The Acca Kappa Lifter Comb is ideal for creating voluminous styles for your clients. The dual functionality of this styling comb allows you to tame hair and add lift for amplified style height.
Lightweight and durable, the Lifter Comb is made from polycarbonate fibres that prevent static on the hair. This helps to maintain a perfectly sleek and smooth style.
The Acca Kappa Lifter Comb is infused with silver ions; a powerful antibacterial which prevents cross contamination during styling.


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Stunning Ford And Shelby Models Head To Auction
by Karl Furlong Auction / Comments
The January 2020 auction will feature over ten jaw-dropping classics.
Ford and Shelby enthusiasts rejoice. Barrett-Jackson, the World's Greatest Collector Car Auctions, will be showing off some of the best examples of Ford and Shelby performance cars at its auction block in Scottsdale next January. As the new Hollywood drama/sport film Ford v Ferrari continues to excite motoring fans everywhere, Barrett-Jackson's latest classics to be put up for auction are sure to cause a stir.
President of Barrett-Jackson, Steve Davis, is looking forward to featuring these illustrious brands. "This is an incredible time to be a Ford and Shelby enthusiast," he said. "These two iconic brands have forever impacted the world of performance driving. Their racing DNA runs through every vehicle Ford Performance and Shelby American builds today."
The list of models on the block at the 49th Annual Scottsdale Auction is impressive. There's a 2008 Shelby GT500 Super Snake Convertible, the only convertible of its generation and with a mere 5,400 miles on the clock. It's not the only drop-top hero that will make an appearance, however, with a 1968 Shelby GT500 Convertible also up for grabs - it is one of just 1,423 GT500s produced that year.
The oldest car is a '67 Shelby GT500 in Candy Apple Red which had a thorough restoration in 2008. Other '60s gems include a '68 Shelby GT500KR Convertible and a '66 GT350 with under 100 miles since its own restoration. Of the more modern cars on the block, a 2017 Ford GT is the newest. It's finished in Liquid Red paint, has just 141 miles, and is straight from the personal collection of one of the retired VPs of the Ford Motor Company.
The auction takes place from January 11-19, 2020 and tickets can now be purchased, with special VIP packages available as well. Even if just to get up close to some of the most desirable Ford Performance and Shelby cars ever made, it's well worth a visit. Chairman and CEO of Barrett-Jackson, Craig Jackson, is looking forward to one of the most memorable line-ups so far: "We're proud to have some of the very best examples of Ford Performance and Shelby vehicles cross our block in Scottsdale."
Tags: #Ford #Auction #Shelby
Lamborghini Aventador S Review: Dramatic V12 Supercar Is Truly Special
2019 Chevrolet Corvette ZR1 Convertible Review: An Under-Appreciated Icon

redpajama_set_name: RedPajamaCommonCrawl


The Box Tops for Education program has helped Augusta Independent raise $5560.47 since participating in the program. It is amazing that this amount of money can be raised by clipping Box Tops off of packages that would normally be recycled or sent to the landfill! Augusta Independent School is once again engaged in a Box Top War. Funds from Box Tops will assist the PTSA in providing scholarships for our seniors, activities for students, and school- wide programs.
Please remember that we collect Box Tops year round! Family and community members are encouraged to collect them and drop them off at school or send them with a student at any time. The rewards from these labels can add up to an amount that will make a big difference for our students. The Box Top War of 2018 begins September 01, 2018, and ends October 30. The winning class with the largest collection will receive a pizza party!


Two Tiered Round Cake covered in fondant with 3D Pram on top.
Categories: 3D Element, Baby Cakes. Tags: 2, 3D, babies, baby, baby's, Bow, Cake, cakes, custom, cute, dot, dots, edible, gender, girl, girl's, girly, peach, pink, polka, polkadot, polkadots, pram, reveal, shower, soft, sweet, tier, tiered, tiers, two, White.


This past Friday I had 6 minutes to share a message about innovation with the world at TEDx NASA. It was a fantastic event with 29 speakers, authors, musicians, aerospace engineers, a neuroscientist and more. 1,700 people were in attendance and it is reported that nearly 100,000 people watched via video streaming on the internet.
Given that my typical speech is 45 minutes long, preparing a 6 minute presentation was a bit of a challenge and required me to script it out to make sure I did not go over my allotted time. Below is what I prepared. Within the next two weeks, I will be able to share the actual video footage – where I am sure I said something completely different.
We hear people use that expression to describe something that's not that complex. And although I would never suggest that aerospace challenges are simple, sometimes, even rocket science isn't rocket science. What I mean by that is sometimes the most creative solutions to aerospace challenges can be found outside the realm of rocket science.
The issue is, you are experts. And your expertise might be the very thing that is preventing you from finding the most creative solutions.
Let me explain why with a simple example.
Think about a time when you lost your keys. After searching everywhere, upon finding them, what did you inevitably say to yourself? "Can you believe it? They were in the last place I looked!" Well of course, who finds something and continues to look for it?
The same thing is true when looking for a solution to a problem. Once your brain finds a solution, it stops looking. And the greater the level of your expertise, the quicker you find a solution. Unfortunately, your idea may not be new, innovative, or the best solution.
The key is to look outside your domain of expertise and to assume that someone else has already solved your problem. Because the odds are, someone HAS solved your problem. So, if you are working on an aerospace challenge, the solution may in fact not be rocket science.
Let me give you a few simple examples.
A high margin item for office supply companies is selling refilled toner cartridges. The challenge is however, very few customers return the used cartridge. During a brainstorming session designed to find creative solutions to this dilemma, I asked the question, "Who else has solved this problem? Who sends you something and is guaranteed that you will send it back?" The first response was the IRS. But the next response was NetFlix. They send you a DVD. You can keep it as long as you want. When you are done you return it and get another one. We investigated and implemented a NetFlix style subscription model for toner cartridges. This worked out great for the company, because they had a 100% return rate on empty cartridges. And customers love it because they never run out of toner and they get great discounts.
It's not rocket science. Someone else solved this problem.
Or consider engineers who have been searching for better ways to locate and seal cracks in gas pipelines. This is a pressing issue for the industry. Then, one day, while a Scottish engineer was working on this issue, he got a paper cut. Unlike most people who would be annoyed, he was thrilled. What he realized is that his finger is like a cracked gas pipeline. By making a connection between capillaries and a pipeline, he was able to quickly develop an inert coagulation ingredient that would seals these cracks.
The solution wasn't rocket science. Someone else, in this case the human body, had already solved this problem.
Or consider a snack food manufacturer that wanted to find a way of reducing the amount of fat in their potato chips. The best solution wasn't found in their laboratory. In fact, the solution wasn't found in any laboratory. The person who discovered the best solution had no experience with food production. He was a musician. He knew that sound vibrations travel through solid objects and that if an object is light enough it, too, will vibrate. The solution was to place speakers above the conveyor belt and use loud music to literally shake the fat out of chips.
Clearly, this was not rocket science.
Quite often the most creative solutions arise when you assume that someone else has already found a solution. When you look outside your domain of expertise.
When you become masterful at connecting dots you find new and creative solutions.
That's the wonderful thing about this conference. They could have put 20 aerospace engineers on the stage. But instead they brought in artists, musicians, authors and neuroscientists. This is a chance for you to connect the dots. To learn from unrelated disciplines. If you have 100 aerospace engineers working on a challenge, the value of adding the 101st would be incremental. But adding a biologist, a neurologist, a nano-technologist, or a musician, may lead to a breakthrough.
It is about making connections. It is about connecting the dots. It is about looking outside of your domain of expertise.
You are all experts. And you are admired for your deep understanding of complex technical issues. Having said that, sometimes, the key to creative thinking is to recognize the best solutions aren't always rocket science.


For today's vintage brooch collection I am delighted to share the collection of Andrea. On Instagram I have seen her brooches and was always amazed by her fabulous style. Luckily she was very sweet and was willing to give us a peek into her collection. Have fun reading and thank you Andrea for sharing your brooch stories!
Could you tell something about the first brooch you owned?
Which brooch is the latest addition to your collection?
Which brooch is on your wishlist?
So, are you ready for everything? Here is the entire collection. Halleluja!
I really love this collection! Wish I had so many dangling brooches. Just like the ice skates. And the bananas! And the pineapples… Well, everything. Which one is your absolute favorite?
If you like to keep updates on Andrea's collection, find her on instagram by the name @galaboutmidtown.
Broesj at Best Kept Secret Festival market!
© 2014 Babette Zijlstra. All Rights Reserved.


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News tagged with tourism
Five ways to be a responsible wildlife tourist
Imagine walking through a lush tropical forest. You hear a rustle overhead, and a half-eaten fruit plops onto the trail. You lock eyes with a howler monkey, before he gives a soft grunt and moves higher into the trees. These ...
Everest: I interviewed people risking their lives in the 'death zone' during one of the deadliest seasons yet
Climbing some of the world's tallest mountains, you enter the "death zone" when you are 8,000 metres from sea level—where oxygen is 34% the concentration it is on the ground below. Climbing here is one of the most dangerous ...
Halal holidays: Islamic values play a significant role in the travel decisions of Muslim tourists
Islamic values are just as important as the destination, quality and value for money for Muslims when choosing a holiday destination, according to a new study by the University of Portsmouth.
NASA and space tourists might be in our future but first we need to decide who can launch from Australia
In a sign the Australian Space Agency is already opening up new doors for Australian industry, NASA says it will be launching rockets from Arnhem Space Centre, in Nhulunbuy in the Northern Territory, in 2020.
NASA said Friday it will open up the International Space Station to business ventures including space tourism as it seeks to financially disengage from the orbiting research lab.
Left behind: How disruptive technology may choose society's winners and losers
New platforms like home- and ride-sharing services often are praised for leveling the playing field, cutting out the middle man and boosting the economy.
Thai bay made famous in 'The Beach' to be shut until 2021
The closure of the glittering Thai bay made famous by the movie "The Beach" has been extended for another two years to allow a full recovery of its corals and wildlife, an official said Thursday, drawing a sharp rebuke from ...
Tourists and fishers key to future of rare manta nursery
Two manta ray hotspots in waters near Bali identified in new research as vital habitats for the threatened species, could be at risk from unregulated tourism and small scale/ artisanal fishing.
Egypt's rebounding tourism threatens Red Sea corals
In serene turquoise waters off Egypt's Red Sea coast, scuba divers ease among delicate pink jellyfish and admire coral—yet a rebounding tourism sector threatens the fragile marine ecosystem.
When coastal hazards threaten your Outer Banks trip
A trip to the Outer Banks is a tradition for some North Carolina families and a bucket-list destination for other tourists. A new study from North Carolina State University asked visitors for their reactions to having travel ...


