Metrics for Linguistic screening | Language Solutions Inc.
We consider the elements such as brand positioning, brand messaging, and product segmentation to be the foundation for analysis in the target market. We leverage the knowledge that was created during the name development to test and analyze in the target market.
Linguistic screening should not only take into account appropriate meaning in other languages but also the ease by which a product name can be pronounced by a person from another country. Pronunciation could be an important success factor in product name adoption. Product names are often ambiguous and created without direct meaning. Therefore, a valuable attribute could be a powerful sounding name. Names could be unintentionally softened through differences in pronunciation in the target market. Understanding how a product sounds in the target market can be valuable information in choosing a product name.
Cultural analysis can include a wide variety of aspects. One example is the use of colors and images that are appropriate and engaging. Another aspect is name associations. In product name development, associations with competitors or other organizations is usually taken into account for different reasons (legal reasons, unique factor, etc.). Powerful associations can be made with similar words used in related or unrelated industries, or for instance in popular culture. Especially with highly ambiguous names, powerful associations that support the brand positioning can be a key success factor and should be tested in the target markets. Cultural views may vary by generation and therefore an important attribute is to understand the target segmentation of the product. Gender roles in purchasing are also important to consider as these differ by country. You may not be marketing to the decision maker!
While actual product testing is not part of the scope for linguistic screening, we also should not discount the value of product analysis for the target market. Product aspects such as packaging and design can be taken into consideration and analyzed for further testing in the target market. Having product aspects analyzed before you test in your target market can help narrow down the goals for expensive tests using local focus groups.
The Linguistic Screening process should benefit from open communication and flow of information between product developers and linguistic and cultural analysts. Too many times, the brand development process is overlooked in product name development for a foreign market. When considering the investment that has gone into the product and the potential it could have, the investment in a carefully executed linguistic screening process should be a drop in the bucket.
The next time your client or your company wants to screen their English product name in other languages, give us a call for a proprietary process that we have using clear metrics for Linguistic Screening.
Website Localization Services….where do you start?


What Tends to make a Author a Writer?
An intriguing dialogue on LinkedIn is swirling around the topic of when a author can phone them selves a writer.. As I've watched the dialogue unfold, some exciting suggestions have cropped up. They are really worth looking at.
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A author is another person who has been revealed offline.
Contemplating that a large phase of the creating get the job done accessible is virtually exclusively on the net now, this definition just can not keep true. Though it is virtually certain that somebody who has broken into challenging print is a very excellent author, it isn't going to preclude somebody who has never had their function released in classic media from staying regarded as a writer.
A writer is another person who understands their grammar, punctuation regulations and how to spell items appropriately.
I am not ready to say this is genuine since I know that publishers, journals and newspapers all retain the services of duplicate editors for a person pretty great explanation. Not each author on the workforce has great spelling techniques. No writer's punctuation capabilities are ideal. And absolutely everyone has particular words they almost often style incorrectly. I've been a copy editor. It really is always less difficult to see many others errors.
For me, I have to check out dropping the "r" on your, incorporating a "d" in faculty and several other persistent misspellings. There are text I consistently insert added letters to and other folks I drop letters from virtually each and every time I type them. And most of the time, they are text, so spell check would not capture them.
At the exact same time, if a writer can not inform the distinction among when to use your and you might be or its and it truly is, it will be an obstacle to obtaining a better pays scale. Excellence in each and every aspect of composing is important if you want to be taken significantly.
A writer is a skilled who would make a steady cash flow from producing.
This can be true. The definition of constant might fluctuate. I know that I began by earning only a several hundred bucks a thirty day period from creating function. I had some months wherever I experienced no money from that source. At the exact time, I was constantly searching for get the job done. As a producing skilled I took motion.
I actively designed my portfolio.
I built a cost-free web-site on Place of work Reside.
I targeted on bridging the hole from when I researched journalism to what the market requires of writers currently.
I utilized each piece of knowledge I gained into strengthening my capacity to generate compelling elements.
To set the title "author" on a resume, propose you want to be much more than someone who has started their very own blog site. Even with the reality that I have a ghostwriting recommendations website, it is just not this blog that tends to make me a writer. It truly is the actuality that persons read through this blog and really reward from it that supports my claim that I am a writer.
A writer is somebody who can make clear various matters in language that the ordinary person can have an understanding of.
This certainly is a ability that not all people possesses. In some methods, each author needs to have a teacher's coronary heart, the ability to break factors down into comprehensible packets. Some writers are gifted with the skill to reach extremely young minds. Which is why there are writers of kid's guides. Other writers just are not able to get down to that amount, yet continue being powerful writers for a diverse viewers.
A writer is additional than somebody who begins their individual weblog.
There are fantastic blogs and so-so weblogs. To really declare to be a writer, the blog site cannot be riddled with grammar mistakes. A several spelling and punctuation glitches are forgivable, particularly as most site writers can't afford to pay for a independent set of eyes to edit their do the job.
A author is another person who crafts words to impact other individuals.
It's not no matter if your do the job appears on the eviscerated remnants of a tree or on the digital representation of a website page that tends to make you a writer. It really is whether or not your terms go and/or encourage. A novelist could shift by means of the development of people and plots. A website writer could inspire to action by diligently preferred terms.
Both of those are writers. Both equally use their electric power about words to generate an expertise in the brain. That working experience wouldn't be there with no the writer's capability to craft words and phrases.


Some 200 Israeli and foreign photographers and as many as 30 curators will take part in the 2012 International Photography Festival, which will be held during the intermediate days of Sukkot (October 2-8) at the Jaffa Port and other locations.
According to organizers, this year's festival will be focused around the themes of the environment, community, and art.
The festival will include a project in collaboration with Google, as well as several exhibitions in which photographers will select the works of their colleagues.
The Shpilman Institute for Photography will present an integrated project of exhibitions and video screenings, and huge photos with "harsh messages on the boundaries between society and art" will be showcased on the port's buildings.
Some of the exhibitions are free, but tickets should be purchased to see the whole festival. A single entry card costs NIS 39 (about $10), and a family card (a couple and up to three kids) costs NIS 78 ($20).
See all talkbacks "Jaffa hosts International Photography Festival"


NEW YORK -- The National Hockey League announced today changes to its Draft Lottery, a weighted system implemented and utilized to determine the order of selection in the first round of the NHL Draft for the 14 Clubs not qualifying for the Stanley Cup Playoffs (or the Clubs that have acquired the first-round drafting positions of those non-playoff teams).
These changes will be phased in over a two-year period, beginning with the Draft Lottery in 2015.
The odds of winning the first overall selection in the NHL Draft for the 14 non-Playoff teams will be adjusted to more appropriately reflect the current state of competitive balance in the League. This will result in a more evenly-balanced allocation of odds, with the 10 highest-finishing non-Playoff qualifying teams receiving higher (better) Draft Lottery odds than they received previously and the four lowest-finishing teams receiving lower (worse) odds. The revised set of odds will remain in effect year-to-year in the future.
Beginning in 2016, the Draft Lottery will be utilized to assign the top three drafting slots in the NHL Draft, an expansion over previous years when the Draft Lottery was used to determine the winner of the first overall selection only.
Three draws will be held: the 1st Lottery draw will determine the Club selecting first overall, the 2nd Lottery draw will determine the Club selecting second overall and the 3rd Lottery draw will determine the club selecting third overall.
As a result of this change, the team earning the fewest points during the regular season will no longer be guaranteed, at worst, the second overall pick. That club could fall as low as fourth overall.
The allocation of odds for the 1st Lottery draw will be the same as outlined above for the 2015 NHL Draft Lottery. The odds for the remaining teams will increase on a proportionate basis for the 2nd Lottery draw, based on which Club wins the 1st Lottery draw, and again for the 3rd Lottery draw, based on which Club wins the 2nd Lottery draw.
The 11 Clubs not selected in the Draft Lottery will be assigned NHL Draft selections 4 through 14, in inverse order of regular-season points.


Can I receive assistance in another language?
The Erie County Department of Social Services assists non-English speaking clients by offering free language services, including utilization of qualified interpreters and information written in other languages. For a full overview of language and other services offered by Erie County, Click Here.
How does HEAP calculate wages?
For Emergency HEAP, what resources are countable?
IRA accounts, including remaining amounts from a closed-out IRA.
Lump sums from sale of property or insurance settlements and balances from any other lump sum not specifically excluded.
401(k) and other retirement accounts.
income tax refunds (except EITC) payments).
Any other available funds not specifically excluded.
Amounts designated for an allowable current monthly living expense such as food, shelter, employment-related expenses, etc.
Money earmarked for payment of the current year's prioperty and/or school taxes for the primary residence.
One written pre-arranged burial agreement with a cash value not exceeding $1,500 per household member and interest on the burial account.
Accounts, such as PASS accounts, designated by the Social Security Administration as exempt from SSI resource limits.
Payments from reverse annuity mortgages.
Loans (including college loans, personal loans, home equity loans).
Credit cards or advances from credit cards.


