday 4K Television Deals 2021
Amazon Has the Best Price on Apple AirPods Right Now
Dell's New G5 Gaming Desktop Offers Punch for Gamers of All Weight Classes
2022 REI Anniversary Sale and Deals Roundup
How to Score This Season's Hottest Gaming Consoles
How New PlayStation Plus Subscribers Can Get 50% Off a 12 Month Subscription
2021 Holiday Shipping Deadlines to Guarantee Christmas Delivery
The Best Black Friday Laptop Deals Are Here
Walmart is Restocking the PlayStation 5 Today — Here's What You Need to Know to Actually Secure One
How to Get the Best Deals on Sundance Now Subscriptions
Tom and Jerry Premieres on HBO Max, But There's Still No Free Trial
Get These 2022 Model TV Deals Before They're Gone
Oliver Pretl-Drummond - January 27, 2023
Experts Guess Which Best Buy Product Is Cheaper
Pete King - January 19, 2023
These Are The Best Blender Deals Of All Time
Pete King - January 9, 2023
We Gave Away Expensive StockX Gifts
Shop Holiday Game Deals at All-Time Low Prices
Oliver Pretl-Drummond - December 20, 2022
How to Score Exclusive Student Coupons and Discounts
What To Do When Amazon Delivers To The Wrong Address
Internet-Based Ads


An acceptable cleaning product. It's a good idea to choose a product that's compatible with the coating of the alloys.
Alloy wheel polish or wax. Make sure it's appropriate for your wheels and if necessary seek advice from a specialist.
When you're ready to clean the wheels, start by rinsing them with water. It can be difficult to access hard to reach places within the wheel, but you should take it a step at a time so as not to damage the surface. Use a sponge to gently clean all the areas of the wheel.
Rinse away the soap or reapply if you think you've missed a spot. If you have a brush then that can help with cleaning the spokes.
Wipe the wheels down with a dry cloth and apply the wax or polish with a seperate cloth. Ensure that the entire surface of each wheel is coated with the substance.
Buff the wheels until they are shining.
How often should you clean your alloy wheels?
It's a good idea to ensure you clean your alloy wheels at least once a year. This could be done in the spring or summer months when the weather is dry. Regular maintenance will go a long way to making sure your car looks attractive when you're out on the road.
Sometimes, alloy wheels can get scuffed or damaged, and that's where specialist help comes in. Our technicians are able to restore your rusted alloy wheels to their original, pristine condition. We also offer a bespoke colour change and finish service that will give your vehicle an extra bit of personalisation.
For more information on our alloy wheels repair service, be sure to contact us via the online form, or call us on 01482 330147.


text:
Carrotmob Rewards Restaurant's Sustainability
By Cari Martens November 21, 2011 6:00 am
By Cari Martens	| November 21, 2011 6:00 am
We've all heard plenty over the last several weeks about the Occupy Wall Street protest movement that began in New York and spread across the country and beyond. Picket signs and sit-ins like this are examples of the "stick" method of free speech and activism.
Then there are the lesser-known "carrot" actions, like those which were carried out by MBA students at Missouri State University this week. The students staged what is called a carrotmob—rewarding a business for doing the right thing (carrot vs. stick), by organizing a "mob" of consumers to show up in support that of that business with open wallets.
Sometimes referred to as a "buycott" and usually organized through social media, carrotmobs have been around for a couple of years now, popping up here and there around the globe. But they seem to have picked up steam in recent months (steamed carrots anyone?). Carrotmobs were staged at some venues last month as part of the first annual National Food Day in the U.S.
In this most recent case, the beneficiary of the carrotmob was Farmers Gastropub, a restaurant in Springfield, Mo., near the MSU campus. The eatery operates as sustainably as possible, using a great many locally-sourced foods. But it wanted to take its efforts even further. Bill Griffiths, co-owner of the Gastropub, found out about a huge greenhouse in the area that wasn't being used, and wanted to put it to use, buying seeds to grow more local, fresh organic foods for the operation.
The MBA students heard about Griffith's idea and decided to reward his efforts with a carrotmob. A mob of more than 400 hungry consumers showed up at the restaurant over a period of just three hours, bringing in about $2,000 more than the usual take for a Wednesday night, earmarked for use in the name of sustainability.
Thanks in large part to the students' carrotmob, Griffiths and his son-in-law plan to have many new vegetables growing in the hydroponic greenhouse within a couple of months. (Perhaps including carrots?) They hope that many of last week's young carrotmobbers will be back to sample the fruits (well, mostly vegetables) of their labor.
For more insights and innovations check out CultureWaves®, the place to go for the latest observations in the World Thought Bank – events, ideas, trends and more. Add your own thoughts about anything in life – entertainment, design, technology, well-being and, yes, food trends. And, take a look at a few of our other Hot & Cool Food Trends.
Food & Drink, Food News
Cari Martens
Chef Cari is the host of The Food Channel's popular cooking series, :90 Seconds In The Kitchen. Her culinary expertise has a foundation in consumer insights and hands-on restaurant management. Martens was a Cultural Strategist for CultureWaves, the consumer insights network that fuels editorial content for The Food Channel, prior to expanding into culinary creative as The Food Channel's chef and host. Before that, Martens served as General Manager for Ristorante Teatro, a high-end Italian restaurant concept in southwest Missouri. Her passion for food inspires fans worldwide, and she's known for her trademark phrase, "Now get in the kitchen!"
Healthy Voyager Visits Quebec
Summer Spritzers with Eszter and Alfred


text:
Q: Ring-theoretic characterization of scalar matrices over a division ring Let $Q$ be a division ring, and let $M_n(Q)$ be the ring of $n \times n$ matrices over $Q$. If $Q' \subset M_n(Q)$ is the subring of scalar matrices, is it generally true that every ring automorphism of $M_n(Q)$ restricts to an automorphism of $Q'$? If $Q$ is a field, the answer is yes, for then $Q'$ is merely the center of $M_n(Q)$. But I'm not sure where to go when commutativity of $Q$ is taken away.

A: No. The subring of scalar matrices is not automorphism-invariant. In fact, the subgroup of $\mathrm{GL}(n,R)$ of scalar matrices may not be inner-automorphism-invariant, i.e. normal.
For example, let $Z$ be the subgroup of $G=\mathrm{GL}(2,\mathbb{H})$ of scalar quaternionic matrices. Given an arbitrary $\lambda\in Z$ we can explicitly compute $N_{\lambda}=\{g\in G:g\lambda g^{-1}\in Z\}$ (which is a subset but not a subgroup). Indeed, writing out $g\lambda =\mu g$ gives
$$\begin{pmatrix} a & b \\ c & d \end{pmatrix}
\begin{pmatrix} \lambda & 0 \\ 0 & \lambda \end{pmatrix}
=\begin{pmatrix} \mu & 0 \\ 0 & \mu \end{pmatrix}
\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
$$ \iff \begin{pmatrix} a\lambda & b\lambda \\ c\lambda & d\lambda \end{pmatrix}
=\begin{pmatrix} \mu a & \mu b \\ \mu c & \mu d \end{pmatrix} $$
If all $a,b,c,d$ are nonzero this gives four equations which, after conjugating, gives $\mu=$
$$ {}^a\lambda={}^b\lambda={}^c\lambda={}^d\lambda.$$
(If any of $a,b,c,d$ are $0$ then we simply omit them from the equality. Note ${}^px:=pxp^{-1}$.)
This is, in turn, equivalent to $a,b,c,d$ being equal modulo $C_G(\lambda)$. Without loss of generality we may assume $\lambda$ is not central, so $C_G(\lambda)\cong\mathrm{GL}(2,\mathbb{C}_\lambda)$ where $\mathbb{C}_\lambda\cong\mathbb{C}$ is the complex subalgebra of $\mathbb{H}$ generated by $\lambda$ (i.e. $\mathrm{span}\{1,\lambda\}$).
Now we may compute the normalizer $N_G(Z)$. It is the intersection of all $N_\lambda$, so if $g\in N_G(Z)$ then it must be in $x\mathrm{GL}(2,\mathbb{C}_u)$ (where $\mathbb{C}_u:=\mathbb{R}\oplus\mathbb{R}u$ and $x$ is one of the nonzero entries of $g$) for all imaginary unit quaternions $u$, or in other words $x^{-1}g$ is in $\bigcap_u \mathrm{GL}(2,\mathbb{C}_u)=\mathrm{GL}(2,\mathbb{R})$. Therefore, $N_G(Z)=Z\cdot\mathrm{GL}(2,\mathbb{R})$ which is proper in $G$, hence $Z$ is not a normal subgroup.
In fact this argument generalizes to any dimension,
$$ N_{\mathrm{GL}(n,\mathbb{H})}(\mathbb{H}^\times\cdot I)=\mathbb{H}^\times\cdot\mathrm{GL}(n,\mathbb{R}). $$

redpajama_set_name: RedPajamaStackExchange


Nestle has a total of 34 product technology centers and R & D centers in the world. The slide spring cases used on coffeemaker ,developed together with Shanghai Nestle R & D Center since 2011 were independently designed and manufactured by us, and were exported to Nestle's assembly plant in Europe, Flextronics, the world's second OEM since 2012 with the accumulated delivery quantity exceeding 2.5 million pcs. This product is our patented product.