At Rhema Sanctuary, we are conscious of our destiny, empowered by intentional teaching of God's word and consistently applying the word by walking in greatness.
We are committed to the development of both personal and corporate spiritual life by communicating with God through prayer, reflection, bible study and teaching which deepens our relationship with God and brings about life transformation.
We are committed to maintaining a high standard of excellence to the glory of God. This will be achieved when each person utilizes their God given spiritual gifts and resources to the best of their ability.
Under the guidance of the Holy Spirit, Rhema Sanctuary is led by Dipo & Yettie Adewunmi. Armed with the knowledge that Praise, Prayer & Service are the core tenets of ministry, they have both been instrumental to the success of multiple programs and outreaches such as the popular 24 Hrs Basket of Praise, WOGO (Wear One Give One) Initiative, etc.


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Tamara Milosevic led the first Learning expedition of students. The expedition took place in Paris from July 11th to 15th 2022, where students of each partner university had a chance to meet each other. The first day was dedicated to the team building and introductory activities, and students were placed in teams depending on their interest in subjects relevant to the mapping of the P4 medicine ecosystem in Europe (IO3) and outreach activities through the P4 medicine awareness survey.
The main objective of this learning activity was to increase the cohesion of the PROMISE students, and to teach them the basic teamwork and collaboration skills. We also wanted the students to learn how to talk to different stakeholders, and how to translate face-to-face interactions into meaningful data that can be fed into a database.
Students from Croatia and Spain used the already existing database elements prepared by the first generation of students in 2021 and curated and updated the database. The students also met with local stakeholders and interacted with them during presentations as well as informal gatherings.
The students visited and met the ollowing stakeholders:
• Learning Planet Institute (formerly Center for Research and Interdisciplinarity)
• Foundation IGEM
• Molecular Diversity of Microbes INSERM lab
• Multitude of research groups and platforms of Institut Cochin
• FIRENDO rare disease network
• Biomedical department, University Paris Cité
After this training, the students went back to their home country and continued the analysis and mapping of their local ecosystem, under the guidance of the local partners. They also continued to disseminate the information about the survey and some of them will continue to collaborate with us on maintaining the survey on a yearly basis, followed by data analysis and opinion articles on how the P4 medicine awareness is evolving across Europe.
As a result of this training, 36 students acquired diverse skills such as how to identify stakeholders, talk to different stakeholders in both formal and informal situations, extract data and input the data into the database of the P4 medicine stakeholders, simplify and translate surveys intended for a wider audience, communicate about the survey using social media.
1st learning expedition Paris
© 2023 promise


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Q: RDLC report with multiple column data display I have a report whose dataset is as below:
ID SeqID Text DisplayName DisplayValue

1   x    xyz   xyz1           []

1   x    xyz   xyz2           [x]

1   x    xyz   xyz3           []

1   x    xyz   xyz4           [X]

1   x    xyz   Other

2   y    abc   abc1           []

2   y    abc   abc2           [X]

2   y    abc   abc3           []

2   y    abc   abc4           [X]

2   y    abc   Other

The above dataset has to below displayed in the below format in my report:
1 xyz

xyz1 [] xyz2 [x]

xyz3 [] xyz4 [x]

Other:

2 abc

abc1 [] abc2 [x]

abc3 [] abc4 [x]

Other:

I'm trying to convert a crystal report that is in the above format to an RDLC report in VS2008 Basically I need a dynamic column display for each of the unique text column values.
Any suggestions would be greatly helpful

redpajama_set_name: RedPajamaStackExchange


Hello everyone. I'm wondering at the probability of a new transmission. I know that it would require a LOT of things, but bare with me. My thinking is that, in a perfect world, you might be able to get away with putting the 6T40 transmission from the Chevrolet Sonic into an Astra since both cars use the 1.8l transverse Ecotec engine. The Sonic is a smaller car, so it's transmission should fit? I'd love to hear any thoughts on this.
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I'm no help as far as getting it done... but it makes sense.
Taking an Astra on the highway gets you less MPG than expected. In 5th at ~55 it's cool and will report high 40s MPG. But if you start getting up to 65-75mph, MPGs plumit to the mid to low 30s. Sure sign that another gear is needed for high speed highway driving.
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Some European boards discuss the 18xer engine possibility with a 6-speed swap (Astra and Vectra).
One of the issues is the very low power of the engine.
The use of 6th gear being only good on the "motorway" translates to me the motorway is higher speed. I don't know about y'all, but I'm at highway speed as much as I am 35-50 mph. 50+ in 6th in my mind would be perfect, just depends on the gearing the 6 speed has.
I've done some research myself into the matter, but I don't think the 6 speed the Vectra uses is available over here is it? I know the bolt pattern on the Cruze and Sonic 1.8's are different from the z18xer, or atleast it appears that way atleast.
'08 Astra - 131,000 miles and counting!
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There may be some issues not mentioned besides physical dimensions for direct bolt on of this six speed auto. Early Saturns used the single PCM to run the EFI system and xmission. Electronic controlled xmissions became the next generation of xmissions. Later models required two separate modules, one for the engine and the other for the xmission, due to more sophistication. Add a third module, the body control module, and Saturns evolved along with other cars in sophistication. The problem of addressing a different xmission from another car may require asking the technical questions of whether or Astra electronics can recognize a foreign xmission and accommodate the extra gears to shift the extra gear two a stock Astra xmission doesn't have.
Will the stock ECM and TCM (transmission control module) need one or both modules (if Astras have two or three modules) updated (if they can) or if they need one or both modules from the other car to make this Astra one off workable. Then the question whether or not the other ECM/TCM will run the Astra engine. Like any complex project, the devil is in the details. To discuss some factors involved in engine/xmission relationships, the engine computer either controls xmission shifts or relegates this control to a separate xmission control module with both ECM and TCM communicating with each other at all times. Engine management deals with all the sensors needed to make an engine run. To make electronically controlled xmissions shift up and down requires more programming to use the same engine sensors like map, throttle position, spark timing, coolant temps, etc. And add xmission sensors to this mix. A lot goes on just running the EFI system. Add xmission programming and things get more complicated and thanks to engineering on many levels, we have 5, 6, 7 and 8 speed xmissions for us shiftless drivers. While a little slow to understand the need for more gears in autos, it didn't occur to me the extra gears allows for quicker off the line acceleration (lower gearing) for things like stoplight racing or more importantly short on- ramps on older roads as well as one or two over drive gears for better fuel mileage at higher speeds while cruising. Separate engine and xmission management systems working together. Xmission shifting looks at engine rpm, load (map sensor) throttle position, coolant temps and spark timing, some factors a xmission control module examines, including the xmission input/output speed sensors to make correct shifts whether stop light racing or granny driving.


Search University Place, Washington Bank Foreclosure homes. See information on particular Bank Foreclosure home or get University Place, Washington real estate trend as you search. Besides our Bank Foreclosure homes, you can find other great University Place, Washington real estate deals on RealtyStore.com.


GazeFlow is the Webcam Eye Tracking engine on which GazeRecorder, GazePointer and GazeBoard rely. GazeFlow is based on analysis of the optical flow of webcam images.
An accuracy and comparison test showed that GazeFlow's accuracy measurements (< 0.9˚-1.0˚) are, higher than the desired level of accuracy indicated by literature, especially when the head is allowed to move freely. These measurements are however comparable to the accuracy measurements of the compared eye tracking device using infrared light (SMI Red 250).


Our restaurant serves genuine dishes, with Km 0 products and some from Biological Agriculture. We often propose the Catch of the Day combined with extra virgin olive oil DOP Tuscia, vegetables and locally grown fruit. Particular attention to the preparation of GLUTEN FREE dishes and Kids menu. The quality of the cuisine, the beautiness of the location, the careful service make unforgettable your events.
Dishes are prepared with Local Products: fish, vegetables, olive oil, cheese and salami. In our menu, the tradition is respected and innovated by our chef's proposal. Torre del Sole *** Hotel & Resort restaurant offers several selection of fish dishes and more. It belongs to Eusepi Hotels group, which operates in catering for over 40 years. Eusepi family manages the facilities, to ensure assistance to its customers: a synonym of guarantee and professionalism.
Garden by the sea, large inner rooms, pool, wide veranda, can be used to realize your own event. Weddings or small receptions: Buffet in the Garden or Swimming pool, lunch in the dining rooms or under the veranda, cutting the cake in the pool, the bonfire on the beach, after dinner with friends, love songs in the moonlight, photos with the sunset over the sea, Playground to entertain the kids. Careful service suited for you. The perfect frame to make real every wish.


When you hook up wires to the terminals of a battery, charge can flow and a complete path called a circuit is formed. This flow of charge is called a current. The symbol for current is the letter I and the unit of measurement is called the ampere. The higher the current running through the wire, the more charge is flowing.
How does charge flow through a circuit?
When a copper wire is attached to terminals of a battery charges flow. If you put a rubber band across the terminals no charge will move. Why is this? The reason has to do with the properties of copper which is a good conductor of charge. Material that are good conductors have loosely held electrons. Movement of electrons occur very rapidly passing from atom to atom along the wire. To move the charge there must be a potential difference between two points.
There is a relationship between electric potential and electric current. This relationship was first demonstrated experimentally by a scientist named George Simon Ohm.
What is the difference between electric current and electron flow? Why are they in different directions?
There is still a lot of confusion on this issue. It comes from when Benjamin Franklin first discovered electricity he thought it was positive charges that was moving along the wire. So the Current was defined as the flow of positive charge that was moving in the metal wires he was playing with (this is often referred to as Convention Current). We now know Franklin was wrong -- it was the negative (electrons) charges moving, in the direction opposite to the direction of his positive charge in the wire. It is important to point out that positive charges do not move in a copper wire but in other cases e.g., in solutions both negative and positive charges move.
Where I is the current in amperes, V is the potential difference in volts, and R is a constant, measured in ohms, called the resistance.
Electrons moving through a wire can move continuously through the wire in the same direction.This is called Direct Current. Electricity from dry cells or batteries is an example of direct current. Electrons may also change or alternate their direction regularly. This is called Alternating Current. The electricity in your home is alternating current. In the United States the current changes direction 120 times per second.
What is the difference between the Advantages and Disadvantages of Direct Current and Alternating Current?
Direct current is produced by by such sources as batteries, thermocouples, solar cells and commutator-type electric machines. Direct current not only can flow through wire but an also flow semiconductors. Direct current can be obtained from alternating current by use of a rectifier.
The first commercial electric power transmission developed by Thomas Edison used direct current.
DC is commonly found in many low-voltage applications especially where they are powered by batteries, Most automotive applications used DC current although the alternator is an AC device which is used to produce DC current. Most electronic devices require a DC current.
AC current is the way electricity is supplied to homes and businesses. The first recorded application of AC current was by Guillaume Duchenne who invented electrotherapy. He concluded that AC was superior to DC for elecrotherpuetic triggering of muscle contractions. A power transformer was first demonstrated in London in 1881 by Lucien gaular and attracted interest by Westinghouse. Although they applied for patents on their technologies, they were overturned because Nikola Tesla was able to show prior work in the field. Nikola Tesla is most well known for developing the modern alternating current electrical supply system.
AC voltage may be increased or decreased with use of a transformer. Use of high voltage leads to significantly greater efficiency in transmission of power.The disadvantage of high voltage is that a greater amount of insulation is required.
How do we measure an electric current?
To measure voltage or Electric Potential you put the volt meter in parallel in the circuit. A voltmeter must be connected in parallel to measure the voltage of a device because objects in parallel experience the same potential difference. See image below.
The relation between electric current, magnetic fields and physical forces was first recognized by Hans Chrisian Orsted in 1820. He observed a compass needle was deflected from pointing North when a current flowed in an adjacent wire. This was know as a tangent galvanometer. The tangent galvanometer was used to measure currents using this effect. The restoring force to zero the meter in this system was the force of the earths magnetic field. So, the meter could only be used when aligned to the Earth's magnetic field. Sensitivity of the instrument was possible by increasing the turns of wire used.
a) he thought it was electrons that moved along the wire.
b) he thought it was positive charges that was moving along the wire.
d) In DC the electrons moving through a wire can move continuously through the wire in the same direction, in AC the electrons periodically change direction.
5. What does an Ammeter do?