Reseller hosting is perfect for people who wish to sell hosting services to their customers. You'll be able to provide a robust environment without having to invest in servers or any other infrastructure. The cost of your hosting reseller account will also likely be covered by your first customers. Everything after that will be pure profit. And the more customers you have, the more money you'll make. Many hosting resellers end up selling add-on services like web design, content writing and traffic generation to help earn even more money from their clients. Here are three important things to know prior to becoming a hosting reseller.
It's quite easy to start offering hosting as a reseller. You'll first need to purchase a reseller hosting account with enough resources for all of your clients. This type of hosting account will allow you to spin up new cPanel instances as you get new customers. But do make sure you're not too generous with your resource allocations. These individual hosting slices come out of the overall allocation of disk space and bandwidth from your reseller account. You are free to resell these resources to your customers as long as you don't go over your limits.
To make sure you don't go over your limits, create your custom packages with your resource limitations taken into consideration. Don't promise your clients unlimited resources if your overall resources are limited. Your customers will have their web hosting control panel where they will be able to see how many resources they're using out of their allocation.
One of the major problems affecting web hosts is customers abusing the server. One rogue customer can monopolize all of your hosting resources, leaving the rest of your clients' websites running very slowly. If you have a few bad customers like this, you'll need some way to isolate them from the rest of your users. You can certainly add CPU, memory and I/O limits to help curb excessive resource usage. There is also a server package known as CloudLinux that makes it simple to place your users in isolation of each other.
CloudLinux is an operating system designed specifically to meet the needs of hosting service providers. It works as a drop-in module for both Litespeed and Apache web servers that's easy to install and easy to configure. It is RPM based and interchangeable with Red Hat Enterprise Linux and Centos. CloudLinux features its own kernel and Apache module that talks directly to the kernel.
Your customers won't notice a difference, and your server architecture will be more robust. The primary benefit of CloudLinux is that it protects your reseller clients from being adversely affected when one client hogs your resources. CloudLinux creates a virtual environment that isolates each tenant or account on the server. It can also set CPU limits the individual user level. This limits the number of resources that any site can use. With CloudLinux in place, no single account can slow down or take down the entire server. Your clients will also be able to monitor what percentage of the CPU they are using. CloudLinux is a great feature to have when you don't want your customers' traffic spikes affecting other people's sites.
Resellers who use CloudLinux will see fewer support tickets and will have to reboot their servers less often. This will improve the overall reliability of your reseller hosting. CloudLinux can also help protect the server from hackers and poorly written scripts. This can help stop scripts from draining resources for other tenants. Better security also means fewer headaches fixing hacks and corrupted databases. And it's always better to spend your time running your hosting business rather than suspending abusive clients or being forced to optimize your server for resource usage.
A reseller controls their customers' hosting accounts through a central management area called Web Host Manager (WHM). The first thing you'll do in WHM is to create your unique hosting plans. You should offer your customers a range of different pricing options that are based on resources and features. You'll just need to decide how much disk space, bandwidth, databases, email accounts and other features each pricing level gets. Some hosts like to add premium features like a cache layer (such as Varnish or CloudFlare's Railgun) or a CDN to their higher priced hosting plans.
After you have all your plans adjusted to your liking, you'll use these plans to create new accounts for each of your customers. Each client will choose a particular package when they sign up to your hosting. You'll need to assign them a username and a password to go along with their chosen package. After the hosting plan is created, each customer will have their own control panel login page. This allows the customers to have full control of their web hosting account. Most hosts will use cPanel as their hosting control panel.
WHM also integrates into a variety of helpdesks (like WHMCS), providing a way for customers to contact support. Prior to becoming a host, you might think that you need multiple methods of providing customer support. This could be via an online form, phone call or even live chat if you have the staff for that. Although some resellers will rely on these alternate means of support, it's really not necessary for you to adequately deal with customer queries. WHM will integrate with a wide variety of helpdesk, ensuring that your clients' questions are answered promptly.
Hosting as a reseller can be a financially rewarding step in your online business. Many resellers endeavor to provide good support so that their customers are happy. Once your customers are happy, they'll likely renew if they can count on you to treat them right.


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redpajama_set_name: RedPajamaGithub


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Member Profile: Kieran McEvoy
Kieran McEvoy, a leading figure internationally on societies transitioning from conflict was admitted as a Member of the Royal Irish Academy on 24 May 2019.
The 2019 John Maddox Prize
The John Maddox Prize recognises the work of individuals who promote sound science and evidence on a matter of public interest, facing difficulty or hostility in doing so.
Pride month DIB entry: the 'Ladies of Llangollen'
To mark Pride 2019 the DIB is publishing its entries on celebrated diarist Sarah Ponsonby (1755–1831) and her life partner Lady Eleanor Butler (c.1739–1829), known as the 'Ladies of Llangollen'.
Member Profile: Tom Lodge
Tom Lodge, contemporary political historian was admitted as a Member of the Royal Irish Academy on 24 May 2019.
Call for contributions: Open Consultation on FAIR data in the Humanities
Working with data in the humanities? Consider contributing to the ALLEA e-Humanities draft recommendations.
Member Profile: Alan Irvine
Alan Irvine who has a long-standing research record in hereditary skin disease was admitted as a Member of the Royal Irish Academy on 24 May 2019.
Member Profile: Moyra Haslett
Professor Moyra Haslett, principal investigator for the Irish Song database was admitted as a Member of the Royal Irish Academy on 24 May 2019.
Celebrating Bloomsday: James Joyce in the DIB
To mark Bloomsday (16 June) the DIB is publishing its full, unedited entry for James Joyce by Bruce Bradley.
Celebrating Bloomsday: Nora Barnacle in the DIB
The DIB is publishing its entry for Nora Barnacle, life-partner of James Joyce. The couple had their first date on 16 June 1904, a date immortalised in his novel Ulysses (1922) and thereafter celebrated as 'Bloomsday'....
Member Profile: Yuri Gunko
Professor Yuri Gunko, a world-leading expert in inorganic materials chemistry was admitted as a Member of the Royal Irish Academy on 24 May 2019.

redpajama_set_name: RedPajamaCommonCrawl


Listed under Gardens in Ontario, Canada.
Bounded by the steep Niagra River Gorge and the famous falls on one side, this park has been a good place to admire the falls since it was 'arranged' here in the 19th Century.
As well as the view, the park also has a rock garden, a tea rose garden, a collection of Canada's native plants, an amphitheatre and, at the right time of year, impressive carpets of flower beds. At a different right time of year you'll be greeted by 500,000 bobbing daffodils.
Although the Queen Victoria Park is 'literally the "heart" of Niagara Parks', that is not in the province of Manitoba in Canada. It is in the province of Ontario. I wouldn't want any travelers to find themselves hundreds of miles away from their destination!
Hi Jane - Thanks very much for letting us know. I've changed the text but if you have a chance could you see if we have the pin in the right place in the map. That's very much for your contribution!
Actually, the pin is still incorrect. If you follow your Niagara Parks link and use their map to zoom out, you should be able to get a better idea of where it is. I am looking forward to visiting both this garden in the future some day. Since it is in Canada, perhaps my chances are better! Thanks for the great website.
Thanks. Should be in the right place now.


All hardware sold are bulk equipment with no drivers and cd included.
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You want a great vehicle to get around Silver Creek whether you're going for a business trip or a vacation. Check out the famous sites around town and park in front of the best restaurants in Silver Creek. We've answered the most frequently asked questions about renting a car in Silver Creek. Find out how to get the best rates on your ideal vehicle.
Where do I get a great deal on a car rental in Silver Creek?
What rental companies have retailers in Silver Creek?
What type of rental car should I get for my trip to Silver Creek?
How old do you have to be to rent a car in Silver Creek?
Typically, the age limit for renting a car in Silver Creek is 21. However, you may find that there is an additional charge if you're under 25 or for larger or higher category cars. Go through the supplier's terms to find what any additional charges is before you book your vehicle.
Will I need insurance to get a car rental in Silver Creek?
Most countries require the driver to have insurance. You may be able to buy temporary insurance with the rental car supplier. Otherwise, as a United States citizen, you can also add on Collision Damage Coverage with CarRentals.com at checkout. Several credit card issuers (Visa, MasterCard, American Express, and Discover) will offer coverage. However, there may be limitations, such as not covering large automobiles like trucks or SUVs. Make sure to call and find out exactly what your credit card will cover and how much before you head to Silver Creek.
Most rental car suppliers provide you a full tank policy. We suggest returning it topped off. To avoid any added expenses, fill up your tank before you bring it back.
Maybe you're traveling solo, maybe you're bringing your partner or kids, or maybe you're carpooling with co-workers to and from the hotel to the conference center. No matter who you're traveling with, CarRentals.com has a car rental that can fit your needs and not break the bank.


Once Shaheen-2 becomes operational, it will give Pakistan the ability to target facilities across most if not all of India and hold all of India's major cities at risk.
By IANS, [RxPG] Islamabad, May 10 - Pakistan is preparing for deployment of its next-generation nuclear-capable ballistic missile, says a report by an eminent group of US scientists.
'The main driver for Pakistan's nuclear modernisation appears to be India's nuclear build-up, although national prestige probably also is a factor,' says the report of the Federation of American Scientists -.
The scientists who worked on the Manhattan Project that developed the world's first atomic bombs founded the federation 60 years ago. Dawn carried excerpts from the report in a Washington-datelined story.
The two countries appear to be entering a new phase in their regional nuclear arms race with medium-range ballistic missiles gradually replacing aircraft as the backbone of their nuclear strike forces, the FAS report added.
At the same time, it warned that in contrast to aircraft, ballistic missiles have a very short flight envelope and cannot be recalled once launched.
The FAS report includes a satellite image taken on June 5, 2005 that the authors say shows 15 transporter erector launchers - for the medium-range Shaheen-2 fitting out at the National Defence Complex near Fatehjang, some 30 km southwest of Islamabad.
The authors say that they discovered the vehicles while preparing for an update on Pakistani nuclear forces for the May/June issue of the Bulletin of the Atomic Scientists.
The authors estimate that Pakistan currently has an arsenal of about 60 nuclear weapons. In the last five-and-a-half years, Pakistan has deployed two new nuclear-capable ballistic missiles, entered the final development stages of a potentially nuclear-capable cruise missile, started construction of a new plutonium production reactor, and is close to completing a second chemical separation facility.
According to the report, Pakistan established the National Defence Complex in 1993 and this has since expanded into a centre for the development of the country's missile force.
The main facilities are spread over a 6x2 km area on a ridge and include what appear to be administrative buildings, missile assembly halls and garages. At two locations, several large six-axle vehicles are clearly visible on the satellite image, as are several smaller four-axle vehicles.
Approximately 1.5 km northwest of the main building is a cluster of what appears to be five recently constructed garages. Parked in front or partially inside the two largest garages to the west are 11 vehicles that, the authors claim, show the characteristic six-axle design of the Shaheen-2 TEL, indicating that the launcher itself has not yet been installed.
The second facility is located just south of the main building and includes what may be four large assembly halls where, the authors claim, the missile launchers are installed on the vehicles. One six-axle vehicle appears to be about to enter the hall.
Outside the other end of the building are what appear to be two Shaheen-2 TELs that have completed instalment of their missile launcher, thereby obscuring the axles of the vehicles.
Two four-axle vehicles are also visible, which the authors identify as Shaheen 1 TELs awaiting assembly.
The authors say that the image is good enough to determine that the large vehicles strongly resemble the six-axle Shaheen-2 TELs photographed at Pakistan Day parades. Each such vehicle is 16-17 meters long with a drivers' compartment that covers the front axle.
Although the Shaheen-2 launchers appear to be fitting out at the National Defence Complex, the authors of the report say that the missile they are intended to carry is not yet thought to be fully operational.
Three test-launches of the 2,000-plus km missile have been conducted since 2004, the most recent in May 2006, and a couple more are probably needed before the missile can be deployed.
As such Shaheen-2 will be Pakistan's response to India's deployment of the Agni-II missile, the authors conclude.