text:
LONGSCAN Examines Fatherhood
April 2002Vol. 3, No. 3LONGSCAN Examines Fatherhood
The Longitudinal Studies of Child Abuse and Neglect (LONGSCAN) (http://www.sph.unc.edu/iprc/longscan) is a consortium of research studies made up of five satellite sites and a coordinating center at the University of North Carolina. The studies operate under common by-laws and procedures, but each site is conducting its own unique research on the causes and impacts of child maltreatment. The goal of LONGSCAN is to follow the children and their families until the children are young adults, conducting assessments regularly and collecting maltreatment data from multiple sources.
Three LONGSCAN studies, released in November 2001, examined various impacts of fathers or father figures in the family environment.
The first, "The Effect of Fathers on Child Behavioral Problems in Families Referred to Child Protective Services," was conducted by the State of Washington Office of Children's Administration Research. It examined some possible effects of the presence and quality of interaction between children and fathers/father figures—defined by the mother as either a primary father in the child's life regardless of biological or nonbiological relationship, or an adult male identified by the mother as residing in the home—on children's behavior in families reported to child protective services. The findings indicated lower levels of aggression and depression in children at age 6 if an adult male in a father-like relationship was present in the child's life.
The second, "Are Father Surrogates a Risk Factor for Child Maltreatment?" found that children who had a father surrogate living at home were twice as likely to be reported for maltreatment than children with no father or a biological father in the home. Conducted by the University of North Carolina (UNC) at Chapel Hill, the study also found that when a surrogate father maltreats a child, the mother is the one substantiated for neglect because she failed to protect her child.
The third study, "Father Involvement and Children's Functioning at Age 6 Years: A Multisite Study," examined:
Whether the presence of a father figure, defined as a supportive male adult, was associated with better child functioning
Whether children's perceptions of father figures' support were associated with better functioning
Whether the association was affected by the father figures' relationship to the child, the child's race, and the child's gender.
The multisite study, conducted by researchers at the University of Maryland School of Medicine, UNC at Chapel Hill School of Medicine, San Diego State University, UNC at Chapel Hill's School of Public Health, the Office of Children's Administration Research, Seattle, and the Juvenile Protection Association, Chicago, found that a father's presence was associated with better cognitive development and increased perceived competence by the children. In addition, children who described greater father support had a greater sense of social competence and fewer depressive signs. There were no significant influences on the father figures' level of support and children's functioning based on the relationship to the child, child's race, and the child's gender.
Lynn Martin, MS (Coordinator)
LONGSCAN Coordinating Center
Center for Child and Family Health
3518 Westgate Dr., Suite 100
Email: Lynn_Martin@med.unc.edu
Study Explores Impact of Alcoholism on Father-Infant Interactions
Role of Teachers in Reporting Child Abuse and Neglect


text:
Navajo Lake State Park
New Mexico State Parks
Navajo Lake State Park marina
With more than 15,000 acres of surface, Navajo Lake is the second largest lake in New Mexico. The state park includes some 21,000 acres around the lake. There are several campgrounds and a full-service marina. The visitor center is at Pine River, where most of the campgrounds, picnic areas, interpretive exhibits and the marina are.
Fisherman find both cold and warm-water fish in these waters. The section of the San Juan River below the dam is world-renowned for the quality of the trout fishery.
Navajo Lake State Park offers a visitor center, group picnic shelters and 246 developed campsites, most with electric hookups. The camping areas also offer restrooms and showers. The park has a centrally located RV dump station. For activities, Navajo Lake State Park offers picnicking, fishing, hunting (in season), sailing, water skiing, wilidlife watching, scuba diving and a plethora of winter sports.
The entry gate at Navajo Lake State Park is open 24 hours a day, every day. There are several ways to get to Navajo Lake State Park but most folks use either New Mexico Highway 511 or New Mexico Highway 539 off of US Highway 64 east of Bloomfield.
Fees: Day-use: $5 per vehicle; Pedestrians and bicyclists get in free. Camping: Primitive sites: $8 per site per night. Developed sites: $10 per site per night. Developed site with either electric or sewer: $14 per site per night. Developed site with both electric and sewer: $18 per site per night. Water hookups aren't always available but when they are, they're free.
Fishing one of the coves at Navajo Lake State Park
Navajo Lake State Park area map
Navajo Lake State Park Related Pages
Carson National Forest - Narrow Gauge Scenic Byway
Heron Lake State Park - El Vado Lake State Park
Photos courtesy of New Mexico State Parks. Area map courtesy of National Geographic Topo!


text:
From "History of Central Oregon," published 1906
Biographical Sketches of Lake County, pgs. 887-888
Transcribed by: Sherrain Glenn
Frank M. DUKE
Frank M. Duke has a home consisting of two hundred and thirty-seven and one-half acres of land three miles south from Lakeview, where he is engaged in farming and stock raising. His land is well improved and is for the most part devoted to the growing of hay for feed for Mr. Duke's large heard of cattle.
Born April 18, 1861, Frank M. Duke is a native of Morgan county, Missouri. His father was William H. Duke, a native of Madison county, Kentucky, and went to Missouri at the age of nineteen years. He came to the Goose Lake country in 1876, and lived there until his death at the age of seventy-three years, March 18, 1904. William H. Duke's father was Patrick Henry Duke and his grandfather served in the patriot army during the Revolutionary War. Our subject's mother was Ann (Thompson) Duke, who was born and who died, in Missouri.
Mr. Duke came west with his father in 1876. He began life for himself in 1882, his start being by working for a salary on a ranch. He located a home stead in 1888 and has been engaged in stock raising and farming since that time.
In 1904 Mr. Duke was the nominee of the Democratic party for the office of county sheriff, but owing to the great strength of the Republican party in Lake county, and to the popularity of its nominee for office to which Mr. Duke aspired, he was defeated at the polls.
Mr. Duke was married November 20, 1887, to Mary E. Feeler, born in Walla Walla county, Washington. Her father is Simon Feeler, a native of Indiana and an early pioneer of Walla Walla county. From Walla Walla he removed to California then to Goose Lake valley, and lastly to the vicinity of Fruitland, Stevens county, Washington, where he is now living. Mrs Duke's mother was Martha (King) Feeler, a nativce of the state of Missouri.
Mr. and Mrs. Duke are parents of one child, Lora Ethel Duke.
Mr. and Mrs. Duke are regarded as being among the most strictly moral and honorable residents of Lake county, and both are members of the Baptist church.
Return to Main Oregon Page
Return to Pioneer Biographies
Copyright © 1999 by Sherrain Glenn for ORGenWeb.


text:
Home Daily Ovation Revlon Introduces LIVE BOLDLY Campaign
Daily Ovation
Revlon Introduces LIVE BOLDLY Campaign
Elizabeth Delphin
Today, Revlon launches its new Live Boldly campaign in New York City, introducing four new Global Ambassadors, who join iconic actress Gal Gadot. Ashley Graham, Adwoa Aboah, Imaan Hammam and Raquel Zimmermann were selected to represent Revlon's new campaign platform because they embody what it is to "Live Boldly."
As a top model and advocate, Graham has used her celebrity and voice to challenge conventional perceptions and inspire women everywhere. Her optimism, compassion and strength have changed the industry's perspective by creating a more inclusive definition of beauty.
"I am thrilled to be part of this timely and groundbreaking campaign with different types of women across races, ages and sizes, and to leverage this platform to continue to create positive change," says Graham. "To 'Live Boldly' is the mantra of my life. Every day in the mirror I say to myself, 'I am bold, I am brilliant, I am beautiful,' and together with Revlon, we can inspire all women to do the same."
Aboah, Hammam and Zimmermann are each inspirations in their own right and exemplify many key characteristics of what it means to "Live Boldly." Aboah was recently named Model of the Year by The British Fashion Council, and in 2015 she founded Gurls Talk, an online community dedicated to providing girls with a platform to share their stories, empowering them through a broader community.
As a top African-Arabic model, Hammam has graced countless magazine covers and is a fixture on fashion runways around the world. A Brazilian-born cover and runway model and environmentalist, Zimmermann was discovered by a scouting agency at the age of 14 and was named by VOGUE Parisas one of the "30 models of the 2000s."
"Revlon gives us a platform that allows us to be accessible to all different types of women," says Aboah. "To me, 'Living Boldly' means being unapologetic, knowing no boundaries, being vulnerable, strong, authentic and yourself."
Revlon's Live Boldly multi-media platform leverages social, digital and in-person interactions to engage, support and empower women through community building, catalytic experiences and inspiring conversations.
Live Boldly launches across all media platforms, beginning today. For additional information on Revlon and to view behind-the-scenes content and additional announcements surrounding Revlon's Live Boldly campaign, visit www.Revlon.com , #liveboldly and follow @Revlon on Facebook, Twitter, Instagram, YouTube and RevlonSnaps on SnapChat.
Imaan Hammam
LIVE BOLDLY
LIVE BOLDLY Campaign
Raquel Zimmermann
Previous articleVineyard Vines Announces Exclusive Golf Collaboration With Renowned Sports Commentator Jim Nantz
Next articleDisney Cruise Line Takes Guests on Epic Adventures in 2019 with Return of Star Wars Day at Sea and Marvel Day at Sea
Elizabeth Delphin loves a good time! A fun concert, a good dinner out with friends, those weird artsy-fartsy festivals. If she's not at the office or at home, she's likely walking her dog Milo at Runyon Canyon (seriously, sometimes she goes 2-3 times a day).
Hollywood Legend Jimmy Stewart's Fight for Holiday Classic 'It's a Wonderful Life'
Bel Air's Vibrato Grill Serves Your Favorite Specials for Take-Out this Holiday
Il Pastaio, Il Segreto, Open Face Food Shop among Top L.A....
Gus's Barbecue Brings Soulful Southern to Porter Ranch w Grand Opening...
Legendary Tower Records Returns As Website Selling Vinyl, Cassettes and more
Bel Air's Vibrato Grill Serves Your Favorite Specials for Take-Out this...
Hollywood Legend Jimmy Stewart's Fight for Holiday Classic 'It's a Wonderful...