Do you know what to do if you discover an archaeological object in Ireland?
Archaeologist Gary Dempsey is undertaking research into how archaeological objects are reported in Ireland.
I wish Gary all the best with the project and I hope you will take the time to fill out the survey and to share it with friends.


Backyards n More is a groundbreaking concept designed to meet all of a homeowner's backyard needs. We are Sarasota and Manatee Counties' Premier Custom Outdoor Kitchen and Outdoor Fireplace design center. Visit our Backyards n More showroom, meet our staff and let us design and build your custom outdoor kitchen and custom outdoor fireplace.
Backyards n More features everything you need to take full advantage of our beautiful Florida weather and expand your living space to include the back yard. Treat yourself, your friends, neighbors and family to a dream backyard patio with a custom outdoor kitchen or matching outdoor fireplace or fire pit. With one stop, we handle all your design needs. We know that each home and home owner is unique. We will be able to design, build and maintain your backyard, with the individuality you deserve. Our Vision is to create another room in your house where you can relax next to your custom fireplace and after a warm meal cooked on your custom designed outdoor kitchen.
Paver Deck with brick coping featuring spa spillway.
Pavers are a popular choice for backyard patios, walkways and driveways. Backyards n More provides a beautiful, custom paving solution for all your hardscape projects. Choosee a paver type from travertine, clay, marble, knockdown from a variety of manufacturers such as Old Castle, Stabil, SCM, CT and more.
Be the center of attention at your next party. Show off your cooking skills with everything right at your finger tips. Become the chef and cook on a custom grill designed and built for the way you grill. Reach over and grab a cold beverage from your custom beverage center or prepare a quick vegetable dish from your custom cold storage drawer.
There is nothing quite like a savoring a steaming cup of coffee or a robust glass of wine in front of a custom hearth fire place built by Backyards n More. Who doesn't like to sit around the fire and tell stories? Let Backyards n More design your custom fireplace or custom fire pit with seating for all your friends to tell about the one that got away.


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The Type 2 rifle grenade launcher was an attachment for the Japanese Type 38 and Type 99 rifles that allowed them to fire special hollow charge grenades. It was a version of the German Schiessbecher grenade launcher. Two grenades were produced for the launcher: a 30 mm calibre grenade and a larger 40 mm calibre grenade, both designated Type 2. The launcher sits over the end of the barrel, held in place with a clamping device. A special crimped blank cartridge or wooden bullet is used to fire the grenades.

The rear of the grenades is pre-rifled to mate with the rifling in the launcher. The rifling ensures that the grenade is spun in flight, giving it stability and arming the rotational fuze. Both grenades use a largely identical fuze, which makes up the rear part of the grenade. On impact, momentum carries the striker assembly forward, overcoming the resistant force of a creep spring into the detonator.

References

See also

World War II infantry weapons of Japan
Grenade launchers

redpajama_set_name: RedPajamaWikipedia


I think God must have been in a really bad mood that he came up with something called algebra to trouble us! I've spent hours working on this math problem which relates to lowest common multiple of variables and I still can't solve it. I'm particularly having problems with rational inequalities, function domain and scientific notation. Can anyone throw some light on how to go about finding a solution to such problems? I've tried various means that I could think of, but none helped. I need some urgent guidance now. Anybody?
Once upon a time those were the only ways out. But thanks to technology today , we have something known as the Algebrator! It's quite easy to use, something which even a newcomer would enjoy working on and what's even better is that it would solve all your questions and also explain the steps it took to reach that answer! Isn't that just great ? Well I think it is, and I'm sure after using it trying it, you'll be on the same page as me.
Yes ! I agree with you! The refund guarantee that comes with the purchase of Algebrator is one of the attractive options. In case you are dissatisfied with the assistance offered to you on any math topic, you can get a refund of the payment you made towards the purchase of Algebrator within the number of days specified on the label. Do have a look at http://www.graph-inequality.com/solving-equations-algebraically-and-graphically.html before you place the order since that gives a lot of information about the topics on which you can expect to get assisted.
That's what I'm looking for! Are you sure this will be helpful with my problems in math ? Well, it doesn't hurt if I try the software. Do you have any links to share that would lead me to the product details?
http://www.graph-inequality.com/graphing-systems-of-linear-equat.html. There you go. Hopefully you will not have to leave math.
Algebrator is a very user friendly product and is surely worth a try. You will also find lot of interesting stuff there. I use it as reference software for my math problems and can swear that it has made learning math more enjoyable.


The UFO at the Novy Most (New Bridge) is a popular place for tourists to visit. From the UFO you can enjoy a beautiful view of the Danube, the Castle and the Old Town of Bratislava. If you are hungry you can also grab something to eat in the UFO restaurant. If you have a table reservation the entrance to the UFO is free, but if not the entrance fees vary between 3,50-6,50 Euro per person.


One December when John and I were first dating, I was fascinated by Belle de Brillet, a Cognac infused with pears–and John wisely took note. The oddly wrapped package on the mantle of our first apartment was none other than a bottle of Belle de Brillet, and now the delicate spirit always reminds me of the holidays. I'm planning to indulge in a tipple of it in a Champagne cocktail this Christmas!
Combine pisco, Calvados, St-Germain, Belle de Brillet and orange bitters in a shaker or mixing glass with ice; stir until chilled. Pour into a flute or coupe, top with Champagne and garnish with an orange peel.
Notes: Belle de Brillet is much easier to find these days, but if collecting all these ingredients at your in-laws proves too difficult, a high-quality pear spirit topped with Champagne and finished with a dash of orange bitters will be just the ticket.
Wishing you and yours a lovely holiday–cheers!
Merry Merry and Happy New Years Lena!
Cheers to you and yours, Johanna!


The Hawthorn Memo Square - White Refill makes for a great gift. With a decorative border frame and a selection of 10 fonts and 8 matte ink colors, your friends will appreciate this low-cost gift. Produced on our high-quality white paper text sheets.


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Back To Neighborhoods
What You'll Find
Why You'll Fall In Lov...
Your Little Spot by the Lake
Edgewater, so goes the name, sits right on the lakeshore, providing its residents with a picturesque spot by Lake Michigan.
But Edgewater is about more than the great views: It's a highly diverse neighborhood perfectly situated right alone the CTA Red Line, surrounded by classic Chicago brownstones, vintage stores and affordable, spacious living spaces in a quiet, family-friendly community.
Edgewater runs along the Red Line L stop Berwyn and then all the way up to a little north of Granville, with an East/West boundary from Ravenswood to the lake.
Its location sits right in the middle of Chicago's north side, and most apartments in the area are a short walking distance from the nearby CTA Red Line stops which will run residents to many of Chicago's most notable sites. These include Wrigley Field, Northwesters, the Magnificent Mile and the Loop.
The Neighbors 01
Edgewater is a highly diverse community that's home to many young, professional singles living on a budget.
The majority of residents fall between the ages of 20 and 34 and make less than $50,000, leading to a demand for fun but affordable options throughout the area.
What You'll Find 02
Edgewater's unique flavor features an amazing array of ethnic restaurants, historic churches and vintage stores up and down the major streets of the neighborhood.
Plus, Edgewater puts its location by the lake to good use with plenty of walking space by the water where you can unwind with some of the most picturesque views in the city.
What You Should Know 03
Though Chicago has a large number of small, storefront theater companies throughout the city, Edgewater is home to an unusually large number of them.
Among the most highly regarded of these include Raven Theatre, City Lit Theater Company, Jackalope Theatre Company and more! These shows tend to be cheaper than the more expensive, downtown options, but don't think that means they're somehow of lesser quality. Over the past few years, many of these smaller theater companies have their work and artists transferred to larger stages here in Chicago, demonstrating that the work done in Chicago's storefront scene is just as strong as the rest of the city's.
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Why You'll Fall In Love With Edgewater 05
In Edgewater, there's always something to discover.
From vintage stores to the plethora of outdoor space, to local favorites like Lickity Split Custard and Moody's Pub, to the delicious Revival Social Club (with some of the best "monkey bread" you'll find in the city), you're bound to find your special spot in this unique and eclectic neighborhood.
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text:
Gunja, selo i općina u Hrvatskoj.
Stara Gunja, u Hrvatskoj
Gunja (Foča-Ustikolina, BiH), selo u BiH
Gunja (Gujrat, Pakistan), selo u Pakistanu
Gunja, naziv za nekoliko lokacija u Južnoj Koreji
Gunja, naziv za nekoliko lokacija u Indiji
Gunja, naziv za lokaciju u Angoli
Gunja, naziv za lokaciju u Indoneziji
Gunjaman, češće nazivani i Gunja, pleme Hottentota koje je živjelo na mjestu današnjeg Cape Towna.