Lindsay Sandiford has been sentenced to death in Bali, Indonesia for drug trafficking.
A woman from Redcar, has been sentenced to death in Indonesia for drug trafficking.
Lindsay Sandiford was arrested in May after police in Bali said they found 10.6lb of cocaine in the lining of her suitcase.
"We can confirm that a British national is facing the death penalty in Indonesia.
"We remain in close contact with that national and continue to provide consular assistance.
"The UK remains strongly opposed to the death penalty in all circumstances."


text:
Sridhar
Pinnapureddy
CtrlS Datacenters
Mr. Sridhar Pinnapureddy is a First Generation Entrepreneur, innovator and Founder, Chairman and Managing Director of CtrlS Datacenters Ltd.
He is considered as a visionary leader in the Indian Datacenter Industry and is credited with launching Asia's largest Tier-4 Datacenter and has orchestrated 200 innovations over the last decade.
Sridhar has been recognized for his contribution to the Industry and has been a recipient of several prestigious awards including E&Y Entrepreneur of the Year.
Today, he steers the Group with over 1,800 employees. CtrlS the flagship company operates five datacenters in India. The group has presence in 20 countries spread across Americas, Europe, Middle East Africa, South East Asia and APAC and plans to establish its footprint in 40 countries by 2020.
Honour & Awards
E&Y Entrepreneur of the Year (Finalist)
Visionary Leader of the Indian Industry
TV5 Business Leader Award
Best Entrepreneur of the Year (ATA)
CEO of the year Award (World Quality Congress)
Rajiv Gandhi Shiromani by Global Economic Council (GEC)
SI Entrepreneur of the Year Award
The Outstanding Entrepreneur of the year for APAC (APEA)
Karamveer Puraskar (ICONGO)
Patents/Innovations
ISP-in-a-Box (Alladdin)
200 Innovation in Datacenter, Cloud Services
Designed World's 1st Tier-4 Public Cloud, Community Cloud (Banking, Manufacturing)


The superintendent of a rural school district engaged Ed Direction to help him turn around a state-defined "failing" elementary school. The students were poorly managed, leading to disengagement and minimal effort. Staff mindset had become stagnant as staff wondered what could be done to turn around decades of poor performance, and an apparent lack of interest from parents and students.
Ed Direction applied its transformation model in full force over a three year period. The staff, parents, and students were re-energized by the quick wins that Ed Direction helped them achieve. Then, the work was sustained because of the strong parental engagement programs, classroom-level coaching, and small-group, job-embedded professional development. At the conclusion of the three year period, the school's grade had risen to "A," and disciplinary referrals had decreased by 50%. In reflecting on the success, the staff was thrilled to see how much impact was possible and the deep growth they had achieved.


text:
\section{Introduction} \label{sec:Introduction}
In some sense, the theory of radiative heat transfer is complete: use Maxwell's equations to determine the Poynting vector and, ultimately, the flow of electromagnetic energy between bodies. For objects and separation distances much larger than the dominant thermal wavelength ($\lambda_{T} \approx$ 10 \si{\micro\meter} at room temperature), radiative heat transfer between engineering surfaces can be simplified to problems involving Planck's blackbody distribution (or the Stefan-Boltzmann law), emissivities, and view factors \cite{Howell2011}. These classical concepts carry readily apparent physical significance.

The story changes when objects and separation distances become comparable to the dominant thermal wavelength and ``near-field effects" such as the diffraction, interference, and tunneling of electromagnetic waves create pronounced deviations from what classical theory predicts. A number of methods to solve Maxwell's equations and account for those effects in near-field radiative heat transfer (NFRHT) have been developed. The most common of these methods involve dyadic Green's functions (DGFs) \cite{Joulain2005, Volokitin2007, Francoeur2008, Narayanaswamy2013a}, spectral densities \cite{Kruger2012}, fluctuating surface currents/boundary element methods (BEM) \cite{Rodriguez2012}, or thermal discrete dipole approximations (T-DDA) \cite{Edalatpour2014}, each with their own advantages and limitations. But even with these formulations of the problem, physical insight can be lacking.

To that end, a great deal of research has been directed towards determining explicit formulas for heat transfer in experimentally important thermal systems. Certain problems are best attacked using DGF and spectral density methods, such as NFRHT in plane-plane \cite{Polder1971}, sphere-sphere \cite{Narayanaswamy2008, Mackowski2008, Kruger2012, Czapla2017}, and sphere-plane \cite{Otey2011, Kruger2012} configurations, where the electromagnetic fields are easily described by vector wave eigenfunction expansions. Thermal systems which do not yield to those methods often require methods that involve surface or volume meshing, such as BEM and T-DDA. Those methods have allowed investigations of cone-plane \cite{Rodriguez2013, Edalatpour2016} and cube-cube \cite{Edalatpour2014} configurations, to name a few.

The goal of this work is simple: provide explicit formulas which completely describe a thermal system consisting of spheres in a linear chain. While this system has been previously investigated for light scattering \cite{Fuller1988, Li2003, Wei2004, Chen2006, Lee2013} and radiative transfer in the dipole limit \cite{Ben-Abdallah2011, Dong2017a, Kathmann2018}, it has not yet been characterized for NFRHT between spheres of arbitrary size, with or without spherical layers. The main results of this work are numerically exact expressions for NFRHT between pairs of spheres in a linear chain, and between any sphere in a chain and its environment. Furthermore, motivated by recent experimental measurements of the Casimir force between microspheres \cite{Garrett2018} and informed by our new expressions, we developed a thermal model for a potential NFRHT experiment between two spheres and provide suggestions on how to best interpret the measured sphere-sphere heat transfer.

The structure of the paper is as follows: first, in Sec. \ref{Geometry}, the geometry of the linear chair is described and geometrical variables are defined. Next, in Sec. \ref{sec:Theory}, the theoretical treatment is discussed and the DGFs of the system are used to determine a formula for energy exchange between spheres in a chain and their environment. Then, in Sec. \ref{sec:CrossValidationofTheoreticalResults}, the formulas are validated against existing results in the literature. Finally, in Sec. \ref{sec:Implications}, the implications of the present work are discussed as they relate to NFRHT experiments between spherical objects.

\section{Geometry} \label{Geometry}
The configuration of the spheres is shown in Fig. \ref{fig:Geometry}. In Fig. \ref{fig:Geometry}A, an individual sphere, labeled sphere $i$, is depicted. Sphere $i$ has an outer radius, $\rho_{i}$. Internally, it may be homogeneous or composed of spherically symmetric layers. Coordinate system $i$ is fixed to the center of sphere $i$. Any position vector, $\boldsymbol{r}$ or $\widetilde{\boldsymbol{r}}$, when written in coordinate system $i$, is denoted $\boldsymbol{r}_{i}$ or $\widetilde{\boldsymbol{r}}_{i}$, respectively.

Figure \ref{fig:Geometry}B depicts a section of a linear chain of $N_{s}$ spheres, which is embedded in free space (referred to as region $f$). The $z$-axis of coordinate system $i$ ($1 \le i \le N_{s}$) is aligned down the central axis of the chain. The $x$-axes of all coordinate systems are parallel, and similarly so are the $y$-axes.

The spheres are numbered $1$ through $N_{s}$, such that their labels increase along the positive $z$-direction (of any coordinate system). Any two spheres, $i$ and $j$, are separated by center-to-center distance $d_{i,j}$ and the minimum separation between them is $D_{i,j} = | d_{i,j} | - \rho_{i} - \rho_{j}$ (not depicted explicitly in Fig. \ref{fig:Geometry}). The sign of $d_{i,j}$ is positive if $j > i$ and negative if $j < i$.
\begin{figure}
\includegraphics[width=3 in]{./Figure1.pdf}
\caption{\label{fig:Geometry} Configuration of spheres in chain. (A) Single sphere $i$ and its associated coordinate system. (B) Section from a linear chain of spheres embedded in region $f$.}
\end{figure}

\section{Theory} \label{sec:Theory}
The net radiative transfer between any two objects may be determined if the DGFs, which describe the electromagnetic fields created by any distribution of sources, are known. To solve electromagnetism problems, the electric and magnetic DGFs ($\overline{\overline{\boldsymbol{G}}}_{e}(\boldsymbol{r}; \widetilde{\boldsymbol{r}})$ and $\overline{\overline{\boldsymbol{G}}}_{m}(\boldsymbol{r}; \widetilde{\boldsymbol{r}})$, respectively) are required. Both variants of DGFs take two position vector arguments. The significance and locations of the position vectors will be explained later in this section.