Our lab is interested in understanding the mechanisms that control the early steps in organogenesis in the vertebrate embryo, and the subsequent outgrowth and patterning of the developing organs. We are particularly interested in the roles played by members of the Fibroblast Growth Factor (FGF) family of signaling molecules and their antagonists in these processes. For the most part we use genetic analysis in mice to uncover the functions of these molecules in the developing embryo.


text:
← Waterloo Adventist Hospital Staff Die From Ebola
Sir Run Run and Adventist 'China Doctor, Dr Harry Miller →
Adventist Hospitals in the News
Posted on 11 November 2014	by Islwyn
David Peterson On Porter Adventist Hospital
The San – Sydney Adventist Hospital's "200m dollar extenstion
Waterloo Adventist Hospital Hit by Ebola
Loma Linda University Hospital's $1.2bn Extension
Sir Run Run Shaw Hospital
We don't see Adventist hospitals in Europe so it is good to read what is happening in some of the many Adventist hospitals around different parts of the world where they serve their communities as well as supporting care facilities further afield.
David Peterson On Porter Adventist Hospital:
David Peterson's post on the death of his wife in the Huffingto Post was a moving tribute to Porter Adventist Hospital. A blogger on Huffington Post, Peterson describes himself as a veteran outdoorsman, and a founder of the Colorado chapter of Backcountry Hunters and Anglers. He was a Marine Corps helicopter pilot, and a sportsman-conservationist. He is also the author or editor of more than a dozen books. Twice he has been honored by the Colorado Wildlife Federation, as Conservationist of the Year, and a Lifetime Achievement Award for Conservation. He is currently involved in a documentary film on ethical hunting.
But there was someone in Peterson's life dearer to him than all that; I found this story very moving as this journalist expresses his feelings and grief over the loss of his dear wife and praising the loving care she received. Peterson's post was titled, 'A Love Letter to Angels',
Another tribute to an Adventist hospital came from Australia's Prime Minister, Tony Abbott. It was the recent opening (17 October) of the new extension to the 12 story, 550-bed Sydney Adventist Hospital, the largest private not-for-profit hospital in New South Wales.
Although the data on this link seems to need updating, it does appear to tell us that 'the San', as it is fondly known, is the flagship of the church's hospitals 'down under', and supports field hospitals and clinics with over 500 volunteers, and according Tony Abbott's speech, has over 2500 staff with 800 doctors.
Not all Adventist hospitals are as fortunate as the 'San'. Those serving on the 'front line' are much more vulnerable, such as Waterloo Adventist Hospital, supporting government and other aid agencies that are overwhelmed with the Ebola crisis in West Africa.
(On the Ebola Virus, "Médecins Sans Frontières/Doctors Without Borders (MSF), the NGO with the largest working presence in the affected countries, had grown increasingly critical of the international response. A WHO spokesperson has said that, " "The Ebola epidemic ravaging parts of West Africa is the most severe acute public health emergency seen in modern times.").
The 'San' isn't the only hospital undergoing expansion; across 'the pond' Loma Linda University Hospital, has plans for a $1.2bn expansion.
Like Australia's 'San', Loma Linda services care facilities further afield as well as having partnerships with other major medical institutions. "The hospital is also a teaching and researching base for medical students and scholars. It has student exchange programs with the United States, Germany, Japan, India, and Hong Kong."
Not in the news but I thought it interesting to read of one such partnership Loma Linda has with the 1200 bed Sir Run Run Hospital. Says Wikipedia, it cooperates with and receives funding from the American Loma Linda University (LLU).
It is named after the successful Chinese billionaire media mogul and philanthropist (knighted by Queen Elizabeth II in 1977). "His only request was that he wanted to partner with the Seventh-day Adventist Church in operating the hospital." Sir Run Run Shaw died January 2014, aged 106.
This entry was posted in Articles, Health, Suffering. Bookmark the permalink.


text:
Q: How can I use span to create a burger-menu in CSS? This won't work for a reason, I think with by using DIV is a different story, could someone please enlighten me? Many thanks!

.bar1,
.bar2,
.bar3 {
  width: 20px;
  height: 20px;
  background-color: black;
}

  1
  2
  3

A: By default span elements are inline, you can't apply height and width to inline elements. In order to apply height and width, you either make them as block or inline-block.
.bar1, .bar2, .bar3{
   width: 20px;
   height: 20px;
   background-color: black;
   display:block
}

In addition to this, in this video I've explained how you can make hamburger menu using only one div with animation.
https://youtu.be/Y2yW1-QYQco


We'll help you find the perfect boat. We look at the WHOLE PICTURE, with our years of experience. Half of our clients are people who come to us for help in the boat buying process. It is free! No cost to you. We can help you find the right boat to let you live your dream. We'll get you into, and out of the boat. We'll help you make the best decisions for your cruising needs. From the right design and sailing characteristics to the quality and condition that will affect your exit strategy. We go anywhere and everywhere. We attend to every aspect of the boat buying process. Our goal is to truly define your requirements so you can fulfill your dreams. While we specialize in liveaboards and blue water boats, we also know that not everyone will cross an ocean. But if you do, you'll be glad you came to RogueWave.
First, we analyze your requirements. Your dream may consist of setting sail over the horizon and sailing on through the seven seas. A beautiful boat is something to love even if it is tied to the dock! Or maybe you'll do coastal cruising or bay sailing or take her around the buoys. Maybe you'll plan to live aboard comfortably full-time. With amazing kids! We will help you find the perfect vessel to match your requirements. Whether you are spending one million or fifty thousand dollars, the level of service will be the same high quality service that you expect and deserve.
Once we know what you want to do, we can pretty much tell you which boats can work for you. Through our knowledge and experience, we know which boats have the right hull shape and keel and rudder design. We can guide you in the rig design and equipment. We know which boats are built to last. We know the resale aspects of boat ownership. We'll help you focus on yachts with the interior layout you need to live aboard and sail. We know the systems that will keep you safe and comfortable. Each designer offers unique characteristics. Whether it's Bob Perry, Chuck Paine, Bill Crealock, Bill Tripp, Ted Hood, Ted Brewer, Al Mason, Lyle Hess or a dozen others we understand the form, the fit and function, of every design element, plus your budget and we can match you with your perfect yacht.
We promise that we will listen to your requirements with an open mind and then advise you as honestly as we can, what will be the best vessel for your specific needs. We will not sell you what's in our inventory if it does not match your particular needs, or what vessel which you might think is right, but we will present to you which sailing vessel will fulfill your requirements the best, backed by facts and supported by technical expertise. Our friend didn't know they wanted a Norseman 447! Perfect.
Our promise is to continue providing service and support for the entire ownership process. Throughout the purchase and sales process, we support you every step of the way. We are members of the Yacht Brokerage Association of America and adhere to the best industry practices. We use all the standardized agreements. We handle everything for you including evidence of clear title and the transfer of title or US Coast Guard documentation. And we don' t just sell a boat and wave goodbye. There is no one else in this business today that can provide you with the service level you deserve. This consists of technical support, planning of and overseeing installation of systems, helping find repair services in foreign ports, navigating passages, providing weather forecasts, finding crew, obtaining dockage, and even delivering your vessel to your dock or home port. We often support proud new owners aboard the maiden voyage to teach them the systems and show them the ropes. We where even line handlers for our friends going through the Panama Canal! Fun. Our promise is to provide you continuous service and support. Wherever your sailing adventures take you, we are a phone call away! 410 571 2955 !
So we invite you to join the party. We would love to represent you. We will be YOUR Buyer's Agent at no cost to you. We will help you find the right boat no matter where she is. We will help with everything before, during, and after your purchase. We do NOT just sell the boat to you and wave good bye. If fact, you are stuck with us. This is a rendezvous of Valiants in 2008 Boat Show Annapolis in Luce Creek. The relationship we build with you is for the long haul. We'll get you into this and we will help you to get out of sailing when that time comes!


text:
\section{Introduction}

In a previous paper $\cite{GM12}$ consistent quantization of massless fields
of any spin was developed from first principles. Probability currents and
Lagrangians were derived \ allowing a first quantized formalism. A simple
procedure was derived for connecting the wavefunctions with potentials and
gauge conditions. Here we will present a simplified version of this
formalism and elaborate an extension of the self-dual representation of
Maxwell's equations. This representation allows us to generalize Maxwell's
equations by adding non-zero time like components $E_{0}$ and $B_{0}$ to the
electric and magnetic four-vectors. \ The existence of these components
allows the formation of scalar electromagnetic waves. We will examine some
results.