As we gear up for 2018, which will be an important turning point for staying on track with the goals of the Paris Agreement, it is interesting to look back to 2017 and take stock of the strong commitments that our C40 cities have made to climate action. Together and individually, we are "the new face of leadership" – as described by former US President Barack Obama at the North American Climate Summit in Chicago earlier this month. Together we offer hopes that we can and will address one of the greatest challenges of this century. The work has started in our cities and this month's announcements in Chicago, Accra and Paris are raising the bar for 2018.


text:
One Shot, Two Kills: MR Exclusive Interviews- The Devil Wears Prada and Upon A Burning Body
Written by XxCrashQueenxX
On day 1 of the Rockstar Energy Drink Mayhem Festival, I had the chance to sit down with the vocalists of two of the most popular bands in today's metal scene, Mike Hranica of The Devil Wears Prada and Upon A Burning Body's Danny Leal . I interviewed both of them and asked them everything from what it felt like to be on the same bill as metal heavy weights such as Slayer and Slipknot, to what they do on their down time when they're not on the road. Both interviews went great, here are their responses to my questions.
The Devil Wears Prada Photo Credit to Richard Rasner of Nakayama Studios.
What is it like to be on the same bill as bands like Slipknot, Slayer, Motorhead, and Anthrax?
Mike Hranica- We've been on stuff like the Download Festival where it was guys like KISS, Judas Priest, really really huge names, and it's awesome that we're doing that now for like 5 or 6 weeks this summer, it's fantastic. Getting to do mayhem this year is awesome. We've wanted to do it for the past 2-3 years. And for us to be on this year which I would say is the best year. I couldn't be much happier.
Danny Leal- Oh, dream come true. These thinks are what we dream about and now we're here. It's amazing.
If someone would have told you ten years ago that you'd be where you are today, would you have believed them?
MH- No, no, no, I never thought I'd be in music at all. I come from a music loving family but not really a musician family, nobody in my family plays music and I just ended up yelling with my friends one day and I don't know, here we are.
DL- We worked to be here. It's phenomenal that we are, but there is so much work left to do.
Anything new you're working on that you want to let the fans know about?
MH- Yeah, but I can't say…I'm really sorry.
DL- The new record Red. White. Green. That's available in stores. Please get it. We worked so hard on it and get it wherever you can.
What is your favorite song to play live?
MH- I really just love new material. It's the most emotional relevant. It's obviously what speaks to me because it's very new. There are old songs that I always, always come back to, that I really enjoy. Especially Don't Dink and Drance, it's always worth playing. But as far as new material, I really love playing Kansas because I get to play guitar and Chicago, which is another one of my favorite songs. It's very rewarding.
DL- Sin City.
When was your most memorable on-stage moment?
MH- We've had some weird situations where like weird fans will come on stage and won't leave or they'll try to take something but nothing specifically to say, I just try to erase it from my mind.
DL- Our entire show.
If you weren't in a band, what profession would you have?
MH- Probably writing something, journalism, maybe.
DL- I always envisioned myself doing this, so if I wasn't able to perform, I'd be pretty bummed out. I'd probably like to have a management position within the industry, work for a label, stay close to what I love.
What do you do on your off time?
MH-I like to ride bikes, play guitar, hangout with family and friends, eat good food, go to church, im trying to get more into my extracurricular church activities, really just enjoy Chicago.
DL- I try to keep myself busy, do odd end jobs, keep myself grounded and get back to being regular. It makes you itch to not work, when you put yourself to work like that, you're like "I just want to get out and tour again and be back on the road." So I just do extra little odd end jobs to make a little extra cash for the family and spend time with the family, we're Mexican, so we know how to work, you know."
Favorite place to play live?
MH-Really anywhere that will accept us well. anywhere in California has always been good for us, anywhere Texas. Chicago is absolutely fantastic for us, Ohio always treats us well, and a lot of places in between.
DL- California always treats us well. germany was pretty sweet to us. We like playing anywhere people are going to come to our shows.
Labels: All-Indie-Magazine, Crash-Queen, Ferret Music, interview, metal, metalcore, The Devil Wears Prada


text:
\section{Introduction}

\thispagestyle{empty}

\par We start by drawing the analogy between limit groups and
coordinate rings of algebraic varieties. To an algebraic subset $V$ of
$\mathbb{C}^n,$ one attaches the coordinate ring. The points of $V$
are in one-to-one correspondence with ring homomorphisms
$\adjoin{\mathbb{C}}{V}\to\mathbb{C}$: If $\adjoin{\mathbb{C}}{V}$ is
the quotient of $\adjoin{\mathbb{C}}{x_i}$ by a radical ideal $I,$
then an assignment $x_i\mapsto z_i\in\mathbb{C},$ $(z_i)$ a point of
$V,$ vanishes on $I$ and gives a ring homomorphism. Conversely, one
associates to such a ring homomorphism $f$ the tuple $(f(x_i))\in V$.

\par The replacement for the notion of a radical ideal in algebraic
geometry over the free group is that of a residually free group. Going
further, we need to extend the notion of prime ideal as well. A
\term{zero-divisor} in a finitely generated group $G$ is a tuple of
elements of $G$ such that every homomorphism $G\to\ensuremath{\mathbb{F}}$ kills at
least one element of the tuple. A group is \term{residually free} if
it has no singleton zero divisors. A group is
\term{$\omega$--residually free}, or is a \term{limit group}, if it
has no zero divisors. It will be convenient to use a slightly
different definition of a limit group.

\begin{definition}[Limit Group \cite{sela::dgog1}]
  \label{limitgroup}
  A sequence of homomorphisms $f_n\colon G\to\Gamma$ is stable if, for
  all $g\in G,$ there exists $n_g$ such that $f_n(g)=1$ for $n>n_g$ or
  $f_n(g)\neq 1$ for $n>n_g$. The \term{stable kernel} of a stable
  sequence of homomorphisms is the set of elements which have trivial
  image for large $n,$ and is denoted $\stabker(f_n)$. The quotient of
  $G$ by the stable kernel of a stable sequence $f_n$ is a
  \term{$\Gamma$--limit group}.
\end{definition}

\par In this paper we study $\Gamma$--limit groups for
$\Gamma\cong\ensuremath{\mathbb{F}}$. A sequence $f_n\colon G\to\ensuremath{\mathbb{F}}$ \term{converges
  to} $G$ if $\stabker(f_n)=\set{1}$. If $G$ is $\omega$--residually
free then clearly there exists a sequence of homomorphisms $f_n\colon
G\to\ensuremath{\mathbb{F}}$ converging to $G$. That a $\ensuremath{\mathbb{F}}$--limit group is
$\omega$--residually free is~\cite[Theorem~4.6]{sela::dgog1}, and
follows from finite presentability.

\par The object analogous to the coordinate ring for an algebraic
subset $V$ of $\ensuremath{\mathbb{F}}^n$ is simply a finitely generated residually free
group $G$ which requires only $n$ generators. With little work one
establishes a one-to-one correspondence between points of $V$ and
elements of $\Hom(G,\ensuremath{\mathbb{F}})$. If an algebraic set $V$ is irreducible
then $\adjoin{\mathbb{C}}{V}$ has no zero divisors. Likewise, for the
set $\Hom(G,\ensuremath{\mathbb{F}})$ to be irreducible, $G$ must have no zero divisors,
hence is a limit group.

\par The \term{Krull dimension} of an algebraic set is the supremum of
lengths of chains of irreducible subvarieties, thus it is natural to
ask whether any sequence of proper epimorphisms of limit groups,
beginning with a fixed free group of rank $n,$ terminates in a uniform
number of steps. Exhibition of such a bound would establish the
finiteness of the Krull dimension of $\ensuremath{\mathbb{F}}^n$. In this paper we make
the first move toward showing this.

\par The key to constructing limit groups is the notion of a strict
resolution. The group $\Mod(L)<\Aut(L)$ is defined in the next
section.

\begin{definition}[Strict; Strict resolution]
  \label{strict}
  A homomorphism $\pi\colon L\to L'$ is \term{strict} if for every
  sequence of homomorphisms $f_n\colon L'\to\ensuremath{\mathbb{F}}$ converging to $L',$
  there exists a sequence of automorphisms $\phi_n\in\Mod(L)$ such
  that the sequence $f_n\circ\pi\circ\phi_n$ converges to $L$.

  A sequence of proper epimorphisms $L\twoheadrightarrow L_1\dotsb\twoheadrightarrow\ensuremath{\mathbb{F}}_k$ is
  a \term{resolution} of $L$.  If every homomorphism appearing in a
  resolution is strict then the resolution is a \term{strict
  resolution}.
\end{definition}

\par By~\cite[Proposition~5.10]{sela::dgog1} every limit group
admits a strict resolution. The first step in our approach to showing
that limit groups have finite Krull dimension is to show that any
strict resolution of limit groups terminates in a uniformly bounded
number of steps.

\begin{theorem}[Strict resolutions have bounded length]
  \label{strictlengthbound}
  Let $\ensuremath{\mathbb{F}}_n\twoheadrightarrow L_0\twoheadrightarrow\dotsb\twoheadrightarrow L_k$ be a sequence of
  proper strict epimorphisms of limit groups. Then $k\leq 3n$.

  Let $\ensuremath{\mathbb{F}}_n\twoheadrightarrow L_1\twoheadrightarrow\dotsb\twoheadrightarrow L_k\cong\ensuremath{\mathbb{F}}_m$ be a
  sequence of proper strict epimorphisms of limit groups. Then $k\leq
  3(n-m)$.
\end{theorem}

\par It is well known that any resolution, strict or not, has finite
length~\cite[Proposition~5.1]{sela::dgog1},~\cite[Corollary~1.9]{bf::lg}. The
importance of strict resolutions lies in the fact that they witness a
group as a limit group. See Definition~\ref{strict}. The main use of
Theorem~\ref{strictlengthbound} is along the way
to~\cite[\ref{STABLE-thr:alignmenttheorem}]{louder::stable}, which
says, roughly, that if there exist arbitrarily long sequences of
proper epimorphisms of rank $n$ limit groups, then there exist
arbitrarily long sequences of rank $n$ limit groups such that all
groups in the sequence share the same \textsc{JSJ}\ decomposition.

\subsection*{Acknowledgments}

The author would like to thank Mladen Bestvina, for wondering aloud if
limit groups have irreducible representation varieties. Thanks must
also go to Ben McReynolds and Chlo\'e Perin for a number of helpful
suggestions.

\section{Splittings and Lifting Automorphisms}

\par The following definition is somewhat non-standard. Its utility
lies in the fact that it streamlines the statements and proofs of the
lemmas leading up to Theorem~\ref{autspreservecomponents}.

\begin{definition}
\label{typesofsplittings}
  Fix a finitely generated group $G$. A splitting
  $G= G_1*_{E}G_2$ over a finitely generated abelian
  subgroup $E$ is an \term{amalgamation}. A splitting
  $G= G'*_{E}$ over a finitely generated abelian subgroup
  $E$ is an \term{\textsc{HNN}\ extension}. In either case, $E$ is
  allowed to be trivial, as is $G_1$ in the former.
\end{definition}

An important subgroup of the automorphism group of a freely
indecomposable finitely generated group is the \term{modular group}
$\Mod$. To make our exposition as efficient as possible, we define the
modular group to be the subgroup of the automorphism group generated
by the following \term{elementary automorphisms}:

\begin{itemize}
\item Automorphisms from amalgamations: $G= G_1*_{E}G_2$: The Dehn
  twist in $e\in Z_{G_2}(E)$ is the automorphism of $G$ which is
  the identity on $G_1$ and which is conjugation by $e$ on $G_2$. This
  automorphism is denoted $\tau_{\Delta,e}$.