For a given angular frequency, $\omega$, we may define a transmissivity function for energy transfer from object $j$ to object $i$, $\tau_{j \rightarrow i}(\omega)$, based solely on the DGFs. The mathematical definition of $\tau_{j \rightarrow i}(\omega)$ is given as Eq. 30 by Narayanaswamy and Zheng \cite{Narayanaswamy2013a} for isothermal objects with isotropic optical properties. In lieu of providing the lengthy definition, key features of the transmissivity function will be described. The transmissivity function is a function of only optical and geometric parameters, which are encoded into the DGFs. Though the exchange of thermal energy is a volumetric phenomenon, the properties of Maxwell's equations allow us to write the formulas for heat transfer in terms of surface integrals. The transmissivity function contains two surface integrals, over the surfaces of the two objects between which heat transfer is being investigated. To evaluate these integrals easily, the two position vector arguments of the DGFs should be located on the surfaces of interest, one on each surface. A surface integral formulation of NFRHT has the advantage of reducing the computations required, a property which is exploited by the BEM \cite{Rodriguez2012}.

In some ways, the double surface integral formula for the transmissivity function appears similar to the formula for a view factor \cite{Howell2011} in classical radiative transfer. The view factor, however, is a purely geometric property of just two objects, irrespective of any other objects present, whereas the DGFs contained within the transmissivity function automatically account for the effects of all objects present. Furthermore classical approaches such as thermal circuits or Gebhart factors \cite{Gebhart1961}, when using view factors in their calculations, assume objects emit diffusely with well-defined emissivities. DGF approaches, and therefore the transmissivity function, are exact in all situations where Maxwell's equations are valid, which includes objects with super-Planckian (greater than that of a blackbody) effective emissivities.

The transmissivity function is defined such that the spectral conductance between objects $j$ and $i$, $G_{j \rightarrow i}$, is given by
\begin{equation} \label{eq:SpectralConductance}
\begin{split}
G_{j \rightarrow i}(\omega, T) &= \lim_{T_{i},T_{j} \rightarrow T} \frac{Q_{j \rightarrow i}(\omega)}{T_{j} - T_{i}}
\\
&= k_{b} \left( \frac{\mathcal{X}}{\sinh{\mathcal{X}}} \right)^{2} \tau_{j \rightarrow i}(\omega)
\end{split}
\end{equation}
where $\mathcal{X}=\hbar \omega / 2 k_{b} T$, $\hbar$ is the reduced Plank constant, $k_{b}$ is the Boltzmann constant, $T$ is the thermodynamic temperature, and $Q_{j \rightarrow i}(\omega) d\omega$ is the contribution to the total heat transfer from radiation at angular frequencies between $\omega$ and $\omega + d\omega$.

The total conductance between objects $j$ and $i$, $G_{t,j \rightarrow i}$, is defined as
\begin{equation} \label{eq:TotalConductance}
G_{t,j \rightarrow i}(T) = \int_{0}^{\infty} \frac{d\omega}{2\pi} G_{j \rightarrow i}(\omega, T) \\
\end{equation}

Spectral conductance is often expressed in different units in different papers, but changes of variable can be performed to transform between units. A definition of spectral conductance is valid so long as the integral definition of total conductance computes to the same value, regardless of the units used. For example, in Fig. \ref{fig:ThreeSpheres_SCUFFEM} we present $\tau_{j \rightarrow i}(\lambda)$ in units of \si{\per\second \per\micro\meter}, where $\lambda = 2 \pi c / \omega$ is the vacuum wavelength and $c$ is speed of light in vacuum. This version of spectral conductance is obtained from $\tau_{j \rightarrow i}(\lambda) = c \lambda^{-2} \tau_{j \rightarrow i}(\omega)$ and the corresponding integral definition for total conductance is
\begin{equation} \label{eq:TotalConductance_wavelength}
\begin{split}
G_{t,j \rightarrow i}(T) &= \int_{0}^{\infty} G_{j \rightarrow i}(\lambda, T) d\lambda
\\
&= \int_{0}^{\infty} k_{b} \left( \frac{\mathcal{X}}{\sinh{\mathcal{X}}} \right)^{2} \tau_{j \rightarrow i}(\lambda) d\lambda
\end{split}
\end{equation}

As explained by Narayanaswamy and Zheng \cite{Narayanaswamy2013a}, computing the transmissivity function is actually an exercise in determining DGFs. The DGFs for just two coated spheres are discussed in depth by Czapla and Narayanaswamy \cite{Czapla2017}. In this work, we have expanded on that methodology to determine DGFs for any number of non-intersecting spheres. The new DGFs reduce to those of Czapla and Narayanaswamy \cite{Czapla2017} in the case of two spheres, but also allow access to longer chains to probe the effect of additional spheres on NFRHT. The appropriate electric DGF is given by
\begin{equation}\label{eq:ElectricDGF}
\begin{split}
& \overline{\overline{\boldsymbol{G}}}_{e}(\boldsymbol{r}; \boldsymbol{\widetilde{r}})
= ik_{f} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty} (-1)^{m}
\\*
& \times \left\{ \! \! \begin{array}{l}
\boldsymbol{M}_{l m}^{(3)}(k_{f} \boldsymbol{r_{i}})
\left[ \! \! \begin{array}{l} \boldsymbol{M}_{l, -m}^{(1)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \\ + R_{l}^{(M)}(\rho_{j}) \boldsymbol{M}_{l, -m}^{(3)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \end{array} \! \! \right]
\\
+ \boldsymbol{N}_{l m}^{(3)}(k_{f} \boldsymbol{r_{i}})
\left[ \! \! \begin{array}{l} \boldsymbol{N}_{l, -m}^{(1)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \\ + R_{l}^{(N)}(\rho_{j}) \boldsymbol{N}_{l, -m}^{(3)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \end{array} \! \! \right]
\end{array} \! \! \right\}
\\
& + ik_{f} \sum\limits_{p=1}^{N_{s}} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty} \sum_{\nu = \widetilde{m}}^{\infty} (-1)^{m}
\\*
& \times \left\{ \! \! \begin{array}{l} \left[ \! \! \begin{array}{l}
R_{\nu}^{(M)}(\rho_{p}) V_{l, \nu,m}^{M,M,p,j} \boldsymbol{M}_{\nu m}^{(3)}(k_{f} \boldsymbol{r_{p}})
\\[8 pt]
+ R_{\nu}^{(N)}(\rho_{p}) V_{l, \nu,m}^{N,M,p,j} \boldsymbol{N}_{\nu m}^{(3)}(k_{f} \boldsymbol{r_{p}})
\end{array} \! \! \right] \\
\otimes \left[ \! \! \begin{array}{l} \boldsymbol{M}_{l, -m}^{(1)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \\ + R_{l}^{(M)}(\rho_{j}) \boldsymbol{M}_{l, -m}^{(3)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \end{array} \! \! \right]
\\[20 pt]
+ \left[ \! \! \begin{array}{l}
R_{\nu}^{(M)}(\rho_{p}) V_{l, \nu,m}^{M,N,p,j} \boldsymbol{M}_{\nu m}^{(3)}(k_{f} \boldsymbol{r_{p}})
\\[8 pt]
+ R_{\nu}^{(N)}(\rho_{p}) V_{l, \nu,m}^{N,N,p,j} \boldsymbol{N}_{\nu m}^{(3)}(k_{f} \boldsymbol{r_{p}})
\end{array} \! \! \right] \\
\otimes \left[ \! \! \begin{array}{l} \boldsymbol{N}_{l, -m}^{(1)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \\ + R_{l}^{(N)}(\rho_{j}) \boldsymbol{N}_{l, -m}^{(3)}(k_{f} \boldsymbol{\widetilde{r}_{j}}) \end{array} \! \! \right]
\end{array} \! \! \right\}
\end{split}
\end{equation}
where $k=(\omega/c) \sqrt{\varepsilon \mu}$; $\varepsilon$ and $\mu$ are the relative permittivity and permeability, respectively; $\times$ denotes a line break (not a cross product); $\otimes$ denotes a dyadic product \cite{Lai2009}; $m$, $l$, $\nu$, and $p$ are summation indices; and $\widetilde{m}=\max{\left\{|m|,1\right\}}$.

$\boldsymbol{M}_{l m}^{(n)}(k \boldsymbol{r})$ and $\boldsymbol{N}_{l m}^{(n)}(k \boldsymbol{r})$ are vector spherical waves (VSWs) of order $(l,m)$ and argument $k \boldsymbol{r}$. VSWs represent incoming (outgoing) waves for $n=1$ ($n=3$). $R_{l}^{(M)}(\rho_{i})$ and $R_{l}^{(N)}(\rho_{i})$ are the effective Mie reflection coefficients at the interface between region $f$ and sphere $i$ for $\boldsymbol{M}_{l m}^{(1)}(k_{f} \boldsymbol{r_{i}})$ and $\boldsymbol{N}_{l m}^{(1)}(k_{f} \boldsymbol{r_{i}})$ waves, respectively. See Czapla and Narayanaswamy \cite{Czapla2017} for the definitions of VSWs and Mie reflection coefficients, which are exactly identical to those used in this work.

$V_{l, \nu, m}^{X,Y,i,j}$ are scattered field coefficients. $X$ and $Y$ may take values of $M$ or $N$, and are determined by the left and right VSWs in a dyadic product, respectively. $i$ and $j$ may take any value from 1 to $N_{s}$, and are determined by the coordinate systems used to express the position vectors arguments of the  left and right VSWs in a dyadic product, respectively. For example, $V_{l, \nu, m}^{X,Y,i,j} \boldsymbol{X}_{\nu m}^{(3)}(k_{f} \boldsymbol{r_{i}}) \boldsymbol{Y}_{l, -m}^{(1)}(k_{f} \boldsymbol{\widetilde{r}_{j}})$ is a valid combination of coefficient and dyadic product.