In our previous paper $\cite{GM12}$ we started our formalism using Dirac's
^{\cite{dirac}}$ derivation of equations for massless particles with spin $s
, which in the ordinary vector notation are,

\begin{equation}
\frac{1}{s}\left[ s\hat{p}_{0}I^{\left( 2s+1\right) }+S_{x}\hat{p}_{x}+S_{y
\hat{p}_{y}+S_{z}\hat{p}_{z}\right] \psi =\left[ \frac{\hat{E}}{c}I^{\left(
2s+1\right) }+\frac{\boldsymbol{S}}{s}\cdot \boldsymbol{\hat{p}}\right] \psi
=0,  \label{a1}
\end{equation}

\begin{equation}
\left[ s\hat{p}_{x}I^{\left( s\right) }+S_{x}\hat{p}_{0}-iS_{y}\hat{p
_{z}+iS_{z}\hat{p}_{y}\right] \psi =0,  \label{a2}
\end{equation}

\begin{equation}
\left[ s\hat{p}_{y}I^{\left( s\right) }+S_{y}\hat{p}_{0}-iS_{z}\hat{p
_{x}+iS_{x}\hat{p}_{z}\right] \psi =0,  \label{a3}
\end{equation}

\begin{equation}
\left[ s\hat{p}_{z}I^{\left( s\right) }+S_{z}\hat{p}_{0}-iS_{x}\hat{p
_{y}+iS_{y}\hat{p}_{x}\right] \psi =0,  \label{a4}
\end{equation
where $\psi $ is a $\left( 2s+1\right) $ component wave function and $S_{n}$
are the $\left( 2s+1\right) \times \left( 2s+1\right) $ spin matrices which
satisfy,

\begin{equation}
\left[ S_{x},S_{y}\right] =iS_{z},\quad \left[ S_{z},S_{x}\right]
=iS_{y},\quad \left[ S_{y},S_{z}\right] =iS_{x},\quad
S_{x}^{2}+S_{y}^{2}+S_{z}^{2}=s(s+1)I^{\left( 2s+1\right) }.  \label{a5}
\end{equation
In the above, the $\hat{p}_{n}$ are the momenta, $\hat{p}_{0}=\hat{E}/c$,
\hat{E}$ the energy, and $I^{\left( 2s+1\right) }$ is a $\left( 2s+1\right)
\times \left( 2s+1\right) $ unit matrix. Eqs. (\ref{a1}-\ref{a4}) were
analyzed extensively by Bacry$^{\cite{bacry}}$, who derived them using
Wigner's condition $^{\cite{wigner}}$ on the Pauli-Lubanski vector $W^{\mu }$
for massless fields,

\begin{equation}
W^{\mu }=s\hat{p}^{\mu },\quad \mu =x_{0},x,y,z,  \label{a6}
\end{equation}

\begin{equation}
W^{\mu }=\frac{-i}{2}\varepsilon ^{\mu \nu \rho \lambda }S_{\rho \lambda
\hat{p}_{\nu },\quad S_{\rho \lambda }=\left(
\begin{array}{cccc}
0 & S_{x} & S_{y} & S_{z} \\
-S_{x} & 0 & -iS_{z} & iS_{y} \\
-S_{y} & iS_{z} & 0 & -iS_{x} \\
-S_{z} & -iS_{y} & iS_{x} &
\end{array
\right) \equiv (\mathbf{S,}i\mathbf{S).}  \label{g0}
\end{equation}

Dirac suggested using Eq. (\ref{a1}) as the basic helicity equation and
substitute from it the $\hat{p}_{0}\psi $ into the other 3 equations (\re
{a2}-\ref{a4}). Free massless particles may have only two helicity
projections (forward and backward along the momentum vector). Using the
Dirac procedure one obtains the $2s+1$ component Eq. (\ref{a1}) and $2s-1$
independent subsidiary conditions which reduce the number of helicity
projections to 2,

\begin{equation}
\left[ \hat{E}I^{\left( 2s+1\right) }+\frac{c}{s}\boldsymbol{S}\cdot
\boldsymbol{\hat{p}}\right] \psi ^{\left( 2s+1\right) }=0,  \label{a7}
\end{equation}

\begin{equation}
\left( \mathbf{\Pi \cdot \hat{p}}\right) \psi ^{\left( 2s+1\right) }=0,
\label{a7a}
\end{equation
where the components of $\mathbf{\Pi }$ are $\left( 2s-1\right) \times
\left( 2s+1\right) $ matrices of the subsidiary conditions. These two sets
of equations can be combined into $\left( 2s+1\right) +\left( 2s-1\right)
=4s $ equations$^{\cite{GM}}$,$\ $

\begin{equation}
\left[ \hat{E}I^{\left( 4s\right) }+c\boldsymbol{\Gamma }^{\left( 4s\right)
}\cdot \boldsymbol{\hat{p}}\right] \Phi ^{\left( 4s\right) }=0,  \label{a9}
\end{equation
equivalent to the former equations, provided that the rows of the $\mathbf
\Pi }$ matrices are normalized so that the eigenvalues of $\boldsymbol
\Gamma }^{\left( 4s\right) }\cdot \boldsymbol{\hat{p}}$ are $\pm p$ (two
helicities) and,

\begin{equation}
\left( \hat{E}I^{\left( 4s\right) }-c\boldsymbol{\Gamma }^{\left( 4s\right)
}\cdot \boldsymbol{\hat{p}}\right) \left( \hat{E}I^{\left( 4s\right) }+
\boldsymbol{\Gamma }^{\left( 4s\right) }\cdot \boldsymbol{\hat{p}}\right)
=\left( \hat{E}^{2}-c^{2}\boldsymbol{\hat{p}}^{2}\right) I^{\left( 4s\right)
},  \label{a10}
\end{equation
i.e. they factorize the d'Alembertian. The wave function $\Phi ^{\left(
4s\right) }$ is of the form$^{\cite{GM}}$ (with 2s-1 zeros),

\begin{equation}
\Phi ^{\left( 4s\right) }=\left(
\begin{array}{c}
0 \\
\vdots \\
0 \\
\psi _{2s+1}^{\left( 2s+1\right) } \\
\vdots \\
\psi _{-2s-1}^{\left( 2s+1\right)
\end{array
\right) ,  \label{a11}
\end{equation
and the components of $\boldsymbol{\Gamma }^{\left( 4s\right) }$ are
4s\times 4s$ matrices, which form a (reducible) representation of the
algebra of the Pauli matrices,

\begin{equation}
\sigma _{0}=\left(
\begin{array}{cc}
1 & 0 \\
0 &
\end{array
\right) ,\quad \sigma _{x}=\left(
\begin{array}{cc}
0 & 1 \\
1 &
\end{array
\right) ,\quad \sigma _{y}=\left(
\begin{array}{cc}
0 & -i \\
i &
\end{array
\right) ,\quad \sigma _{z}=\left(
\begin{array}{cc}
1 & 0 \\
0 & -
\end{array
\right) .\quad  \label{n3}
\end{equation}

\section{Wave equations for free massless fields}

We shall use the following relations$^{\cite{gersten2}}$,

\begin{equation}
W_{\mu }W^{\mu }=-s\left( s+1\right) \hat{p}_{\mu }\hat{p}^{\mu }I^{\left(
s\right) },\quad W_{\mu }\hat{p}^{\mu }=0,  \label{g1}
\end{equation
with the aim of obtaining the Wigner condition Eq. (\ref{a6}) and
simultaneously to factorize the d'Alembertian (in the form $\hat{p}_{\mu
\hat{p}^{\mu }$). One can easily see that,

\begin{equation}
\left( W_{\mu }-s\hat{p}_{\mu }\right) \left( W^{\mu }+s\hat{p}^{\mu
}\right) =-s\left( 2s+1\right) \hat{p}_{\mu }\hat{p}^{\mu }I^{\left(
s\right) },  \label{g3}
\end{equation
or

\begin{equation}
\left( W_{\mu }+s\hat{p}_{\mu }\right) \left( W^{\mu }-s\hat{p}^{\mu
}\right) =-s\left( 2s+1\right) \hat{p}_{\mu }\hat{p}^{\mu }I^{\left(
s\right) }.  \label{g4}
\end{equation}

From Eqs. (\ref{g3}-\ref{g4}) one can see that if $\psi $, the wavefunction,
satisfies,

\begin{equation}
\left( W^{\mu }+s\hat{p}^{\mu }\right) \psi =0,\quad or\quad \left( W^{\mu
}-s\hat{p}^{\mu }\right) \psi =0,\quad \mu =0,1,2,3,  \label{g5}
\end{equation
then the basic massless particle requirement,

\begin{equation}
\hat{p}_{\mu }\hat{p}^{\mu }I^{\left( s\right) }\psi =0,  \label{g6}
\end{equation
will be satisfied. \bigskip Explicitly we have,

\begin{equation}
W^{0}=W_{0}=-S_{x}\hat{p}_{x}-S_{y}\hat{p}_{y}-S_{z}\hat{p}_{z},  \label{g61}
\end{equation
$\allowbreak $

\begin{equation}
-W^{1}=W_{x}=-S_{x}\hat{p}_{0}-iS_{y}\hat{p}_{z}+iS_{z}\hat{p}_{y},
\label{g62}
\end{equation}

\begin{equation}
-W^{2}=W_{y}=-S_{y}\hat{p}_{0}-iS_{z}\hat{p}_{x}+iS_{x}\hat{p}_{z},
\label{g63}
\end{equation}

\begin{equation}
-W^{3}=W_{z}=-S_{z}\hat{p}_{0}-iS_{x}\hat{p}_{y}+iS_{y}\hat{p}_{x}.
\label{g64}
\end{equation}