\item Automorphisms from \textsc{HNN}\ extensions: $G'*_{E}$: Let $t$ be the
  stable letter such that $t E t^{-1}= E_1$ and $e\in
  Z_{G'}(E)$. Then $\tau_{\Delta,e}$ is the automorphism which is
  the identity on $G'$ and maps $t$ to $te$.
\end{itemize}

\par The modular group as defined above is the group of
\scare{geometric} automorphisms arising from one edged splittings. If
$G$ is freely indecomposable, then $\Mod(G)$ agrees with the modular
group as defined in~\cite{bf::lg} and~\cite{sela::dgog1}.

\par Given an \textsc{HNN}\ extension or amalgamation of $G,$ we build a
free group $\wt{G}$ and a homomorphism
$\wt{G}\twoheadrightarrow G$ so that the automorphism of $G$
engendered by the splitting lifts to an automorphism of
$\wt{G}$.

\begin{definition}[Lifts of Automorphisms, $\wt{G}$]
\label{liftsofautomorphisms}
  Let $\Delta$ be a splitting of $G$ as $G=G_1*_{E}G_2$ over a
  finitely generated abelian group $E,$ $e\inZ_{G_2}(E)$. ($G_1$
  and $G_2$ are finitely generated.) Let $F_1=\langle
  x_1,\dotsc,x_{n_1}\rangle$ and $F_2=\langle
  y_1,\dotsc,y_{n_2}\rangle$ be free groups with homomorphisms
  $\pi_i\colon F_i\twoheadrightarrow G_i$. Define $\wt{G}$ to be the group
  $F_1*F_2,$ calling this free splitting $\wt{\Delta},$ and let
  $\pi=\pi_1*\pi_2\colon\wt{G}\twoheadrightarrow G$ be the obvious
  surjection. This particular free factorization of $\wt{G}$ is
  the lift of $\Delta$. Choose $\wt{e}\in F_2$ such that
  $\pi_2(\wt{e})=e$. Then the automorphism
  $\tau_{\wt{\Delta},\wt{e}}$ of $\wt{G}$ makes
  the following diagram commute.

\label{liftdiagram}
\[
    \xymatrix{%
      \wt{G}\ar[r]^{\tau_{\wt{\Delta},\wt{e}}}\ar[d]^{\pi} & \wt{G}\ar[d]^{\pi}\\
     G\ar[r]^{\tau_{\Delta,e}} &  G }
    \eqno{(\diamondsuit)}
\]

\par If $\Delta$ is an \textsc{HNN}\ extension $G=G'*_{E}$ we define $\wt{G}$
similarly. Choose $F'=\langle x_1,\dotsc,x_n\rangle,$ a homomorphism
$\pi'\colon F'\twoheadrightarrow G',$ and $\wt{G}$ the \textsc{HNN}\ extension $F'*\langle
\wt{t}\rangle$. Set $\pi(\wt{t})=t$. Choose a lift $\wt{e}\in F'$ of
$e$ and define an automorphism $\tau_{\wt{\Delta},\wt{e}}$ which is
the identity on $F'$ and maps $\wt{t}$ to $\wt{t}\cdot\wt{e}$.

\end{definition}

\section{Dehn twisting $\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$}

\par Our approach to Theorem~\ref{strictlengthbound} is to analyze the
action of the modular group of a limit group on its $\ensuremath{{SL}(2,\mathbb{C})}$
representation variety.

\par The set of homomorphisms of a finitely generated group to a
complex algebraic Lie group is an affine subvariety of $\mathbb{C}^n$
for some $n$ \cite{cullershalen0}. The $\ensuremath{{SL}(2,\mathbb{C})}$ representation
variety $\Hom(G,\ensuremath{{SL}(2,\mathbb{C})})$ will be denoted by $\ensuremath{\mathcal{R}}(G)$. For $g\in G,$
$\ensuremath{\mathrm{ev}}_g$ will denote the evaluation map $\ensuremath{\mathcal{R}}(G)\to\ensuremath{{SL}(2,\mathbb{C})}$.

\par We saw above that if $\tau_{\Delta,e}$ is elementary then it
lifts to an elementary automorphism of $\wt{G}$. The
representation variety $\ensuremath{\mathcal{R}}(G)$ has a natural embedding
\[\ensuremath{\mathcal{R}}(G)\hookrightarrow\ensuremath{\mathcal{R}}(\wt{G}) =\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}}_n)
=\ensuremath{{SL}(2,\mathbb{C})}^n\subset\mathbb{C}^{4n}\] where $n$ is the rank of
$\wt{G}$. The lift $\tau_{\wt{\Delta},\wt{e}}$
acts on $\ensuremath{\mathcal{R}}(\wt{G})$ and by commutativity of
($\diamondsuit$) the restriction
$\tau_{\wt{\Delta}}\vert_{\ensuremath{\mathcal{R}}(G)}$ agrees with
$\tau_{\Delta,e}$.

\par The exponential map
$\exp\colon M(2,\mathbb{C})\to GL(2,\mathbb{C})$ is
given by the formula
\[\exp(M)=\sum_{i=0}^{\infty}\frac{M^i}{i!}\]
This power series converges everywhere. The following lemma is well
known. See~\cite[Chapter~1, Example~9]{rossmann} for the computation
in the real case.

\begin{lemma}
  The exponential map is biholomorphic in a neighborhood
  of all points $v\neq 0\in{\mathfrak sl}_2\mathbb{C}\subset M(2,\mathbb{C})$ such that
  $\exp(v)\neq\pm I_2$.
\end{lemma}

Since all maps we deal with are either polynomials or are power series
in matrices of polynomials we suppress mention of the ambient space
$\mathbb{C}^k$.

\par The image of an edge group under a representation $\rho$
(usually) lives in a 1-parameter subgroup of $\ensuremath{{SL}(2,\mathbb{C})}$. We can
therefore twist $\rho$ by elements in the 1-parameter subgroup to
produce new representations. It turns out that the twisted
representations can be chosen to vary analytically in $\rho$ and a
parameter $z$ as long as $z$ is chosen carefully and the
representation $\rho$ doesn't map the edge group to an element whose
trace is $-2$.

\par To get the ball rolling we need to know where we can take
logarithms and how to define small pieces of 1-parameter subgroups.

\begin{lemma}
  \label{complexlemma}
  Let $P_{\epsilon}={N}_{\epsilon}(\set{x+0i}:{0\leq x\leq
  1})\subset\mathbb{C}$ be the epsilon neighborhood of
  $\left[0,1\right]\subset\mathbb{R}\subset\mathbb{C}$.

  For all $g\in\ensuremath{{SL}(2,\mathbb{C})},$ $\trace(g)\neq-2,$ there is an element
  $v_g\in{\mathfrak sl}_2\mathbb{C},$ a neighborhood $U_g\subset\ensuremath{{SL}(2,\mathbb{C})},$
  $v_g\in\wt{U}_g(=\log(U_g)$), and $\epsilon>0$ such
  that
  \begin{itemize}
    \item $P=P_{\epsilon}$
    \item $\exp(v_g)=g$
    \item
      $\exp(P\cdot\wt{ U}_g)\subset\ensuremath{{SL}(2,\mathbb{C})}\setminus\set{-I}$
    \item $\exp\vert_{N_{\epsilon}(\left[0,1\right]\cdot v_g)}$ is
      biholomorphic onto its image.
    \item $P\cdot\wt{ U}_g\subset
      N_{\epsilon}(\left[0,1\right]\cdot v_g)$
  \end{itemize}
\end{lemma}

\begin{proof}
  The argument is an easy adaptation of the fact that if $N\subset
  M$ is an embedded smooth, compact, submanifold and $f\colon M\to
  M'$ is smooth, injective on $N,$ and a local diffeomorphism at
  every point of $N,$ then $f$ is a diffeomorphism on a neighborhood
  of $N$.
\end{proof}

\begin{definition}
  \label{standardneighborhood}
  A tuple $S=(U_g,\wt{U}_g,P)$ satisfying
  Lemma~\ref{complexlemma} is a \term{standard neighborhood} of $g$ in
  $\ensuremath{{SL}(2,\mathbb{C})}$. Note that $S$ involves a particular choice of the logarithm
  $\log\colon U_g\to{\mathfrak sl}_2\mathbb{C}$. If $h\in U_g$ then $\log(h)$ shall
  be taken to be the element $v_h\in\wt{U}_g$ such that
  $\exp(v_h)=h$.
\end{definition}

\begin{lemma}
  \label{autfnanalysis}
  Let $\langle x_1,\dotsc,x_n,y_1,\dotsc,y_m\rangle=\ensuremath{\mathbb{F}},$
  $e\in\langle y_i\rangle,$ $\rho\in\Hom(\ensuremath{\mathbb{F}},\ensuremath{{SL}(2,\mathbb{C})})=\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$
  such that $\trace(\rho(e))\neq-2$. Choose a triple $(e,S,V)$ such
  that $\rho\in V$ and $\ensuremath{\mathrm{ev}}_e(V)\subset U_{\rho(e)}$. Then
  the map $\tau_H\colon V\times P\to\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$ defined by

  \[(\eta,z)\xrightarrow{\tau_H}
    \Big\lbrace \begin{array}{cll} x_i&\mapsto&\eta(x_i)\\
      y_i&\mapsto&\eta(y_i)^{\exp(z\cdot\log(\eta(e)))}
    \end{array} \]
  is holomorphic. Similarly, if $\ensuremath{\mathbb{F}}=\langle y_1\ldots
  y_{n-1}\rangle*\langle t\rangle=F*\langle t\rangle,$ $e\in F,$ then,
  after choosing an appropriate triple $(e,S,V),$ the map
  $\tau_H\colon V\times P\to\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$ defined by
  \[(\eta,z)\xrightarrow{\tau_H}\Big\lbrace\begin{array}{cll}
  x_i&\mapsto&\eta(x_i)\\
  t&\mapsto&\eta(t)\exp(z\cdot\log(\eta(e)))
  \end{array}\] is holomorphic.
\end{lemma}

\begin{proof}
  $\tau_H$ is the composition of holomorphic functions.
\end{proof}

\section{After lifting, restricting}

\par Let $\Delta$ be a one-edged splitting of $G,$
$\tau_{\Delta,e}$ an elementary automorphism, $\wt{G}$ the
lifted group and $\tau_{\wt{\Delta},\wt{e}}$ the lift of
$\tau_{\Delta,e}$ to $\wt{G}$. There is a natural inclusion
$\ensuremath{\mathcal{R}}(G)\subset\ensuremath{\mathcal{R}}(\wt{G})$. Since
$\ensuremath{\mathcal{R}}(\wt{G})\subset\ensuremath{{SL}(2,\mathbb{C})}^M\subset\mathbb{C}^{4M},$ if
$V\subset\ensuremath{\mathcal{R}}(G)$ is an open set, then
$V=\ensuremath{\mathcal{R}}(G)\cap W$ for some open subset
$ W\subset\mathbb{C}^{4M}$. If $\varphi\colon W\to\mathbb{C}$ is
analytic, its restriction to $V$ is analytic by definition.

\begin{lemma}
\label{maintwistlemma}
  Let $(\wt{e},S,V)$ be as in Lemma~\ref{autfnanalysis} and
  choose $\rho\in V\subset\ensuremath{\mathcal{R}}(G)$. Regard $\rho$ as a
  representation of $\wt{G}$ by inclusion,
  $S=(U_g,\wt{U}_g,P)$. Then
  $\tau_H((V\cap\ensuremath{\mathcal{R}}(G))\times P)\subset\ensuremath{\mathcal{R}}(G)$.