For given values of $m$ and $j$, $V_{l, \nu, m}^{X,Y,i,j}$ may be obtained by solving the coupled set of linear equations generated from all possible combinations of $X=M$ or $N$, $Y = M$ or $N$, and $i = 1,2,...,$ or $N_{s}$ using
\begin{equation}\label{eq:ScatteredFieldEquations}
\begin{split}
&  \sum_{p=1}^{N_{s}} \sum_{n = \widetilde{m}}^{\infty}
\left[ \begin{array}{r}
V_{l,n,m}^{M,Y,p,j} R_{n}^{(M)}(\rho_{p}) C_{n,\nu,m}^{X,M,i,p}
\\
+ V_{l,n,m}^{N,Y,p,j} R_{n}^{(N)}(\rho_{p}) C_{n,\nu,m}^{X,N,i,p}
\end{array} \right]
\\
& \enskip = V_{l, \nu, m}^{X,Y,i,j} - C_{l, \nu, m}^{X,Y,i,j}
\end{split}
\end{equation}
where
\begin{equation}\label{eq:TranslationCoefficients}
C_{l, \nu, m}^{X,Y,i,j} \! = \! \left\{ \! \!
\begin{array}{cll}
0 & \! \! \text{if} & \! \! i \! = \! j
\\
A_{\nu,m}^{l,m}\left( k_{f} d_{j,i} \right) & \! \! \text{if} & \! \! i \! \neq \! j \text{ and } X \! = \! Y
\\
\! B_{\nu,m}^{l,m}\left( k_{f} d_{j,i} \right) & \! \! \text{if} & \! \! i \! \neq \! j \text{ and } X \! \neq \! Y
\end{array}
\! \! \right.
\end{equation}
and $A_{\nu,m}^{l,m}$ and $B_{\nu,m}^{l,m}$ are vector addition translation coefficients \cite{Chew1992, Chew1995, Kim2004a, Dufva2008}. The linear system of equations for scattered field coefficients is obtained by evaluating boundary conditions between the surfaces of the spheres and region $f$. It contains information on the optical properties and internal configurations of the spheres (encoded by the Mie reflection coefficients) and the geometric configuration of the ensemble of spheres (encoded by the vector additional translation coefficients). Further detail on how to solve this linear system is provided in \ref{ap:SolutionToLinearSystem}.

At this point, it is important to point out that the electric DGF given in Eq. \ref{eq:ElectricDGF} is valid for any cluster of spheres, not just a linear chain. Equations \ref{eq:ScatteredFieldEquations} and \ref{eq:TranslationCoefficients}, however, require modification before they may be applied to arbitrary clusters. See Mackowski and Mishchenko \cite{Mackowski1996} for further details on light scattering in clusters of spheres.

The magnetic DGF may be obtained from Eq. \ref{eq:ElectricDGF} by substituting $M \leftrightarrow N$ in every superscript of the reflection and VSW coefficients. Additionally, we define $\overline{\overline{\boldsymbol{G}}}_{E} = \nabla \times \overline{\overline{\boldsymbol{G}}}_{e}$ and $\overline{\overline{\boldsymbol{G}}}_{M} = \nabla \times \overline{\overline{\boldsymbol{G}}}_{m}$, where the curl operates on the first term only in each dyadic product summand of the DGFs. $\overline{\overline{\boldsymbol{G}}}_{e}$, $\overline{\overline{\boldsymbol{G}}}_{m}$, $\overline{\overline{\boldsymbol{G}}}_{E}$, and $\overline{\overline{\boldsymbol{G}}}_{M}$ are the four DGFs required to evaluate the transmissivity function.

As stated earlier, the position vector arguments of the DGFs are each located on one of the two surfaces over which the surface integrals in the transmissivity function are computed. For ease of computation, it is important to express those position vectors in the coordinate system most convenient to that goal. The choice of coordinate system therefore varies, depending on the objects between which the transmissivity function is being computed.

To obtain heat transferred from sphere $j$ to sphere $i$, $\widetilde{\boldsymbol{r}}$ must be written in the $j$-coordinate system and be located just outside the surface of sphere $j$. Similarly, $\boldsymbol{r}$ must be written in the $i$-coordinate system and be located just outside the surface of sphere $i$. Hence, we choose to represent the DGFs as $\overline{\overline{\boldsymbol{G}}}(\boldsymbol{r}_{i}; \widetilde{\boldsymbol{r}}_{j})$. The DGFs may then be simplified by using Eq. \ref{eq:ScatteredFieldEquations} to remove explicit appearances of the vector addition translation coefficients.

To obtain heat transferred from a sphere $j$ to its environment, $\widetilde{\boldsymbol{r}}$ must remain on the surface of sphere $j$ and $\boldsymbol{r}$ must lie on a large fictitious surface, whose size expands to infinity. For ease of computation, we choose the fictitious surface to be spherical. For any value of $i$, VSWs with arguments of $k_{f} \boldsymbol{r}_{i}$ asymptotically become equal as $| \boldsymbol{r} |/d_{1,N_{s}} \rightarrow \infty$. For this reason, $\boldsymbol{r}$ may be written in the coordinate system of any sphere. For ease, we will also write $\boldsymbol{r}$ in the $j$-coordinate system. Hence, we choose to represent the DGFs as $\overline{\overline{\boldsymbol{G}}}(\boldsymbol{r}_{j}; \widetilde{\boldsymbol{r}}_{j})$.

Using the simplified DGFs and assuming region $f$ is non-dissipative, the transmissivity function from sphere $j$ to sphere $i$ is given by
\begin{equation} \label{eq:Transmissivity_SphereSphere}
\begin{split}
& \tau_{j \rightarrow i}\left( \omega \right)
= \left( k_{f} \rho_{i} \right)^{2} \left( k_{f} \rho_{j} \right)^{2} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty}\sum_{\nu = \widetilde{m}}^{\infty}
\\*
& \times \left[ \! \! \begin{array}{r}
\left[ \! \! \begin{array}{r}
\epsilon_{\nu}^{(M)}(\rho_{i})
\left| V_{l,\nu,m}^{M,M,i,j} \right|^{2}
\\
+ \epsilon_{\nu}^{(N)}(\rho_{i})
\left| V_{l,\nu,m}^{N,M,i,j} \right|^{2}
\end{array} \! \! \right]
\epsilon_{l}^{(M)}(\rho_{j})
\\
+ \left[ \! \! \begin{array}{r}
\epsilon_{\nu}^{(M)}(\rho_{i})
\left| V_{l,\nu,m}^{M,N,i,j} \right|^{2}
\\
+ \epsilon_{\nu}^{(N)}(\rho_{i})
\left| V_{l,\nu,m}^{N,N,i,j} \right|^{2}
\end{array} \! \! \right]
\epsilon_{l}^{(N)}(\rho_{j})
\end{array} \! \! \right]
\end{split}
\end{equation}
where
\begin{equation}
\epsilon_{\nu}^{(P)}(\rho_{i}) = \frac{2}{\left( k_{f} \rho_{i} \right)^{2}} \left[ \Re \left( R_{\nu}^{(P)}(\rho_{i}) \right) + \left| R_{\nu}^{(P)}(\rho_{i}) \right|^{2} \right]
\end{equation}
and $P=M$ or $N$. $\Re(z)$ and $\left| z \right|$ denote the real part and magnitude of complex number $z$, respectively. This result was reported previously by Czapla and Narayanaswamy \cite{Czapla2017} for the two sphere case but here we show that the same formula, with modified scattered field coefficients, holds true for any number of spheres in a chain.

$\epsilon_{\nu}^{(P)}(\rho_{i})$ is defined such that the spectral emissivity of an isolated sphere \cite{Kattawar1970} is given by
\begin{equation}\label{eq:SpectralEmissivity}
\epsilon\left( \omega \right)
= \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty}
\left[ \epsilon_{l}^{(M)}(\rho_{i}) + \epsilon_{l}^{(N)}(\rho_{i}) \right]
\end{equation}
The spectral emissivity of an isolated sphere determined by Kattawar and Eisner \cite{Kattawar1970} can alternatively be derived using the DGF formalism from this work. To do so, we first compute the transmissivity function from a single sphere to a large ficticious spherical surface surrounding it. For $N_{s}=1$, Eq. \ref{eq:ScatteredFieldEquations} tells us $V_{l, n, m}^{X,Y,1,1}=0$ for all values of $l$, $n$, $m$, $X$, and $Y$. The transmissivity function for an isolated sphere $j$ to its environment, $\tau_{j \rightarrow E}^{iso}$, is given by
\begin{equation}\label{eq:Transmissivity_IsoSphereEnv}
\begin{split}
& \tau_{j \rightarrow E}^{iso} (\omega) = 2 \left( k_{f} \rho_{j} \right)^{2} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty}
\\
& \times \left[ \epsilon_{l}^{(M)}(\rho_{j}) + \epsilon_{l}^{(N)}(\rho_{j}) \right]
\end{split}
\end{equation}

Next, we determine the transmissivity function for a blackbody sphere, $\tau_{j \rightarrow E, BB}^{iso}$, given by \cite{Narayanaswamy2013a}
\begin{equation}\label{eq:Transmissivity_BBSphereEnv}
\begin{split}
\tau_{j \rightarrow E, BB}^{iso} (\omega) = \frac{k_{f}^{2}}{2 \pi} A_{j} F_{j \rightarrow E}
= 2 \left( k_{f} \rho_{j} \right)^{2}
\end{split}
\end{equation}
where $A_{j} = 4 \pi \rho_{j}^{2}$ is the surface area of sphere $j$ and $F_{j \rightarrow E}$ is the view factor from sphere $j$ to its environment ($F_{j \rightarrow E}=1$ for an isolated sphere in a large enclosure). Dividing the true amount of heat emitted (Eq. \ref{eq:Transmissivity_IsoSphereEnv}) by the amount emitted by a blackbody (Eq. \ref{eq:Transmissivity_BBSphereEnv}) yields the emissivity (Eq. \ref{eq:SpectralEmissivity}).