Now the main problem is to choose the basis of a space on which the above
operators will act. In Ref. $\cite{GM12}$ we have shown that the angular
momentum basis of the $D^{\left( s-1/2,1/2\right) }$ representation of the
Lorentz group is the proper one to use. This basis is sum of the bases of
spins $s$ and spin $s-1$ with

\begin{equation*}
\left( 2s+1\right) +\left( 2s-1\right) =4s\text{ components.}
\end{equation*
In this basis the wavefunction is,

\begin{equation}
\Phi ^{\left( 4s\right) }=\left(
\begin{array}{c}
\psi _{s-1}^{\left( 2s-1\right) } \\
\vdots \\
\psi _{-s+1}^{\left( 2s-1\right) } \\
\psi _{s}^{\left( 2s+1\right) } \\
\vdots \\
\psi _{-s}^{\left( 2s+1\right)
\end{array
\right) \implies \left(
\begin{array}{c}
0 \\
\vdots \\
0 \\
\psi _{s}^{\left( 2s+1\right) } \\
\vdots \\
\psi _{-s}^{\left( 2s+1\right)
\end{array
\right) .  \label{a14}
\end{equation}

The advantage of the formalism, as we have shown in Ref. $\cite{GM12}$, is
that by equating to zero the spin\ $\left( s-1\right) $ components of the
wavefunction $\psi _{\mu }^{\left( 2s-1\right) }$, the $2s-1$ subsidiary
conditions (needed to eliminate the non-forward and non-backward helicities,
according to Wigner's analysis $\cite{wigner}$ are automatically satisfied.
So we are left with equations Eq. $\left( \ref{g5}\right) $ with $\psi =\Phi
^{\left( 4s\right) },$ but not all equations are needed, the equations with
\mu =1,2,3$ are the equations Eqs. $\left( \ref{a2}-\ref{a4}\right) $ from
which the subsidiary conditions were derived. Now they are not needed and
instead of Eqs. $\left( \ref{g5}\right) $ we have,

\begin{equation}
\left( s\hat{p}^{0}+W^{0}\right) \Phi ^{\left( 4s\right) }=0,\quad or\quad
\left( s\hat{p}^{0}-W^{0}\right) \Phi ^{\left( 4s\right) }=0,  \label{b1}
\end{equation
which are the generalized helicity equations having solutions only in the
forward and backward direction. Note that in Eq. $\left( \ref{b1}\right) $
W^{0}$ is a $4s\times 4s$ matrix. The explicit form of Eq. $\left( \ref{b1
\right) $ is given in Refs. $\cite{GM},\cite{GM12}$ with the result,

\begin{equation}
\left[ \hat{E}\Gamma _{0}^{\left( 4s\right) }-c\boldsymbol{\Gamma }^{\left(
4s\right) }\cdot \boldsymbol{\hat{p}}\right] \Phi ^{\left( 4s\right)
}=0,\quad or\quad \left[ \hat{E}\Gamma _{0}^{\left( 4s\right) }+c\boldsymbol
\Gamma }^{\left( 4s\right) }\cdot \boldsymbol{\hat{p}}\right] \Phi ^{\left(
4s\right) }=0,  \label{b2}
\end{equation
where $\Gamma _{0}^{\left( 4s\right) }=I^{\left( 4s\right) }$ is the
4s\times 4s$ unit matrix, $\hat{E}=\hat{p}^{0}/c$, and the $\Gamma $
matrices have the form (in the angular momentum basis),

\begin{equation}
\Gamma _{k}^{\left( 4s\right) }=\frac{1}{s}\left(
\begin{array}{cc}
\left( -1\right) ^{k+s-1}S_{k}^{\left( 2s-1\right) } & \Pi _{k} \\
\Pi _{k}^{H} & \left( -1\right) ^{k+s}S_{k}^{\left( 2s+1\right)
\end{array
\right) ,\quad k=1,2,3,  \label{b3}
\end{equation
where $S_{k}^{\left( 2s-1\right) }$ are the spin $(s-1)$ matrices of Eq.
\left( \ref{a5}\right) $, $S_{k}^{\left( 2s+1\right) }$ are the spin $(s)$
matrices of Eq. $\left( \ref{a5}\right) $, $\Pi _{k}$ is the $\left(
2s-1\right) \times \left( 2s+1\right) $\ normalized matrix of the subsidiary
conditions and $\Pi _{k}^{H}$ is the Hermitian conjugate of $\Pi _{k}$. The
matrix elements of $\Pi _{k}$ can be evaluated directly from the normalized
subsidiary conditions

\begin{equation}
\psi _{\mu }^{\left( 2s-1\right) }=\sqrt{s\left( 2s+1\right)
\tsum\limits_{m_{1},m_{2}}\langle 1m_{1};sm_{2}|(1s)s-1,\mu \rangle
p_{m_{1}}\psi _{m_{2}}^{\left( 2s+1\right) }=0,  \label{b4}
\end{equation
where the expansion is in terms of Clebsch-Gordan coefficients and the
factor $\sqrt{s\left( 2s+1\right) }$ comes from the normalization factor of
the r.h.s. of Eq. $\left( \ref{g3}\right) $.

For example, for spin 1, one obtains,

\begin{equation}
\Pi _{x}=\left(
\begin{array}{ccc}
-1 & 0 &
\end{array
\right) ,\quad \Pi _{y}=\left(
\begin{array}{ccc}
0 & -1 &
\end{array
\right) ,\quad \Pi _{z}=\left(
\begin{array}{ccc}
0 & 0 & -
\end{array
\right) ,  \label{b4a}
\end{equation
In a Cartesian basis, the $S_{k}^{\left( 3\right) }$ are

\begin{equation}
S_{x}=\left(
\begin{array}{ccc}
0 & 0 & 0 \\
0 & 0 & -i \\
0 & i &
\end{array
\right) ,\quad S_{y}=\left(
\begin{array}{ccc}
0 & 0 & i \\
0 & 0 & 0 \\
-i & 0 &
\end{array
\right) ,\quad S_{z}=\left(
\begin{array}{ccc}
0 & -i & 0 \\
i & 0 & 0 \\
0 & 0 &
\end{array
\right) ,  \label{n8}
\end{equation}

\begin{equation}
\Gamma _{k}^{\left( 4\right) }=\left(
\begin{array}{cc}
0 & \Pi _{k} \\
\Pi _{k}^{H} & S_{k}^{\left( 3\right)
\end{array
\right) ,\quad k=1,2,3,\quad \Gamma _{0}^{\left( 4\right) }=\text{unit
matrix,}  \label{b4b}
\end{equation}

For spin 2, one obtains,

\begin{equation}
\Pi _{x}=\left(
\begin{array}{ccccc}
\sqrt{3} & 0 & -\frac{1}{\sqrt{2}} & 0 & 0 \\
0 & \sqrt{\frac{3}{2}} & 0 & -\sqrt{\frac{3}{2}} & 0 \\
0 & 0 & \frac{1}{\sqrt{2}} & 0 & -\sqrt{3
\end{array
\right) ,  \label{b5}
\end{equation}

\begin{equation}
\Pi _{y}=i\left(
\begin{array}{ccccc}
-\sqrt{3} & 0 & -\frac{1}{\sqrt{2}} & 0 & 0 \\
0 & -\sqrt{\frac{3}{2}} & 0 & -\sqrt{\frac{3}{2}} & 0 \\
0 & 0 & -\frac{1}{\sqrt{2}} & 0 & -\sqrt{3
\end{array
\right) ,  \label{b6}
\end{equation}

\begin{equation}
\Pi _{z}=\left(
\begin{array}{ccccc}
0 & -\sqrt{3} & 0 & 0 & 0 \\
0 & 0 & -2 & 0 & 0 \\
0 & 0 & 0 & -\sqrt{3} &
\end{array
\right) .  \label{b7}
\end{equation}

\begin{equation}
\Gamma _{k}^{\left( 8\right) }=\frac{1}{2}\left(
\begin{array}{cc}
\left( -1\right) ^{k+1}S_{k}^{\left( 3\right) } & \Pi _{k} \\
\Pi _{k}^{H} & \left( -1\right) ^{k}S_{k}^{\left( 5\right)
\end{array
\right) ,\quad k=1,2,3,  \label{b10}
\end{equation}

\bigskip More details can be found in Refs. $\cite{GM}-\cite{GM12}.$

\section{\protect\LARGE First quantization}

\bigskip As is in the case of the Klein-Gordon or Dirac equations, we
substitute in Eqs. (\ref{b2})

\begin{equation}
\hat{E}\Longrightarrow i\hbar \frac{\partial }{\partial t},\quad \mathbf
\hat{p}}\mathbf{\Longrightarrow -}i\hbar \mathbf{\nabla },\quad
\end{equation
with a result

\begin{equation}
i\hbar \left( \Gamma _{0}^{\left( 4s\right) }\frac{\partial }{\partial t}+
\boldsymbol{\Gamma }^{\left( 4s\right) }\cdot \mathbf{\nabla }\right) \Phi
^{\left( 4s\right) }=0.  \label{a16}
\end{equation}