  Suppose $\ensuremath{\mathcal{R}}(G)_1,\dotsc,\ensuremath{\mathcal{R}}(G)_k$ are the
  irreducible components of $\ensuremath{\mathcal{R}}(G)$ containing $\rho$. If
  $V_i=V\cap\ensuremath{\mathcal{R}}(G)_i$ is irreducible as an analytic
  variety, then $\tau_H(V_i\times P)\subset\ensuremath{\mathcal{R}}(G)_i$.
\end{lemma}

\begin{proof}
  $\tau_H$ is cooked up in such a way that
  $\tau_H\vert_{V\cap\ensuremath{\mathcal{R}}(G)\times P}$ has image in
  $\ensuremath{\mathcal{R}}(G)$. We prove the lemma for elementary automorphisms
  arising from amalgamations. The argument in the case of an
  \textsc{HNN}\ extension is identical.

  Let $K_i=\Ker(\wt{G}_i\twoheadrightarrow G),$ and
  $\set{r_j^i}_{j=1..\infty}$ an enumeration of $K_i$.  Since finitely
  generated rings of polynomials over $\mathbb{C}$ are Noetherian,
  there exists $k<\infty$ such that
  \[\rho_i\in\ensuremath{\mathcal{R}}(G_i)\iff\forall j\leq k\left(\ensuremath{\mathrm{ev}}_{r^i_j}(\rho_i)=I_2\right)\]
  The inclusions $E\hookrightarrow G_i$ induce restriction maps
  $\ensuremath{\mathcal{R}}(G_i)\to\ensuremath{\mathcal{R}}(E)$.  Since $G$ is the pushout of the
  diagram $\set{E\hookrightarrow G_i},$ the representation variety $\ensuremath{\mathcal{R}}(G)$
  is the pullback of the diagram $\set{\ensuremath{\mathcal{R}}(G_i)\to\ensuremath{\mathcal{R}}(E)},$
  and we identify $\ensuremath{\mathcal{R}}(G)$ with the set of pairs
  $(g,h)\in\ensuremath{\mathcal{R}}(G_1)\times\ensuremath{\mathcal{R}}(G_2)$ such that the restrictions
  $g\vert_E$ and $h\vert_E$ agree. Since $E$ is finitely generated
  there are relations $g^l_i\in F_i,$ $l=1..m,$ corresponding to
  generators of $E,$ such that

  \[\rho=(\rho_1,\rho_2)\in\ensuremath{\mathcal{R}}(G)\subset\ensuremath{\mathcal{R}}(G_1)\times\ensuremath{\mathcal{R}}(G_2)\iff\forall l\left(\ensuremath{\mathrm{ev}}_{g_l^1}(\rho_1)=\ensuremath{\mathrm{ev}}_{g_l^2}(\rho_2)\right)\]

  The Dehn twists $\tau_H$ clearly preserve the relations
  $\ensuremath{\mathrm{ev}}_{r_i^j}$ and since $e\inZ_{G_2}(E),$
  \[
    \rho_2(g_l^2)^{\exp(z\cdot\log(\eta(e)))}=\rho_2(g_l^2)
    \]
  for all $g_l^2$. Since $\tau_H$ doesn't change the values of this
  finite set of equations, $\tau_H(V\times P)\subset\ensuremath{\mathcal{R}}(G)$.

  The intersection of an irreducible algebraic variety with an open
  subset of $\mathbb{C}^{4n}$ is an analytic variety. If the
  intersection $V_i=V\cap\ensuremath{\mathcal{R}}(G)_i$ is irreducible then
  $V_i\times P$ is also irreducible. The image of an irreducible
  complex analytic variety under a holomorphic map has irreducible
  closure (preimages of closed sets are closed), hence must have image
  in an irreducible component of the range, in this case
  $\ensuremath{\mathcal{R}}(G)$. Thus, since $V_i\nsubseteq\cup_{j\neq
  i}\ensuremath{\mathcal{R}}(G)_j,$ $\tau_H(V_i\times
  P)\subset\ensuremath{\mathcal{R}}(G)_i$.
\end{proof}

\begin{definition}
  Let $\ensuremath{\mathcal{R}}_2(G)$ be the union of the irreducible components of
  $\ensuremath{\mathcal{R}}(G)$ such that for all $g\in G,$ $\trace(\ensuremath{\mathrm{ev}}_g(\text{ }))+2$
  doesn't vanish. A component $V$ of $\ensuremath{\mathcal{R}}(G)$ is a component of
  $\ensuremath{\mathcal{R}}_2(G)$ if, for every $g\in G,$ there is $\rho\in V$ such
  that $\trace(\rho(g))\neq-2$.
\end{definition}

\begin{theorem}
\label{autspreservecomponents}
  Suppose $\tau_{\Delta,e}$ is an elementary automorphism of $G,$
  $\rho\in\ensuremath{\mathcal{R}}(G)_i,$ and $\trace(\rho(e))\neq -2$. Then
  $\tau_{\Delta,e}(\ensuremath{\mathcal{R}}(G)_i)=\ensuremath{\mathcal{R}}(G)_i$.

  The modular group acts trivially on the set of irreducible
  components of $\ensuremath{\mathcal{R}}_2(G)$.
\end{theorem}

\begin{proof}
  By Lemma~\ref{maintwistlemma} for an appropriate triple
  $(\wt{e},S,V),$ the 1-parameter family of Dehn twists $\tau_H$ maps
  $V_i\times P$ to $\ensuremath{\mathcal{R}}(G)_i$ as long as $V_i$ is irreducible. The
  restrictions $\tau_H\vert_{V_i\times\set{0}}$ and
  $\tau_H\vert_{V_i\times\set{1}}$ agree with the restrictions of
  $id_{G}$ and $\tau_{\Delta,e},$ respectively. Thus $\tau_{\Delta,e}$
  maps $V_i$ to $\ensuremath{\mathcal{R}}(G)_i,$ and since $\tau_{\Delta,e}$ is an
  automorphism, $\tau(V_i)$ cannot lie in the intersection
  $\ensuremath{\mathcal{R}}(G)_i\cap(\bigcup_{j\neq i}\ensuremath{\mathcal{R}}(G)_j)$. Thus
  $\tau(\ensuremath{\mathcal{R}}(G)_i)$ shares a point with
  $\ensuremath{\mathcal{R}}(G)_i\setminus(\bigcup_{j\neq i}\ensuremath{\mathcal{R}}(G)_j),$ hence
  $\tau(\ensuremath{\mathcal{R}}(G)_i)=\ensuremath{\mathcal{R}}(G)_i$.

  If $\tau_{\Delta,e}$ is an elementary automorphism of $G$ and
  $V$ is a component of $\ensuremath{\mathcal{R}}_2(G),$ then there is a
  representation $\rho\in V$ such that $\trace(\rho(e))\neq-2$. By
  the above, $\tau(V)=V$. Since the modular group is generated
  by elementary automorphisms, the claim holds.
\end{proof}

\par If $\phi\colon G\to H$ is a homomorphism then
$\phi^{-1}(\ensuremath{\mathcal{R}}_2(H))\subset\ensuremath{\mathcal{R}}_2(G)$. If $V$ is a
component of $\ensuremath{\mathcal{R}}_2(H)$ then $\phi^{-1}(V)$ is contained
in some irreducible component $W$ of $\ensuremath{\mathcal{R}}(G)$. If
$g\in G$ and $\phi(g)\neq 1$ then $\trace(\ensuremath{\mathrm{ev}}_g(\text{ }))+2$ doesn't
vanish on $W$ since it doesn't vanish on $V$. If $\phi(g)=1$
the same holds since $\trace(I_2)=2$.

\section{Application to strict resolutions of limit groups}

\par In this section we give our main application of
Theorem~\ref{autspreservecomponents}: a bound on the length of a
strict resolution of a limit group which depends only on its
rank. Limit groups possess two qualities which make the theory
developed so far useful: many maps to free groups, which have large
representation varieties, and large automorphism groups generated by
Dehn twists in one-edged splittings.

\par We give only enough definitions to make sense of the statement of
the theorem and its proof. They will be very economical. For more
information on limit groups see the exposition by Bestvina and Feighn
\cite{bf::lg} or Sela's original work \cite{sela::dgog1}.

\par A homomorphism $\ensuremath{\mathbb{F}}\to\ensuremath{{SL}(2,\mathbb{C})}$ is \term{nondegenerate} if it is
injective and every element has image with trace not equal to $-2$.

\begin{definition}
  The \term{essential subvariety}, $\ensuremath{\mathcal{R}}_{e}(L),$ comprises the
  irreducible components $V$ of $\ensuremath{\mathcal{R}}(L)$ such that there is a
  nondegenerate $i\in\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$ and a sequence $f_n\colon
  L\to\ensuremath{\mathbb{F}}$ converging to $L,$ such that $i\circ f_n\in V$.
\end{definition}

\par The important feature the essential subvariety has is that for
all $g\in L$ the evaluation map $\ensuremath{\mathrm{ev}}_g$ takes non-identity values
on every component. The essential subvariety for a limit group is
non-empty since $\ensuremath{\mathbb{F}}$ has a nondegenerate embedding in $\ensuremath{{SL}(2,\mathbb{C})},$
limit groups are $\omega$--residually free, and $\ensuremath{\mathcal{R}}(L)$ has
finitely many components. Since there exist nondegenerate elements of
$\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}}),$ $\ensuremath{\mathcal{R}}_{e}(L)\neq\emptyset$. By definition
$\ensuremath{\mathcal{R}}_{e}(L)\subset\ensuremath{\mathcal{R}}_2(L)$.

\begin{lemma}
  \label{basicdimensioninequality}
  If $\pi\colon L\twoheadrightarrow L'$ is strict then
  $\ensuremath{\mathcal{R}}_{e}(L')\subset\ensuremath{\mathcal{R}}_{e}(L)$ and if
  $V'\subset V$ are irreducible components of
  $\ensuremath{\mathcal{R}}_{e}(L')$ and $\ensuremath{\mathcal{R}}_{e}(L),$ respectively,
  then $\dim V'<\dim V$. Thus
  $\dim\ensuremath{\mathcal{R}}_{e}(L')<\dim\ensuremath{\mathcal{R}}_{e}(L)$.
\end{lemma}

\begin{proof}
  To prove the first part of the claim, choose an irreducible
  component $V'$ of $\ensuremath{\mathcal{R}}_{e}(L')$ and an irreducible
  component $V$ of $\ensuremath{\mathcal{R}}(L)$ containing $V'$. We show
  that $V\subset\ensuremath{\mathcal{R}}_{e}(L)$.