In the presence of additional spheres, the conductance from sphere $j$ to its environment is given by
\begin{equation}\label{eq:Transmissivity_SphereEnv}
\begin{split}
& \tau_{j \rightarrow E}(\omega) = \tau_{j \rightarrow E}^{iso} (\omega)
\\
& +
4 \left( k_{f} \rho_{j} \right)^{2} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty}
\\
& \times \left\{ \begin{array}{r}
\Re \left[ S_{l,l,m}^{M,M,p,j} \right] \epsilon_{l}^{(M)}(\rho_{j})
\\
+ \Re \left[ S_{l,l,m}^{N,N,p,j} \right] \epsilon_{l}^{(N)}(\rho_{j})
\end{array} \right\}
\\
& +
2 \left( k_{f} \rho_{j} \right)^{2} \sum\limits_{m=-\infty}^{\infty} \sum\limits_{l=\widetilde{m}}^{\infty} \sum_{\nu = \widetilde{m}}^{\infty}
\\
& \times \left\{ \begin{array}{r}
\left[ \begin{array}{r}
\left| S_{l,\nu,m}^{M,M,p,j} \right|^{2}
\\
+ \left| S_{l,\nu,m}^{N,M,p,j} \right|^{2}
\end{array} \right] \epsilon_{l}^{(M)}(\rho_{j})
\\
+ \left[ \begin{array}{r}
\left| S_{l,\nu,m}^{M,N,p,j} \right|^{2}
\\
+ \left| S_{l,\nu,m}^{N,N,p,j} \right|^{2}
\end{array} \right] \epsilon_{l}^{(N)}(\rho_{j})
\end{array} \right\}
\end{split}
\end{equation}
where $S_{l,\nu,m}^{X,Y,i,j} = \sum_{i=1}^{N_{s}} R_{\nu}^{(X)}(\rho_{i}) V_{l,\nu,m}^{X,Y,i,j}$.

Equations \ref{eq:Transmissivity_SphereSphere} and \ref{eq:Transmissivity_SphereEnv} are the main results of this work. It is important to note that these equations are valid, in principle, for spheres of any outer radii, number of coatings, separation gaps, and isotropic optical properties. This stands in contrast to the many prior works where explicit results for sphere-sphere NFRHT are only given for special cases such as small radii \cite{Joulain2005, Ben-Abdallah2011, Dong2017a, Nikbakht2018}, large separation gaps \cite{Kruger2012}, or small skin depths \cite{Volokitin2001, Sasihithlu2011}. Furthermore, Eq. \ref{eq:Transmissivity_SphereEnv} now allows us to probe sphere-environment NFRHT, using the same scattered field coefficients that are necessary to compute for sphere-sphere interactions. Essentially, a second useful quantity can now be determined for free, as a post-processing step.

\section{Cross-Validation of Theoretical Results} \label{sec:CrossValidationofTheoreticalResults}
In this section, we will compare the results of our work against existing methods in the literature. Equations \ref{eq:Transmissivity_SphereSphere} and \ref{eq:Transmissivity_SphereEnv} were implemented in the Wolfram language of Mathematica \cite{Wolfram2016} and validated against T-DDA and BEM. All code and data displayed from here on are available in the supplemental files to this work.

The Mathematica code is written to take the number, outer radii, optical properties, and configuration of the spheres as inputs. Although the code, as attached, assumes identical homogeneous spheres, it may easily be modified to compute NFRHT between layered spheres whose properties are all unique. The lines of code which would require modification are labeled. Furthermore, the algorithm used to compute vector addition translation coefficients is optimized for spheres of approximately equal radii. Though the algorithm works, in principle, for spheres of any size, the time required grows rapidly for spheres with large size disparity. We direct researchers interested in that situation to Sasihithlu and Narayanaswamy \cite{Sasihithlu2014} for asymptotic approximations which improve computation time.

\subsection{Validation Against Thermal Discrete Dipole Approximation}
Edalatpour et al. \cite{Edalatpour2016a} used T-DDA to simulate the NFRHT between three spheres in a chain.  In the notation of this work, Edalatpour et al. simulated three identical spheres with $\rho=0.8$ \si{\micro\meter} and $D = 100$ \si{\nano\meter}. They set $T_{1} = 300$ K and $T_{2}=T_{3} = 0$ K and simulated values of $Q_{j \rightarrow i}$ for $\lambda = 10$ \si{\micro\meter} and two different values of the relative permittivity: $\varepsilon_{res} = -1.36+1.36i$ and $\varepsilon_{non-res} = 9+0.06i$. $\varepsilon_{res}$ and $\varepsilon_{non-res}$ are values of the dielectric function near and away from resonance, respectively.

T-DDA requires volume discretization of the spheres. Edalatpour et al. discretized the outer spheres (1 and 3) into 27,564 non-uniform subvolumes and the middle sphere into 45,800 non-uniform subvolumes. The smallest subvolumes were concentrated at locations nearest to other spheres, to achieve high resolution in the volumes which absorb most heavily. Although it is not mentioned in Edalatpour et al. \cite{Edalatpour2016a}, the authors have stated in other works that T-DDA computation time can be lengthy \cite{Edalatpour2016}. Time, of course, is the price paid for the ability to simulate any geometry.

A comparison of the results of the T-DDA method and this work (labeled DGF) appears in Tables \ref{tab:ThreeSphereResonant} and \ref{tab:ThreeSphereNonResonant}. This work shows excellent agreement with the results of T-DDA. The maximum percent error of the T-DDA results is 2.82\% compared to our DGF results. Edalatpour et al. did not, however, report results for heat transfer to the environment.

\begin{table}
	\caption{\label{tab:ThreeSphereResonant}Comparison of results from current work (DGF) and the thermal discrete dipole approximation (T-DDA) for a three sphere chain using a resonant value of dielectric function. Values from T-DDA are taken from Edalatpour et al. \cite{Edalatpour2016a}.}
	\begin{center}
		\renewcommand{\arraystretch}{1.15}
		\setlength{\tabcolsep}{0.10cm}
		\begin{tabular}{ccccccccc}
			\hline
			\multicolumn{1}{c}{} &
			\multicolumn{1}{c}{T-DDA (\si{\nano\watt\per\electronvolt})} &
			\multicolumn{1}{c}{DGF  (\si{\nano\watt\per\electronvolt})} \\
			\hline
			%
			$Q_{1 \rightarrow 2}$ & 197.2 & 193.8 \\
			$Q_{1 \rightarrow 3}$ & 2.41 & 2.48 \\
			\hline
		\end{tabular}
	\end{center}
\end{table}

\begin{table}
	\caption{\label{tab:ThreeSphereNonResonant}Comparison of results from current work (DGF) and the thermal discrete dipole approximation (T-DDA) for a three sphere chain using a non-resonant value of dielectric function. Values from T-DDA are taken from Edalatpour et al. \cite{Edalatpour2016a}.}
	\begin{center}
		\renewcommand{\arraystretch}{1.15}
		\setlength{\tabcolsep}{0.10cm}
		\begin{tabular}{ccccccccc}
			\hline
			\multicolumn{1}{c}{} &
			\multicolumn{1}{c}{T-DDA  (\si{\pico\watt\per\electronvolt})} &
			\multicolumn{1}{c}{DGF  (\si{\pico\watt\per\electronvolt})} \\
			\hline
			%
			$Q_{1 \rightarrow 2}$ & 0.425 &  0.430 \\
			$Q_{1 \rightarrow 3}$ & 0.0285 & 0.0287 \\
			\hline
		\end{tabular}
	\end{center}
\end{table}

\subsection{Validation Against Boundary Element Method}
To compare results for larger spheres and conductance to the environment, numerical computations were performed using {\sc scuff-em}, a free, open-source software implementation of the boundary-element method \cite{scuffem, Reid2015} which models fluctuating-surface-currents as the source of thermal radiation. Three identical spheres of $\rho=10$ \si{\micro\meter} and $D = 1$ \si{\micro\meter} were simulated. These sizes were chosen specifically to be comparable to the thermal wavelength. The optical properties of the spheres chosen to be those of amorphous silicon dioxide, which were given by the built-in Lorentz oscillator model of dielectric function found in {\sc scuff-em}:
\begin{equation}\label{eq:LorentzOscillatorModel}
\varepsilon(\omega) = \varepsilon_{\infty} + \sum_{k} \left[ \frac{S_{k}}{1-\left( \frac{\omega}{\omega_{0,k}} \right)^{2} - i \Gamma_{k} \left( \frac{\omega}{\omega_{0,k}} \right)} \right]
\end{equation}
where all the parameters of the model are given in Table \ref{tab:DielectricFunction}.

The {\sc scuff-em} software can compute both sphere-sphere and sphere-environment heat transfer. Figure \ref{fig:ThreeSpheres_SCUFFEM}A shows the transmissivity between each pair of spheres and between each sphere and the environment. Due to the symmetry of the three spheres, redundant curves are suppressed. Solid lines are computed using the DGF formulas outlined in this work and markers are from {\sc scuff-em} calculations. For most wavelengths, there is fairly good agreement between the two methods, with approximately 10\% error (see Fig. \ref{fig:ThreeSpheres_SCUFFEM}B). Sphere-sphere errors tend to be lower compared to sphere-environment errors. Additionally, larger errors are apparent for the shortest wavelengths. This may be due to an insufficiently dense mesh. Each sphere's outer surface was meshed into 442 roughly equal triangular areas. Shorter wavelengths should be more sensitive to the deviations from a spherical shape that a mesh introduces and the deviant behavior should be explored further in future work. Fortunately, the $k_{b} (\mathcal{X}/\sinh{\mathcal{X}})^{2}$ term in Eq. \ref{eq:SpectralConductance} is small for short wavelengths, tempering error in total conductance.