Similarly to the Schroedinger and Dirac equations we define the Hamiltonian
\mathcal{H}$ from Eq. (\ref{a16}),

\begin{equation}
i\hbar \frac{\partial }{\partial t}\Phi ^{\left( 4s\right) }=-i\hbar
\boldsymbol{\Gamma }^{\left( 4s\right) }\cdot \mathbf{\nabla }\Phi ^{\left(
4s\right) }=\mathcal{H}\Phi ^{\left( 4s\right) },  \label{a17}
\end{equation
and find a conserved probability current (the superscript $H$ denotes the
Hermitian conjugate),

\begin{equation}
\partial _{t}\left( \left( \Phi ^{\left( 4s\right) }\right) ^{H}\Phi
^{\left( 4s\right) }\right) +\frac{c}{s}\mathbf{\nabla }\mathbf{\cdot
\left( \left( \Phi ^{\left( 4s\right) }\right) ^{H}\mathbf{\tilde{S}}\Phi
^{\left( 4s\right) }\right) =0.  \label{a18}
\end{equation
Thus the probability density (which should be normalized) is,
\begin{equation}
\rho =\left( \Phi ^{\left( 4s\right) }\right) ^{H}\Phi ^{\left( 4s\right)
},\quad \int \int \int dxdydz\rho =1.  \label{a18a}
\end{equation
In the above the density is non-negative and the scalar product is positive
definite. Having this result we can find a Lagrangian density,

\begin{equation}
\mathcal{L=}i\hbar \left( \Phi ^{\left( 4s\right) }\right) ^{H}\left( \Gamma
_{0}^{4s}\frac{\partial }{\partial t}+c\boldsymbol{\Gamma }^{\left(
4s\right) }\cdot \mathbf{\nabla }\right) \Phi ^{\left( 4s\right) },
\label{a19}
\end{equation
and using the definition of the energy momentum tensor $T^{\mu \nu }$ , we
find$^{\cite{GM}}$,

\begin{center}
\begin{equation}
\int \int \int dxdydzT^{00}=\int \int \int dxdydz\left( \Phi ^{\left(
4s\right) }\right) ^{H}\mathcal{H}\Phi ^{\left( 4s\right) }=<\mathcal{H}>,
\label{a20}
\end{equation
$\qquad $
\end{center}

\begin{equation}
\int \int \int dxdydzT^{0k}=\int \int \int dxdydz\left( \Phi ^{\left(
4s\right) }\right) ^{H}\left( c\hat{p}_{k}\right) \Phi ^{\left( 4s\right)
}=<c\hat{p}_{k}>,\quad k=1,2,3,  \label{a21}
\end{equation
i.e. consistent with the expectation values of energy and momentum.

\section{\protect\bigskip Wave equations for free fields}

From the Lagrangian Eq. (\ref{a19}) we obtain the two equations Eqs. (\re
{b2}), for particles of spin $s$ (4$s$ is the dimension of the matrices)
\begin{equation}
i\hbar \left( \Gamma _{0}^{\left( 4s\right) }\frac{\partial }{\partial t}+
\boldsymbol{\Gamma }^{\left( 4s\right) }\cdot \mathbf{\nabla }\right) \Phi
^{\left( 4s\right) }=0,  \label{b8}
\end{equation}

\begin{equation}
i\hbar \left( \Gamma _{0}^{\left( 4s\right) }\frac{\partial }{\partial t}-
\boldsymbol{\Gamma }^{\left( 4s\right) }\cdot \mathbf{\nabla }\right) \Phi
^{\left( 4s\right) }=0.  \label{b9}
\end{equation}

The $\Gamma $\ matrices form a reducible representation of the Pauli
matrices Eq. (\ref{n3}). For the spin
$\frac12$
Eqs. ( \ref{b8}-\ref{b9}) coincide with the massless neutrino equations. The
$\Gamma $\ matrices have the same eigenvalues as the Pauli matrices $\pm 1$
(2$s$ degenerate). With the built-in subsidiary conditions only two
solutions of each of the equations Eqs. ( \ref{b8}-\ref{b9}) are possible.
Thus Eqs. ( \ref{b8}-\ref{b9}) are the restricted to forward or backward
helicity equations for free massless particles. As the energy operator is
proportional to the helicity the two solutions only differ in sign of the
energy, i.e. one solution corresponds to positive energy and the second to
negative energy. One can also note that the solutions of Eq. (\ref{b8}) are
also solutions of Eq. (\ref{b9}) with the opposite sign of the helicity.
Therefore Eq. (\ref{b8}) has positive energy solution in the helicity's
forward direction; its negative energy solution in the helicity's backward
direction is the positive energy solution of Eq. (\ref{b9}) for the
helicity's backward direction.

In Summary Eq. (\ref{b8}) is the equation of the helicity in the forward
direction and Eq. (\ref{b9}) is the equation for the helicity in the
backward direction, if the physical requirement of positive energy is
imposed.

\subsubsection{Examples}

For spin 1, the photon with helicity $\pm 1$ and total momentum $P=\sqrt
p_{x}^{2}+p_{y}^{2}+p_{z}^{2}}$, the normalized solution of Eq. (\ref{b8})
(in Cartesian basis) for positive energy and forward helicity is

\begin{equation}
\Phi ^{\left( 4\right) }=\frac{1}{\sqrt{2}P}\allowbreak \allowbreak \left(
\begin{array}{c}
0 \\
-\frac{p_{x}p_{z}-ip_{y}P}{\sqrt{p_{x}^{2}+p_{y}^{2}}} \\
-\frac{ip_{x}P+p_{y}p_{z}}{\sqrt{p_{x}^{2}+p_{y}^{2}}} \\
\sqrt{p_{x}^{2}+p_{y}^{2}
\end{array
\right) \exp (\frac{1}{i\hbar }(Et-\boldsymbol{p\cdot x)),}  \label{b11}
\end{equation}

and the normalized solution of Eq. (\ref{b9}) (in Cartesian basis) for
positive energy and backward helicity is

\begin{equation}
\Phi ^{\left( 4\right) }=\frac{1}{\sqrt{2}P}\left(
\begin{array}{c}
0 \\
-\frac{ip_{y}P+p_{x}p_{z}}{\sqrt{p_{x}^{2}+p_{y}^{2}}} \\
-\frac{p_{y}p_{z}-ip_{x}P}{\sqrt{p_{x}^{2}+p_{y}^{2}}} \\
\sqrt{p_{x}^{2}+p_{y}^{2}
\end{array
\right) \exp (\frac{-1}{i\hbar }(Et-\boldsymbol{p\cdot x)).}  \label{b12}
\end{equation}

For spin 2, the graviton with helicity $\pm 2$ and total momentum $P=\sqrt
p_{x}^{2}+p_{y}^{2}+p_{z}^{2}}$, the normalized solution of Eq. (\ref{b8})
(in angular momentum basis) for positive energy and forward helicity is

$\allowbreak
\begin{equation}
\Phi ^{\left( 8\right) }=\frac{\left( p_{x}^{2}+p_{y}^{2}\right) ^{2}}{4P^{4
}\left(
\begin{array}{c}
0 \\
0 \\
0 \\
\frac{1}{2}\left( \frac{p_{z}-P}{p_{x}-ip_{y}}\right) ^{2} \\
\left( \frac{p_{z}-P}{p_{x}-ip_{y}}\right) \\
\sqrt{\frac{3}{2}} \\
\frac{p_{x}-ip_{y}}{p_{z}-P} \\
\frac{1}{2}\left( \frac{p_{x}-ip_{y}}{p_{z}-P}\right) ^{2
\end{array
\right) \exp (\frac{1}{i\hbar }(Et-\boldsymbol{p\cdot x)),},  \label{b13}
\end{equation}

and the normalized solution of Eq. (\ref{b9}) (in angular momentum basis)
for positive energy and backward helicity is

\begin{equation}
\Phi ^{\left( 8\right) }=\frac{\left( p_{x}^{2}+p_{y}^{2}\right) ^{2}}{4P^{4
}\left(
\begin{array}{c}
0 \\
0 \\
0 \\
\frac{1}{2}\left( \frac{p_{z}+P}{p_{x}-ip_{y}}\right) ^{2} \\
\left( \frac{p_{z}+P}{p_{x}-ip_{y}}\right) \\
\sqrt{\frac{3}{2}} \\
\frac{p_{x}-ip_{y}}{p_{z}+P} \\
\frac{1}{2}\left( \frac{p_{x}-ip_{y}}{p_{z}+P}\right) ^{2
\end{array
\right) \exp (\frac{-1}{i\hbar }(Et-\boldsymbol{p\cdot x)).}  \label{b14}
\end{equation}