  Choose a sequence $f_n\in\Hom(L',\ensuremath{\mathbb{F}})$ converging to $L',$ and a
  nondegenerate $i\in\ensuremath{\mathcal{R}}(\ensuremath{\mathbb{F}})$ such that $i\circ f_n$ is
  contained $V'$ for all $n$. Choose $\phi_n\in\Mod(L)$ such that
  $g_n=f_n\circ\pi\circ\phi_n$ converges to $L$. Since
  $\ensuremath{\mathcal{R}}_2(L')\subset\ensuremath{\mathcal{R}}_2(L)$ we have
  $\ensuremath{\mathcal{R}}_{e}(L')\subset\ensuremath{\mathcal{R}}_2(L)$. By
  Theorem~\ref{autspreservecomponents}, the $\phi_n$ fix $V$ setwise
  and we have $i g_n\in V$ for all $n,$ hence $V$ is a component of
  $\ensuremath{\mathcal{R}}_{e}(L)$ and we have the claim.

  To prove the second claim choose some $g\neq
  1\in\Ker(L\to L')$. By the definition of the essential
  subvariety, the evaluation map $\ensuremath{\mathrm{ev}}_g$ doesn't vanish on any
  irreducible component of $\ensuremath{\mathcal{R}}_{e}(L)$ and, since
  $g\in\Ker(\pi),$ $\ensuremath{\mathrm{ev}}_g$ vanishes on $\ensuremath{\mathcal{R}}_{e}(L'),$ hence the
  inequality on dimensions of irreducible components is strict.

  The last statement follows immediately from the first two.
\end{proof}

\begin{proof}[Proof of Theorem~\ref{strictlengthbound}]
  We prove only the second assertion. Let
  $\ensuremath{\mathbb{F}}_n\twoheadrightarrow L_1\twoheadrightarrow\dotsc\twoheadrightarrow L_k\cong\ensuremath{\mathbb{F}}_m$ be a strict
  resolution and consider the sequence of essential subvarieties
  \[\ensuremath{\mathcal{R}}_{e}(L_k)\cong\ensuremath{{SL}(2,\mathbb{C})}^m\subset\dotsb\subset\ensuremath{\mathcal{R}}_{e}(L_1)\subset\ensuremath{{SL}(2,\mathbb{C})}^n\]
  Let $d_i=\dim(\ensuremath{\mathcal{R}}_{e}(L_i))$. Since
  $L_i\twoheadrightarrow L_{i+1}$ is strict and proper, by
  Lemma~\ref{basicdimensioninequality}, $d_i>d_{i-1}$. Since $d_k=3m$
  and $d_1\leq 3n,$ $k$ must be at most $3(n-m)$.
\end{proof}

\section{Accessibility for limit groups}

\par Sela proves~\cite[Theorem~4.1 and Proposition~4.3]{sela::dgog1}
that the height of the cyclic analysis lattice of a limit group is
quadratic in the first Betti number. One application of
Theorem~\ref{strictlengthbound} is the following companion to Sela's
result. This kind of argument is used
in~\cite[Theorem~\ref{STABLE-lem:depthbound}]{louder::stable}
and~\cite[Theorem~\ref{ROOTS-analysislatticebound}]{louder::roots}.

\begin{definition}[Analysis lattice]
  The abelian (cyclic) analysis lattice of a finitely generated group
  $G$ is the following tree of groups. Free and abelian groups
  have no children.
  \begin{itemize}
    \item Level 0 consists of $G$.
    \item Level 0.1 consists of the freely indecomposable free factors
      of $G$ and the free group of some Grushko free factorization
      of $G$. The groups in level 0.1 are the children of the node
      labeled $G$.
    \item Level 1 consists of the rigid, abelian, and quadratically
      hanging subgroups in the abelian (cyclic) \textsc{JSJ}'s of the freely
      indecomposable free factors of $G$ at level 0.1. The parent of a
      group at level 1 is the freely indecomposable free factor it is
      a subgroup of.
    \item Level 1.1 is constructed exactly as level 0.1 was.
\end{itemize}
\end{definition}

\begin{theorem}
  The height of the abelian analysis lattice of a limit group is
  bounded by three times its rank.
\end{theorem}

\begin{remark}
  Before we begin, note if that $L_v$ is a vertex group of the abelian
  \textsc{JSJ}\ decomposition of $L$ then the restriction of every modular
  automorphism to $L_v$ agrees with the restriction of an inner
  automorphism since $ L_v$ is elliptic in every splitting of $L$ over
  an abelian subgroup. If $\pi\colon L\to L'$ is strict and
  $g\in\ker(L_v\to L'),$ then $g$ is in the kernel of every element of
  $\pi\circ\Mod(L)$. Since $\pi$ is strict $g$ must be the identity
  element, therefore $L_v$ embeds in $L'$.
\end{remark}

\begin{proof}
  Let $L$ be a limit group generated by $n$ elements. We prove
  something slightly more general: that the height of the abelian
  analysis lattice is bounded linearly by the length of the shortest
  strict resolution $L$ admits. Observe that if $L'< L$ then any
  strict resolution of $L$ restricts to a strict resolution of $L'$.

  Let $L=L_1\twoheadrightarrow L_2\twoheadrightarrow\dotsb\twoheadrightarrow L_k$ be a shortest strict
  resolution of $ L$. If $k=1$ then $L$ has height $0$ and we may
  stop. Otherwise, let $L''$ be a group at level 1 of the analysis
  lattice. If $L''$ is free or abelian it has height 0 so we may stop
  the procedure. If not, then by the previous paragraph $L''$ embeds
  in $L_2,$ and by induction the height of the abelian analysis
  lattice of $L_2$ is at most $k-1,$ the height of the analysis
  lattice of $L''$ is at most $k-1$. Since the analysis lattice of $L$
  is obtained by grafting the analysis lattices of the vertex groups
  of the freely indecomposable free factors of $L$ (the groups $L''$)
  to the leaves at level $0.1$ in the analysis lattice of $L,$ its
  height is at most $k$. Since $k\leq 3n$ the theorem is proven.
\end{proof}

\section{Remarks}

\par There is an easier proof of Theorem~\ref{strictlengthbound} which
does not use modular group and generalizes to limit groups over linear
groups. One uses equational Noetherianness, the fact that the
representation variety has only finitely many components, and a
diagonal argument to achieve the same end.

The preprint~\cite{houcine-2008} of Ould-Houcine is written in more
model theoretic language than this paper, and uses an argument like
the above. Theorem~\ref{strictlengthbound} follows from his bound on
the Cantor-Bendixon rank of the closure of the space of marked free
groups plus finite presentability. To clarify, if a sequence of marked
limit groups $(G,S_i)$ converges to a marked limit group $(H,S),$ then
$H$ has a strict homomorphism onto $G$. Conversely, let $S$ be a
generating set for $H,$ and fix a strict homomorphism $\pi\colon
H\twoheadrightarrow G$. Suppose $f_i\colon G\to\ensuremath{\mathbb{F}}$ converges to $G$. If
$f_i\circ\pi\circ\phi_i,$ $\phi_i\in\Mod(H),$ converges to $H,$ then
the sequence of marked limit groups $(G,\pi\circ\phi_i(S))$ converges
to the marked limit group $(H,S)$.

\bibliographystyle{amsalpha}

redpajama_set_name: RedPajamaArXiv


We all have spiritual gifts … more than one. Do you know what yours are?
Taking a spiritual gifts quiz can be very eye opening, and a HUGE help in pointing you in the direction of your awesome destiny.
One of my gifts is the Gift of Encouragement … shocking, I know! Another is the Gift of Faith. It's part of what makes me believe in the impossible and reach for the stars. Total Thrive is a perfect example of how I'm using both of those spiritual gifts to fulfill my destiny.
This link takes you to a site with a 10-12 minute quiz. You'll get some awesome feedback on what your results say about how God uniquely wired YOU!
It's OK! You can come back as soon as you've discovered your spiritual gifts!


Laura offers a variety of different types of readings. Set up an appointment and we'll discuss the right one for you!
30 minute readings are not done in person. They are offered by phone and Skype.
15 minute readings are not done in person. They are offered by phone and Skype.
What Is A Psychic Soul Reading and Spiritual Clearing?
Eckhart Tolle, spiritualist and author of the The Power of Now states that "…there is such a thing as old emotional pain living inside you." It is an accumulation of painful life experience that were not fully faced and accepted in the moment it arose. It leaves behind an energy form of emotional pain. The energy from the emotional pain comes together with other energy forms from other instances, and so after some years you have a "pain-body" an energy entity consisting of old emotion. Pain-body is an accumulation of stagnant negative emotions caused by experiences that were not faced, accepted and eventually integrated with the victim's energy field.
My work primarily consists of channeling into my client's unconscious and sabotaging habits, conditions and reflexes (pain-body) that block them from manifesting their own desires. I psychically connect with one's soul in order to advise them in their specific needs and guide them to their soul's path and purpose. Through a step-by-step and individualized program, I provide life coaching and design strategies to ensure success for my clients in order to holistically improve their well-being in a spiritual, mental and physical sense.
A soul's reading allows me to explore the many layers of you, while revealing untruths and distorted perceptions of how you see yourself and the world around you. These perceptions cause individuals to have poor life experiences. A soul reading will help you identify what unconscious and sabotaging habits, conditions, and reflexes are blocking happiness, health, wealth, and success from manifesting within your life.
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Aura Tuners to Clear and Balance Chakras. Repairs Rips, holes, and Tears. Remove psychic hooks, attachments and raise energy vibration.
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Hypnosis to clear sabotaging programs and reprogram the subconscious mind.
Laura will help couples become aware of their own emotional and psychological blocks which trigger their partners and sabotage the happiness and wellness of the relationship.
Laura Taps into what unconscious wounds trigger sabotaging behaviorism which block emotional fulfilling and overall healthy relationships.
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Members of Grassroots Alexandria in front of the Confederate monument in Old Town.
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Wonderfully designed monument in Old Town. Really wonderful.