\begin{table}
	\caption{\label{tab:DielectricFunction}Lorentz oscillator model parameters for the dielectric function of amorphous silicon dioxide, as given by {\sc scuff-em}. Unlisted is $\varepsilon_{\infty}=2.03843$.}
	\begin{center}
		\renewcommand{\arraystretch}{1.15}
		\setlength{\tabcolsep}{0.10cm}
		\begin{tabular}{ccccccccc}
			\hline
			\multicolumn{1}{c}{k} &
			\multicolumn{1}{c}{$\hbar \omega_{0,k}$ (eV)} &
			\multicolumn{1}{c}{$\lambda_{0,k}$ (\si{\micro\meter})} &
			\multicolumn{1}{c}{$S_{k}$} &
			\multicolumn{1}{c}{$\Gamma_{k}$} \\
			\hline
			%
			1 & 0.05624 & 22.04432 & 0.93752 & 0.09906\\
			2 & 0.09952 & 12.45818& 0.05050 & 0.05511 \\
			3 & 0.13355 & 9.28364 & 0.60642 & 0.05246 \\
			\hline
		\end{tabular}
	\end{center}
\end{table}

\begin{figure}
\includegraphics[width=3 in]{./Figure2.pdf}
\caption{\label{fig:ThreeSpheres_SCUFFEM}Cross-validation of DGF and BEM methods. (A) Transmissivity function for energy transfer from source to destination ($j \rightarrow i$) between three identical silicon dioxide spheres with $\rho=10$ \si{\micro\meter} and $D = 1$ \si{\micro\meter}. Values were computed by the DGF (present work) and BEM methods. (B) Magnitude of percent error between two methods in (A).}
\end{figure}

\section{Implications for Near-Field Radiative Heat Transfer Experiments} \label{sec:Implications}
Until the recent advances in NFRHT between MEMS devices \cite{Song2016, Cui2017, Fiorino2018}, experiments measuring NFRHT in sub-micron gaps were performed in the microsphere-plane configuration, much like the configurations used in Casimir and van der Waals force experiments \cite{Lamoreaux1997, Mohideen1998, Roy1999, Harris2000}. Recent experimental work investigating the Casimir force \cite{Garrett2018} demonstrates that sphere-sphere geometry is also a feasible configuration to investigate NFRHT. To better understand how such a sphere-sphere NFRHT experiment would work, we must first understand how sphere-plane experiments have been performed.

In past sphere-plane NFRHT experiments \cite{Rousseau2009,Shen2009}, experimenters attached the sphere to a bimaterial microcantilever. Bimaterial cantilevers, such as atomic force microscopy cantilevers, are extremely sensitive calorimeters which deflect with any change in temperature. The planar substrate was fixed at a temperature, either passively to the ambient or heated to a temperature above ambient. If the substrate was fixed at ambient temperature, then the sphere was heated using a laser to create a temperature difference between the two objects. Otherwise, the heated substrate supplied the temperature difference.

The sphere was initally located at some distance above the substrate, typically between 2.5 \si{\micro\meter} and 10 \si{\micro\meter}. The separation between the sphere and the substrate was then decreased until contact was made. Due to surface imperfections and the resolution of the system controlling the separation distance, the minimum distance achievable was approximately 30 \si{\nano\meter}.

As the substrate approaches the sphere, the temperature of the sphere changes which results in deflection of the cantilever; angular deflection is the measurable experimental parameter. Because the initial orientation of a cantilever is large determined by events preceding the experiment (such as fabrication), only the change in the orientation of the cantilever is meaningful and the experiment is sensitive only to changes in total conductance from its value at the initial separation distance to its value at its current separation distance. The angular deflection is a result of all the pathways heat has to flow into and out of the sphere, and it must be related to the change in conductance between the two objects by using a thermal model.

The thermal model used to infer sphere-plane conductance must account for all means of heat transfer occurring. Critically, it must reflect the fact that the sphere-plane system is really a sphere-plane-environment system with exchanges of thermal energy between both objects and their environment. Prior works employing sphere-plane geometries have used a variety of approaches to account for heat transfer to the environment. For example, some works have used Mie theory to compute sphere-environment conductances \cite{Narayanaswamy2008a}, assumed a constant but unnamed value \cite{Shen2009}, ignored environmental heat transfer effects all together \cite{Rousseau2009, Guha2012}, or not reported their treatment of far-field radiation at all \cite{Kim2015}. Any improper treatment of the sphere-environment conductance will introduce a systematic error.

\begin{figure}
\centering
\includegraphics[width=3 in]{./Figure3.pdf}
\caption{\label{fig:DistanceDependence} Total conductance in a system of two identical silicon dioxide spheres with outer radii of 10 \si{\micro\meter}. The legend in (A) is common to both subfigures. (A) Sphere-sphere conductances determined by DGF method. (B) Sphere-environment conductances (normalized by the maximum value of each curve) predicted by the DGF method. See Table \ref{tab:ErrorInSphereSphere} for values of $\mathrm{max}\{G_{t,1 \rightarrow E}\}$.}
\end{figure}

To investigate the magnitude of that error in a potential sphere-sphere experiment, we simulate the NFRHT for two identical silicon dioxide spheres with outer radii of 1, 2.5, 5, and 10 \si{\micro\meter}. Figure \ref{fig:DistanceDependence}A shows sphere-sphere conductances and Fig. \ref{fig:DistanceDependence}B shows normalized sphere-environment conductances. The legend in Fig. \ref{fig:DistanceDependence}A is common to the entire figure. As expected, the sphere-sphere conductances determined by the DGF method show a super-Planckian monotonic decrease in the near-field.

More interestingly, it is readily apparent from Fig. \ref{fig:DistanceDependence}B that the character of the sphere-environment conductances has a strong size dependence. The smallest spheres show strong signs of diffraction for large separation distances, reminiscent of recent work involving point particles (see Fig. 8 by Asheichyk et al. \cite{Asheichyk2017}). The smallest sphere ($\rho$ = 1 \si{\micro\meter}) actually shows a decrease in sphere-environment conductance with decreasing distance. The next smallest sphere ($\rho$ = 2.5 \si{\micro\meter}) shows an eventual increase over its far-field value, though it has a global maximum at an intermediate gap. The largest spheres ($\rho$ = 5 \si{\micro\meter} and 10 \si{\micro\meter}) show near-monotonic decreases and a maximum value at the smallest gap simulated. This demonstrates that the intense electric and magnetic fields between objects which contribute to NFRHT can dampen or enhance far-field emission, with a seeming size dependence. The one common trend is that all sphere-environment conductances eventually level off for sufficiently small $D/\rho$.

The fact that the curves level off is key to taking a valid measurement of sphere-sphere conductance using a cantilever. The angular deflection of a cantilever, $\Delta\theta$, is proportional to the change in total conductances into the sphere attached to the cantilever. Mathematically, that is
\begin{equation} \label{eq:ExperimentalBalance}
\begin{split}
\Delta\theta &\propto G_{t,1\rightarrow 2}(D) - G_{t,1\rightarrow 2}(D_{0}) \\ & \quad + G_{t,1\rightarrow E}(D) - G_{t,1\rightarrow E}(D_{0})
\end{split}
\end{equation}
where $D_{0}$ is the separation distance at which the experiment begins.

Sphere-sphere conductance increases significantly and rapidly in the extreme near-field, such that $G_{t,1\rightarrow 2}(D) \gg G_{t,1\rightarrow 2}(D_{0})$ for most values of $D$ and $D_{0}$. By starting an experiment at a sufficiently small initial separation gap, where the curves in Fig. \ref{fig:DistanceDependence}B have leveled off, $G_{t,1\rightarrow E}(D) - G_{t,1\rightarrow E}(D_{0}) \approx 0$ and an isolation of the sphere-sphere conductance can be achieved.

The largest values of $D_{0}$ for which we can neglect the distance dependence of $G_{t, 1 \rightarrow E}$ and introduce a relative error of no more than approximately 5\% are given in Table \ref{tab:ErrorInSphereSphere}. Although we do not propose a universal criterion at this time, the current results suggests that smaller spheres allow for a larger range of separation distances to be probed. This is contrary to the larger spheres used in past sphere-plane experiments \cite{Rousseau2009,Shen2009}. It can be seen from Table \ref{tab:ErrorInSphereSphere} that, by reducing the radius by one order of magnitude (from 10 \si{\micro\meter} to 1 \si{\micro\meter}), $\mathrm{max}\{ G_{t,1 \rightarrow E} \}$ can be reduced by 2 orders of magnitude. This allows $G_{t, 1 \rightarrow 2}$ to dominate Eq. \ref{eq:ExperimentalBalance} for appropriately chosen sphere sizes. Furthermore, since metallic spheres with coatings of polar materials have been shown to achieve conductances comparable to purely polar spheres in the extreme near-field but lower metal-like conductances at larger gaps (see Fig. 3 by Czapla and Narayanaswamy \cite{Czapla2017}), layered spheres may prove better at suppressing $G_{t,1\rightarrow 2}(D_{0})$ in Eq. \ref{eq:ExperimentalBalance}. All together, these evidence indicate sphere-sphere geometries have great potential as an experimental platform for measuring NFRHT.

\begin{table}
	\caption{\label{tab:ErrorInSphereSphere}Initial values of $D$ which will ensure a relative error of approximately 5\% or less in a hypothetical sphere-sphere experiment which neglects to quantify the distance dependence of sphere-environment conductance. Also listed are the maximum values of sphere-environment conductance which are used to normalize Fig. \ref{fig:DistanceDependence}B.}
	\begin{center}
		\renewcommand{\arraystretch}{1.15}
		\setlength{\tabcolsep}{0.10cm}
		\begin{tabular}{ccccccccc}
			\hline
			\multicolumn{1}{c}{$\rho$ (\si{\micro\meter})} &
			\multicolumn{1}{c}{$D_{0}$ (\si{\micro\meter})} &
			\multicolumn{1}{c}{$\mathrm{max}{\{G_{t,1 \rightarrow E}}\}$ (\si{\nano\watt\per\kelvin})} \\
			\hline
			%
			1 & 1.00 & 0.02978 \\
			2.5 & 1.00 & 0.3175 \\
			5 & 0.50 & 1.723 \\
			10 & 0.60 & 7.196 \\
			\hline
		\end{tabular}
	\end{center}
\end{table}

\section{Conclusions}
We theoretically and numerically investigated the NFRHT between pairs of spheres in a linear chain and between individual spheres and their environment using a DGF formalism. The formulas we derived are numerically exact for spheres of any size, spacing, optical properties, and number of spherically symmetric layers. We cross-validated our work against meshed approaches to NFRHT, namely T-DDA and BEM, and demonstrated excellent agreement.