\section{Generalized Maxwell's equations}

\subsection{Maxwell's equations}

Maxwell's equations $\cite{Jackson}$\ in Gaussian system units are,

\begin{equation}
\mathbf{\nabla }\cdot \mathbf{E}=\alpha j_{0},  \label{b15}
\end{equation}

\begin{equation}
\mathbf{\nabla }\times \mathbf{B-}\partial _{0}\boldsymbol{E}=\alpha
\boldsymbol{j},  \label{b16}
\end{equation}

\begin{equation}
\mathbf{\nabla }\cdot \mathbf{B}=0,  \label{b17}
\end{equation}

\begin{equation}
\mathbf{\nabla }\times \mathbf{E+}\partial _{0}\boldsymbol{B}=0,  \label{b18}
\end{equation
where $\alpha =\frac{4\pi }{c}\allowbreak ,\quad j_{0}=c\rho ,\quad \partial
_{0}=\frac{1}{c}\frac{\partial }{\partial t}.$

Minkowski$\left[ \cite{minkowski}\right] $ found the covariant form of
Maxwell's equations,

\begin{equation}
\partial _{\mu }F^{\mu \nu }=\alpha j^{\nu },\quad \partial _{\mu }\tilde{F
^{\mu \nu }=0,\quad \nu =0,1,2,3,  \label{40}
\end{equation
where the antisymmetric tensor $F^{\mu \nu }$ and its dual $\tilde{F}^{\mu
\nu }$ are defined via the electric and magnetic fields $\mathbf{E}\mathbf{\
}$and $\mathbf{B}$ respectively as,

\begin{equation}
\left( F^{\mu \nu }\right) =\left(
\begin{array}{cccc}
0 & -E_{x} & -E_{y} & -E_{z} \\
E_{x} & 0 & -B_{z} & B_{y} \\
E_{y} & B_{z} & 0 & -B_{x} \\
E_{z} & -B_{y} & B_{x} &
\end{array
\right) ,  \label{40a}
\end{equation}

\begin{equation}
\tilde{F}^{\mu \nu }=\frac{1}{2}\epsilon ^{\mu \nu \alpha \beta }F_{\alpha
\beta }=\left(
\begin{array}{cccc}
0 & -B_{x} & -B_{y} & -B_{z} \\
B_{x} & 0 & E_{z} & -E_{y} \\
B_{y} & -E_{z} & 0 & E_{x} \\
B_{z} & E_{y} & -E_{x} &
\end{array
\right) ,  \label{40c}
\end{equation
where $\epsilon ^{\mu \nu \alpha \beta }$ is the totally antisymmetric
tensor ($\epsilon ^{0123}=1,\quad \epsilon ^{\mu \nu \alpha \beta
}=-\epsilon _{\mu \nu \alpha \beta }$). The sum of the $F^{\mu \nu }$ and $
\tilde{F}^{\mu \nu }$ is the self-dual antisymmetric tensor, which depends
only on the combination

\begin{equation}
\mathbf{\Psi }=\left( \mathbf{E}\mathbf{+}i\mathbf{B}\right) ,  \label{40d}
\end{equation}

\begin{equation}
F^{\mu \nu }+i\tilde{F}^{\mu \nu }=\left(
\begin{array}{cccc}
0 & -E_{x}-iB_{x} & -E_{y}-iB_{y} & -E_{z}-iB_{z} \\
E_{x}+iB_{x} & 0 & iE_{z}-B_{z} & B_{y}-iE_{y} \\
E_{y}+iB_{y} & B_{z}-iE_{z} & 0 & iE_{x}-B_{x} \\
E_{z}+iB_{z} & iE_{y}-B_{y} & B_{x}-iE_{x} &
\end{array
\right) ,  \label{41}
\end{equation}

$\ \ \ \ \ \ \allowbreak
\begin{equation}
=\left(
\begin{array}{cccc}
0 & -\Psi _{x} & -\Psi _{y} & -\Psi _{z} \\
\Psi _{x} & 0 & i\Psi _{z} & -i\Psi _{y} \\
\Psi _{y} & -i\Psi _{z} & 0 & i\Psi _{x} \\
\Psi _{z} & i\Psi _{y} & -i\Psi _{x} &
\end{array
\right)  \label{41a}
\end{equation
$.$

The self dual Maxwell's equations take the form $\cite{GM}$,

\begin{equation}
\partial _{\mu }\left( F^{\mu \nu }+i\tilde{F}^{\mu \nu }\right) =-\left(
\Gamma _{\mu }^{\left( 4\right) }\right) ^{\nu i}\partial _{\mu }\Psi
_{i}=\alpha j^{\nu },  \label{43}
\end{equation
where the $\Gamma _{\mu }^{\left( 4\right) }$ matrices are the spin 1
matrices defined by Eq. (\ref{b4b}). Thus within the $D^{\left(
{\frac12

{\frac12
\right) }$ representation of the Lorentz group, Maxwell's equation can be
written as,

\begin{equation}
\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}+\boldsymbol{\Gamma
^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \Phi ^{\left( 4\right)
}=-\alpha J,\quad \Phi ^{\left( 4\right) }=\left(
\begin{array}{c}
0 \\
\Psi _{x} \\
\Psi _{y} \\
\Psi _{z
\end{array
\right) ,\quad J=\left(
\begin{array}{c}
c\rho \\
j_{x} \\
j_{y} \\
j_{z
\end{array
\right) .  \label{44}
\end{equation}

\bigskip Eq. (\ref{44}) is the same as Eq. (\ref{43}) which is Lorentz
covariant, thus Eq. (\ref{44}) is also Lorentz invariant. This invariance
also applies to the zero component of $\Phi ^{\left( 4\right) }$, which was
proven explicitly by Lomont $\cite{lomont}.$ For $J=0$, the free Maxwell
equations takes the form,

\begin{equation}
\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}+\boldsymbol{\Gamma
^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \Phi ^{\left( 4\right) }=0,
\label{45}
\end{equation}

which is exactly Eq. (\ref{b8}). The zero component is the perpendicularity
condition for the photon equation and it ensures that the helicity can be
only in the forward or backward direction. It also insures that the photon
will be a particle of spin 1. This condition also remains for the
inhomogenious Maxwell's equations Eq. (\ref{44}). But in the presence of
interactions it is not obvious that the spin 1 property should remain.
Therefore we will now generalize the non-homogenious Maxwell equations and
replace the zero component with $\Psi _{0}=E_{0}+iB_{0}.$

\subsection{The generalized equations}

The generalized equations are,

\begin{equation}
\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}+\boldsymbol{\Gamma
^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \Phi ^{\left( 4\right)
}=-\alpha J,\quad \Phi ^{\left( 4\right) }=\left(
\begin{array}{c}
\Psi _{0} \\
\Psi _{x} \\
\Psi _{y} \\
\Psi _{z
\end{array
\right) ,\quad J=\left(
\begin{array}{c}
c\rho \\
j_{x} \\
j_{y} \\
j_{z
\end{array
\right) .  \label{46}
\end{equation
from which one can extract the generalized Maxwell's equations in the form

\begin{equation}
\partial _{0}E_{0}+\boldsymbol{\nabla }\cdot \boldsymbol{E}=\alpha j_{0},
\label{65}
\end{equation}

\begin{equation}
\partial _{0}\boldsymbol{E+}\mathbf{\nabla }E_{0}-\mathbf{\nabla \times B
=-\alpha \boldsymbol{j},  \label{66}
\end{equation}

\begin{equation}
\partial _{0}B_{0}+\nabla \cdot \boldsymbol{B}=0,  \label{67}
\end{equation}

\begin{equation}
\boldsymbol{\nabla }\times \boldsymbol{E+\partial }_{0}\boldsymbol{B+\nabla
B_{0}=0.  \label{68}
\end{equation}

Similar equations were derived by Dvoeglazov$\cite{dvoeglazov}.$ \ We will
now look for new features of these equations.

\subsection{Energy density}

According to Eqs. (\ref{a17}) and (\ref{a20}) the energy density is
proportional to,

\begin{equation}
\left(
\begin{array}{cccc}
\Psi _{0}^{\ast } & \Psi _{x}^{\ast } & \Psi _{y}^{\ast } & \Psi _{z}^{\ast
\end{array
\right) \left( i\hbar c\partial _{0}\right) \left(
\begin{array}{c}
\Psi _{0} \\
\Psi _{x} \\
\Psi _{y} \\
\Psi _{z
\end{array
\right) =i\hbar c\left( \Psi _{0}^{\ast }\partial _{0}\Psi _{0}+\mathbf{\Psi
}^{\ast }\mathbf{\cdot }\left( \partial _{0}\mathbf{\Psi }\right) \right)
\label{46a}
\end{equation}

\begin{equation}
=i\hbar c\left[ \left( E_{0}-iB_{0}\right) \partial _{0}\left(
E_{0}+iB_{0}\right) +\left( \mathbf{E}-i\mathbf{B}\right) \mathbf{\cdot
\left( \partial _{0}\left( \mathbf{E}+i\mathbf{B}\right) \right) \right] ,
\label{46b}
\end{equation
which is different from the conventional form proportional to

\begin{equation*}
\mathbf{\Psi }^{\ast }\mathbf{\cdot \Psi }=\left( \mathbf{E}-i\mathbf{B
\right) \mathbf{\cdot }\left( \mathbf{E}+i\mathbf{B}\right) =\mathbf{E}^{2}
\mathbf{B}^{2}
\end{equation*}