Our work shows a strong distance dependence for the energy radiated by a sphere to its environment in the near-field regime, which levels off in the extreme near-field. Our numerical results should serve as a warning to scientists when analyzing their experimental results and will hopefully spur investigation into more sophisticated thermal models for common NFRHT experimental configurations. Additionally, once implemented, these thermal models can potentially serve as a characterization tool for other factors that impact NFRHT, such as separation distance, variation in optical properties, surface roughness, or surface contamination.

\section*{Acknowledgment}
This work was supported partially by NSF IGERT (DGE-1069240).

redpajama_set_name: RedPajamaArXiv


text:
Animation: Memory loss...
"I just need a bit more understanding"
Watch the story
Our Memory loss after brain injury animation was produced in response to the findings of a survey conducted by Headway – the brain injury association which found that 72% of brain injury survivors feel that the people in their life don't understand their memory problems.
Launched at the start of the charity's Action for Brain Injury (ABI) Week 2020 campaign, which focuses on memory loss after brain injury, the animation aims to raise awareness and understanding of the challenges faced by those affected.
It tells the story of Tony, a father who sustained a brain injury in a car accident. After waking from a coma, he didn't recognise his family and closest friends.
The animation, which was created by The Like Minded, goes on to explore themes of relationship breakdown and the frustration of not remembering everyday events, while taking the viewer along a journey as Tony and his family try to get to grips with a new way of life.
Importantly, the animation gives brain injury survivors and their loved ones guidance on seeking support - whether that be through ringing Headway's nurse-led, freephone helpline or accessing information on coping strategies within its factsheets and booklets.
"My memories had been erased": Dad supports national memory loss campaign
Dad-of-two supports national memory loss campaign.
Raising awareness of the ways in which memory problems can affect brain injury survivors and their families.
Charity animation highlights devastating impact of memory loss
An emotional campaign video has been launched by Headway to highlight the complex and devastating effects of memory loss after brain injury.


text:
Тимофе́й (; конец VI века – первая половина VII века) — пресвитер Собора Святой Софии в Константинополе, церковный писатель.

О его жизни практически ничего неизвестно. Известно лишь сочинение этого автора под названием «Τιμοθέου πρεσβυτέρου τῆς άγιωτάτης μεγάλης ἐκκλησίας Κωνσταντινουπόλεως, πρός Ιωάννην πρεσβύτερον τῆς άγιωτάτης τοῦ θεοῦ καθολικῆς ἐκκλησίας, καί σκευοφύλακα τῆς ἀγίας Θεοτόκα τῆς ἐν τοῖς Χαλκοπρατείοις περί διαφοράς τῶν προσερχόμενων τῆ εὐαγεστάτη ημών πίστει.» («Тимофея пресвитера, пресвятые и великие Церкви Константинополя: Иоанну пресвитеру святой, божественной, кафолической церкви и скевофилаксу святой Богородицы в Халкопатрии. О различии приходящих к непорочной нашей вере»). Эта работа представляет  ересиологический трактат, в котором описываются ереси и распределяются на три категории. Первая категория это еретики, которых нужно принимать через Крещение, вторая — еретики, принимаемые через миропомазание, третья — еретики, принимаемые через проклятие ереси. Как видно из названия труд написан для иерея и скевофилакса церкви святой Богородицы в Халкопатрии. Точная дата написания трактата — неизвестна, но из содержания сочинения понятно, что оно написано после Второго Константинопольского собора 553 года. В трактате Тимофея упоминается сочинение Иоанна Филопона «О воскресении», написанное в 560 году. По этой причине время написания сочинения Тимофеем датируется как конец VI века  или как начало VII века.

На древнерусский язык с греческого сочинение Тимофея переведено достаточно давно, в домонгольский период, до середины XIII века. Это произведение включали в состав Кормчих книг. Отрывок из книги Тимофея Никон Черногорец включил в свою книгу «Пандекты». В 1650 году этот отрывок книги Тимофея из «Пандектов» был напечатан в Москве на церковнославянском, он вошёл в состав, так называемой, Иосифской Кормчей, как 70 глава.

На языке оригинала сочинение было напечатано впервые Йоханнесем Меурзием в Лейдене в 1619 году, произведение Тимофея напечатано в 86 томе Греческой Патрологии.

Ссылки
 PG 86a
 «Тимофея пресвитера, пресвятые и великие Церкви Константинополя. О различии приходящих к непорочной нашей вере» в книге Бенешевич В. Н. Древлеславянская Кормчая. том 1, Издание 1906 год. стр. 733
 Jean-Baptiste Cotelier. Ecclesiæ græcæ monumenta, Том 3. Apud Franciscum Muguet, 1686 p. 400
 «Кормчая» 1650 года. стр. 1384
 В. М. Лурье. ИДЕНТИЧНОСТЬ ЧЕЛОВЕЧЕСКОЙ ЛИЧНОСТИ ПО ИОАННУ ФИЛОПОНУ: ФИЗИЧЕСКОЕ ТЕЛО В ПРОСТРАНСТВЕ И ЧЕЛОВЕЧЕСКОЕ ТЕЛО ПО ВОСКРЕСЕНИИ
 Бенешевич В. Н. Номоканонъ Іоанна Комнина, архіепископа Ахридекаго
Церковные деятели VI века
Писатели по алфавиту

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text:
Catechism of the Catholic Church #1030-1032
uCatholic - November 2, 2013
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven. 1031 The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned. The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. the tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:
Catechism of The Catholic Church #2291
uCatholic - August 3, 2013
2291 The use of drugs inflicts very grave damage on human health and life. Their use, except on strictly therapeutic grounds, is a grave offense. Clandestine production of and trafficking in drugs are scandalous practices. They constitute direct co-operation in evil, since they encourage people to practices gravely contrary to the moral law.
uCatholic - March 15, 2014
2688 The catechesis of children, young people, and adults aims at teaching them to meditate on the Word of God in personal prayer, practicing it in liturgical prayer, and internalizing it at all times in order to bear fruit in a new life. Catechesis is also a time for the discernment and education of popular piety. The memorization of basic prayers offers an essential support to the life of prayer, but it is important to help learners savor their meaning.
Catechism of The Catholic Church #966
uCatholic - August 15, 2014
966 "Finally the Immaculate Virgin, preserved free from all stain of original sin, when the course of her earthly life was finished, was taken up body and soul into heavenly glory, and exalted by the Lord as Queen over all things, so that she might be the more fully conformed to her Son, the Lord of lords and conqueror of sin and death."The Assumption of the Blessed Virgin is a singular participation in her Son's Resurrection and an anticipation of the resurrection of other Christians: In giving birth you kept your virginity; in your Dormition you did not leave the world, O Mother of God, but were joined to the source of Life. You conceived the living God and, by your prayers, will deliver our souls from death.
uCatholic - February 4, 2013
1033 We cannot be united with God unless we freely choose to love him. But we cannot love God if we sin gravely against...
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488 "God sent forth his Son", but to prepare a body for him, he wanted the free co-operation of a creature. For this, from all eternity God chose for the mother of his Son a daughter of Israel, a young Jewish woman of Nazareth in Galilee, "a virgin betrothed to a man whose name was Joseph, of the house of David; and the virgin's name was Mary": The Father of mercies willed that the Incarnation should be preceded by assent on the part of the predestined mother, so that just as a woman had a share in the coming of death, so also should a woman contribute to the coming of life.
2270 Human life must be respected and protected absolutely from the moment of conception. From the first moment of his existence, a human being must...


Small businesses are a ready target for scammers, with the latest scam targeting innocent companies trying to do the right thing.
ASIC announced today that scammers pretending to be from ASIC have been contacting Registry customers by email, requesting that they pay fees and provide personal information to renew their business or company name (click here to view an example of a scam email). It has also been reported that these phishing emails may contain malware and links to invoices with false payment details.
provide your credit card or bank details directly by email or phone.
If you think you have received a scam email, ASIC has requested recipients to immediately forward the entire email to ReportASICEmailFraud@asic.gov.au or contact ASIC on 1300 300 630.
Similar phishing emails are often sent to trade mark registrants asking them to provide personal information and pay fees associated with trade marks or domain names. Further information is contained in our previous article on this scam (please click here to read).
The ACCC Scamwatch website contains useful information on common scams and steps you can take to protect your small business.


"Teaching geriatrics on the internet - integrating technology with medi" by Michael L. Malone, G Graham et al.
Malone ML, Graham G, Steber D, Bell DS. Teaching geriatrics on the internet - integrating technology with medical education.:P485. Journal of the American Geriatrics Society. 2004;52 Supplement(1):S183.


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Mindful Communication in Veterinary Practice
Dr. Bethanie Poe, LMSW - August 5, 2022
Helping your veterinary clients feel heard and understood improves communication and relationships, and resolves conflicts. The veterinary setting has always been a prime area for...
How natural remedies promote healthy balance in animals
Veterinarians and One Health
TCVM: A Model for Sustainable Medicine
Technicians as teachers: tapping their expertise to educate clients about nutrition
Kara M. Burns, MS, MEd, LVT, VTS (Nutrition) - February 17, 2021
By initiating discussions about nutrition each time pet parents visit the practice, veterinary technicians can directly impact the lifelong health of their patients. Nutrition...
Integrative training for technicians
Preventing injuries in canine athletes
Pet insurance for holistic and integrative practices
IVC Journal - July 27, 2022
A recent study released by Veterinarians.org has revealed the highest- and lowest-paying American states for veterinarians. The states were ranked using 2020 U.S. Bureau...
While the majority of horses have been exposed to the Equine Herpes Virus, it doesn't cause serous problems for most. Nevertheless, learning more about...
Sungwon Lim, PhD - April 4, 2022
AI is a valuable tool that can help veterinarians do their jobs with greater speed and precision, freeing them up to focus on complex...


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