\subsection{The potentials}

Let us introduce the potentials,

\begin{equation}
A^{\left( 4\right) }=\left(
\begin{array}{c}
A_{0} \\
A_{x} \\
A_{y} \\
A_{z
\end{array
\right) ,  \label{47}
\end{equation
where the scalar potential $V=cA_{0}$.\ \ Their relation to the wavefunction
$\Phi ^{(4)}$ can be obtained by requiring that in the Lorenz gauge they
satisfy the wave equation,

\begin{equation}
\partial _{\mu }\partial ^{\mu }A^{(4)}=\alpha J.  \label{48}
\end{equation
The $\Gamma $ matrices, which are a representation of the Pauli matrices,
will factorize the d'Alembertian the same way as the Pauli matrices
factorize it, i.e.,
\begin{equation}
\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}-\boldsymbol{\Gamma
^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \left( \Gamma _{0}^{\left(
4\right) }\partial _{0}+\boldsymbol{\Gamma }^{\left( 4\right) }\cdot \mathbf
\nabla }\right) =\Gamma _{0}^{\left( 4\right) }\partial _{\mu }\partial
^{\mu }  \label{49}
\end{equation
In order to get Eq. (\ref{48}), using Eqs. (\ref{46}) and (\ref{49}) the
relation between the $\Phi ^{(4)}$ and $A^{\left( 4\right) }$ has to be

\begin{equation}
\Phi ^{\left( 4\right) }=\left(
\begin{array}{c}
E_{0}+iB_{0} \\
E_{x}+iB_{x} \\
E_{y}+iB_{y} \\
E_{z}+iB_{z
\end{array
\right) =-\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}-\boldsymbol
\Gamma }^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \left(
\begin{array}{c}
A_{0} \\
A_{x} \\
A_{y} \\
A_{z
\end{array
\right)  \label{50}
\end{equation}

\begin{equation}
=-\left(
\begin{array}{c}
\partial _{0}A_{0}+\partial _{1}A_{x}+\partial _{2}A_{y}+\partial _{3}A_{z}
\\
\partial _{0}A_{x}+\partial _{1}A_{0}+i\left( \partial _{2}A_{z}-\partial
_{3}A_{y}\right) \\
\partial _{0}A_{y}+\partial _{2}A_{0}-i\left( \partial _{1}A_{z}-\partial
_{3}A_{x}\right) \\
\partial _{0}A_{z}+\partial _{3}A_{0}+i\left( \partial _{1}A_{y}-\partial
_{2}A_{x}\right
\end{array
\right) ,  \label{51}
\end{equation
from which the relation between the fields and the potentials (in the Lorenz
gauge) is,

\begin{equation}
E_{0}=-\partial _{0}A_{0}-\nabla \cdot \mathbf{A,}  \label{52}
\end{equation}

\begin{equation}
B_{0}=0,  \label{53}
\end{equation}

\begin{equation}
\mathbf{E=-\nabla }A_{0}-\partial _{0}\mathbf{A,}  \label{54}
\end{equation}

\begin{equation}
\mathbf{B=\nabla \times A.}  \label{55}
\end{equation}

Eqs. (\ref{52}) and (\ref{53}) are new relations of the generalized
Maxwell's equations, but the Lorenz condition,

\begin{equation}
\partial _{0}A_{0}+\nabla \cdot \mathbf{A}=0,  \label{56}
\end{equation
enforces the spin 0 component $E_{0}$\ to be zero, this result should be
gauge invariant as the electric and magnetic fields are. Thus only when the
Lorenz condition is not satisfied (while Eq. (\ref{48}) is valid) the $E_{0}$
can be different from zero. This result indicates that spin 1 is conserved
in Maxwell's equations. In order to have $E_{0}\neq 0$ a spin changing
interaction must be added to the 4-current, as the $E_{0}$\ component
belongs to the spin 0 part of the four vector $E_{\mu }$ which belongs to
the $D^{\left(
{\frac12

{\frac12
\right) }$\ representation of the Lorentz group with an angular momentum
basis of spin 0 and spin 1.\ \ \

\subsection{Wave equations}

Let us multiply Eq. (\ref{46}) by $\left( \Gamma _{0}^{\left( 4\right)
}\partial _{0}-\boldsymbol{\Gamma }^{\left( 4\right) }\cdot \mathbf{\nabla
\right) ,$

\begin{equation}
\Gamma _{0}^{\left( 4\right) }\partial _{\mu }\partial ^{\mu }\Phi ^{\left(
4\right) }=\left( \Gamma _{0}^{\left( 4\right) }\partial _{0}-\boldsymbol
\Gamma }^{\left( 4\right) }\cdot \mathbf{\nabla }\right) \left( \Gamma
_{0}^{\left( 4\right) }\partial _{0}+\boldsymbol{\Gamma }^{\left( 4\right)
}\cdot \mathbf{\nabla }\right) \Phi ^{\left( 4\right) }=-\alpha \left(
\Gamma _{0}^{\left( 4\right) }\partial _{0}-\boldsymbol{\Gamma }^{\left(
4\right) }\cdot \mathbf{\nabla }\right) J,  \label{57}
\end{equation
from which we obtain,

\begin{equation}
\square E_{0}=\alpha \left( \partial _{0}j_{0}+\mathbf{\nabla \cdot j
\right) ,  \label{58}
\end{equation}

\begin{equation}
\square B_{0}=0,  \label{59}
\end{equation}

\begin{equation}
\square \mathbf{E=}\alpha \left( \mathbf{\partial }_{0}\mathbf{j+\mathbf
\nabla }}j\mathbf{_{0}}\right) ,  \label{60}
\end{equation}

\begin{equation}
\square \mathbf{B=-}\alpha \mathbf{\nabla \times j,}  \label{61}
\end{equation
where $\square =\partial _{\mu }\partial ^{\mu }.$

Current conservation requires,

\begin{equation}
\partial _{0}j_{0}+\mathbf{\nabla \cdot j=0,}  \label{62}
\end{equation
therefore when the current is conserved

\begin{equation}
\square E_{0}=0,  \label{63}
\end{equation
and only if the current is not conserved the possibility of $\square
E_{0}\neq 0$ will exist. As indicated before, a spin changing interaction
can induce the $E_{0}$ component$.$

\subsection{\protect\bigskip Scalar electrodynamic waves}

There are claims that scalar electrodynamic waves have been detected \cit
{monstein}. As we have shown, within the framework of electrodynamics with
conserved currents the scalar waves cannot exist. There exists a
misconception that longitudinal waves are the scalar waves. Longitudinal
waves can exist as solutions of Maxwell's equations when the
perpendicularity condition $\mathbf{\nabla \cdot E=\nabla \cdot B=0}$ is \
violated, for instance when $\mathbf{\nabla \cdot E=}\alpha j\mathbf{_{0}}$,
i.e. in the presence of a charge distribution. Therefore in Ref. \cit
{monstein} the longitudinal waves were actually vector waves. Other claims
of scalar electromagnetic waves come from K. Meyl \cite{meyl}, which are
based on a theory different from Maxwell's. A modification of Maxwell's
equation to allow for current non-conservation was proposed by Hively and
Giacos \cite{hively} with the aim to experimentaly detect scalar
electromagnetic waves.

\subsection{Summary and conclusions}

A simplified formalism of first quantized massless fields of any spin is
presented. Angular momentum basis for particles of zero mass and finite spin
\ $s$\ of the $D^{\left( s-1/2,1/2\right) }$ representation of the Lorentz
group is used to describe the wavefunctions. The advantage of the formalism
is that by equating to zero the \ $s-1$ components of the wavefunctions, the
$2s-1$ subsidiary conditions (needed to eliminate the non-forward and
non-backward helicities) are automatically satisfied. Probability currents
and Lagrangians are derived \ allowing a first quantized formalism. A simple
procedure is derived of connecting the wavefunctions with potentials and
gauge conditions.

The spin 1 case is of particular interest and is described with the
D^{\left( 1/2,1/2\right) }$ vector representation of the well known
self-dual representation of the Maxwell's equations Eq. (\ref{44}). The wave
function is the 4-vector

\begin{equation}
\Phi ^{\left( 4\right) }=\left(
\begin{array}{c}
0 \\
\Psi _{x} \\
\Psi _{y} \\
\Psi _{z
\end{array
\right) =\left(
\begin{array}{c}
0 \\
E_{x}+iB_{x} \\
E_{y}+iB_{y} \\
E_{z}+iB_{z
\end{array
\right) .  \label{64}
\end{equation}

The zero component remains unchanged under Lorentz transformations \cit
{lomont},\cite{GM}. It is well known that the vector $D^{\left(
1/2,1/2\right) }$ representation has an angular momentum basis of spin 1
plus spin 0. The meening of it is that the wave function Eq. (\ref{64
)contains only the spin 1 contribution. Thus Maxwell's equations contain an
intrinsic spin 1. This representation allows to generalize Maxwell's
equations by adding the $E_{0}$ and $B_{0}$ timelike components to create
the electric and magnetic four-vectors, \

\begin{equation}
\Phi ^{\left( 4\right) }=\left(
\begin{array}{c}
E_{0}+iB_{0} \\
E_{x}+iB_{x} \\
E_{y}+iB_{y} \\
E_{z}+iB_{z
\end{array
\right) .  \label{70}
\end{equation}

We found that as long as the electromagnetic current is conserved, $E_{0}$
and $B_{0}$ have to be zero. Thus scalar electromagnetic waves can be
created only if charged conservation is violated, or if a spin changing
interaction is added to the conserved current.

\bigskip

redpajama_set_name: RedPajamaArXiv