San Onofre is much more than a wave and much more than a beach. It is a community of incredible people. A place where many go to escape. San Onofre has brought the world together, drawing interest from surfers everywhere. It has been featured in Hollywood films and TV shows, magazines, and is a key Southern California destination for anyone looking to experience untainted classic California surf vibes. It is our home.
SanO is also borrowed land from the military — on a lease with the military that ends in 2021. We can only hope that the history, the vibes, the community, and all that this place means to us are enough for the military to renew that lease.
If you didn't know, there once was a time you had to be a member of the San Onofre Surfing Club in order to access this beach. The club was also instrumental in the negotiations of the lease between the military and state, offering to preserve the historical vibe of Classic San Onofre. If there's any way we can all help this, it is to show our strength in numbers by becoming a member of the club. The contributions to the club help with keeping the dirt road a dirt road (not paved), it keeps the beach accessible through road grading, it has helped with preserving the access point when the rains and tides nearly washed away and narrowed our entry road, they've maintained our showers, act as our main source of contact with the state, and the list goes on. If you love SanO as much as I and you aren't a member, you absolutely should be. It's the only thing we can really do to help show the military how much of us really love this place. I don't know about you, but I'm not really sure what I would do without this amazing stretch of paradise.


text:
Leading criminals from Russian literature
Culture.ru
Georgy Taratorkin as Rodion Raskolnikov in 1970 Crime and Punishment.
kinopoisk.ru
A host of writers, from Gogol to Dostoevsky, were fascinated by the act of killing and its effect on the human psyche. We look at some of the best depictions of murder from Russia's rich literary history.
Rodion Raskolnikov ('Crime and Punishment' by Fyodor Dostoevsky)
Georgy Taratorkin as Rodion Raskolnikov in 1970 'Crime and Punishment' movie. Source: kinopoisk.ru.
Raskolnikov is, without doubt, the most famous criminal in the annals Russian literature. His is the eponymous crime, of killing an elderly pawnbroker, in the beginning of Dostoevsky's novel 'Crime and Punishment.' After the murder, he is tormented about his act for the rest of the novel. Many other writers and filmmakers have taken inspiration from this crime and its psychological implications. Even though he is an impoverished student, Raskolnikov does not kill the pawnbroker for money. Instead, he kills him to understand "whether he is a trembling creature or whether he has the right …"
Katerina ('Lady Macbeth of Mtsensk' by Nikolai Leskov)
Natalia Andreichenko as Lady Macbeth. Source: kinopoisk.ru
The cold-blooded Katerina first poisons her father-in-law, who has seen her lover leaving her room at night, and then threatens to tell her husband. Then her lover says he wants to marry her; and get her money; after which the pair kill Katerina's husband. They then kill her young nephew, who is standing in the way of Katerina inheriting her husband's estate. When she finds her lover in bed with another woman, she throws her off a ferry, causing both to drown.
Yuli Karandyshev ('Without a Dowry' by Alexander Ostrovsky)
Oleg Myagkov as Yuli Karandyshev in Nikita Mikhalkov's 'Cruel Romance.' Source: kinopoisk.ru
This pathetic, cowardly fellow from Ostrovsky's play Without a Dowry is riddled with neuroses. Initially, he gains the reader's respect, as he wants to marry and save Larisa Ogudalova, a poor young woman without a dowry, whom nobody else wants to wed. She, however, falls in love with another man. When Karandyshev discovers that she has slept with the other man, he shoots the beautiful woman.
Taras Bulba ('Taras Bulba' by Nikolai Gogol)
Bogdan Stupka as Taras Bulba. Source: kinopoisk.ru
The Cossack Taras Bulba from Gogol's eponymous novel is cruel and merciless to his enemies – even if he is related to them. When Taras goes to war against Poland with his two sons, the younger one falls in love with a Polish girl and switches sides. This is considered an act of treason by the Cossacks, and when he meets his son in battle, Taras shouts "I gave you life, I will also kill you!" and shoots him. This is now a famous saying in Russian.
Gerasim ('Mumu' by Ivan Turgenev)
Gerasim and Mumu in 1987 animation film. Source: kinopoisk.ru
If ever there was a sad story for animal lovers, it's Turgenev's Mumu. The deaf and dumb peasant Gerasim calls his dog "Mumu" because these are the only sounds he can make. However, his old mistress forces him to kill the dog because it barks loudly and keeps her awake at night. Gerasim drowns the trusting dog in the river by tying bricks around its neck. Never again does he get another trusty companion.
RIR Literature


text:
Interview: Kyle Watson On His Favorite 'In The Morning' Remixes, Growing South African House Scene
Kyle Watson gives us his three favorite remixes from the new remix album.
Alexander Dias
Kyle Watson
Andre Labrune
Kyle Watson's debut album, Into The Morning, outlined the mind of a diverse musical talent and expanded the South African producer's sound well beyond anything he had produced in the ten years prior. While Watson had always been ahead of the curve and is arguably one of the architects of the current bass forward, tech-influenced sound that is dominating house music. His first attempt at a long-form work proved that he could express his artistic capabilities in many more meaningful ways. And now just less than a year from its release, he's handed the reigns to a small collection of friends and family to reinterpret what This Ain't Bristol calls "probably [it's] most exciting release."
Working in concert with his homies at This Ain't Bristol, Kyle has selected a handful of current heavyweights to create a remix album that is nearly as diverse as the original. The lineup includes label co-founders Maximono and Billy Kenny as well as Bart B More, OMNOM, Hood Rich, Stace Cadet, Mark Milgraves, Zeal and Mat.Joe. Drawing heavily from the tastemaker label's stable of innovative artists.
Into The Morning - The Remixes covers a lot of ground so we asked Kyle to pick out three of his favorite remixes and offer his thoughts on each. You can listen and buy the whole collection now from your favorite retailer/ streaming service. We also caught up with him to chat about the process of putting the original album together, how it felt to see the remix album come together, and what's next for the South African scene.
Can you pick 3 remixes and tell us a little about each?
You Boy (Billy Kenny Remix)
The thing I love most about this remix is that peaced out buildup that starts from the first second of the track. Billy built the tension so well with that single pitched string note, and when it all finally kicks in it just slaps you in the face with this crazy weight and energy!
Control Ya (Bart B More Remix)
The thing I love most about this particular remix is that main buildup in the middle of the track. The way it drops in with that glitchy synth pattern and ravey stabs is just so effective and the tune just works so well in the second half of my sets.
Lights On (Zeal Remix)
The original is one of my personal top 3 tunes that I have produced, so I had high expectations for the remix. I'm a MAJOR fan of drum n bass, and we decided that the tempo changes in "Lights On" would work perfectly in this genre. Zeal did an amazing job on the remix here.
Those are just some of my favorites but honestly, the whole pack is so so strong, All the remixers just smashed it, and you can easily listen to it from start to finish without losing interest.
It's been a year since you released your album "Into The Morning". Do you feel like your approach to production and DJing has changed as a result?
I can't believe it's been a year already! I definitely think that after writing "Into The Morning" I definitely have become a bit more experimental in the studio, trying out different things and not necessarily limiting myself to what I've been familiar with in the past.
Was a remix album always part of the plan?
I think it was a given that the remix album would happen right from the start. Into The Morning is an eclectic album with very remixable tracks, and I was very excited to see how others would interpret my music off of it. Every artist on the record has exceeded my expectations. I have said in an earlier interview that I can listen to the whole package from start to finish and not get bored, so it's been very exciting to hear my original ideas re-interpreted!
How did you go about selecting who would be good for remixing each song?
This was a very organic process between myself and This Ain't Bristol. We both had our suggestions, so we put a wishlist together and started sending out the remix stems to the artists. Some we gave the choice to choose a track, others we selected particular songs for that we felt they would resonate with.
With artists like yourself, Das Kapital, and Black Coffee really beginning to dominate house music, where do you see South Africa going in the next few years as a destination for performers?
Firstly I'd really love to see more South Africans touring globally. There are local artists that are absolutely smashing it lately on a global level - Das Kapital being one of them – so I think the potential is there for touring on a bigger scale. Secondly, exciting things are happening in South Africa at the moment in the scene, with brands like Mixmag doing their Lab series here and great artists visiting our venues. I'd like to see that momentum keep up over the next few years.
How has becoming a touring DJ expanded your sonic palette?
Without a doubt, both on a production and a performance level. Since I started touring properly, I've noticed that my sets now have more depth and I find myself playing out records that I probably would have scrolled past before. I think it's great to get that experience on a global level and take that back to your home country because it helps you as an artist and also helps the scene you go back to at the end of the day. It all feeds into the production as well and has helped me grow creatively as an artist.
MaximonoMat.JoeThis Ain't BristolBart B MoreStace CadetKyle WatsonBilly KennyHood RichOmnomHouse MusicInto The MorningBass House
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Magnetic Exclusive: Kyle Watson 'Into The Morning' Album Mix & Tour Announcement
Premiere: Kyle Watson Blows Up Like A 'Landmine' With New Single
By Ryan Middleton
Event: Kyle Watson [Halcyon SF] + Exclusive Mix & Interview
By Kane


text:
May 15: ON THIS DAY in 1948, bombings in Tel Aviv
ON THIS DAY IN 1935, the Brooklyn Daily Eagle reported, "Auxiliary Bishop Raymond A. Kearney yesterday confirmed a class of 310 children and 40 adults at the Holy Innocents R.C. Church, Beverly Road and E. 17th St., where he served as a curate in the early days of his priesthood. The church was filled to overflowing for the service, which was held in the late afternoon. Impressing upon the children the importance of the sacrament of confirmation, the bishop said that, in its reception, they would become 'soldiers of Jesus Christ.'"
ON THIS DAY IN 1939, the Eagle reported, "Quebec, May 15 (U.P.) – King George and Queen Elizabeth, surfeited with fog and ice, got their first glimpse of the New World today. The liner Empress of Australia, carrying the British monarchs on their first voyage to America, came in sight of the southern tip of Newfoundland at 7:30 a.m. Shortly thereafter, according to radio messages from the vessel, the ship passed within 18 miles of St. Pierre and Miquelon Islands, whose snow-covered hills glistened in the sunlight. Delayed two days, first by fog and then by icebergs which floated dangerously close, the liner finally found perfect sailing weather as it made the first landfall of the voyage."
ON THIS DAY IN 1945, the Eagle reported, "Oslo, Norway, May 15 (U.P.) – Vidkun Quisling, the world's most famous traitor, is cleaning the toilets of Olso's biggest prison, the United Press learned exclusively today. My informant, one of only six men who have seen the arch-traitor since he surrendered six days ago, said Quisling has been given the most menial tasks at the prison at Moellergarten 19. Nevertheless Quisling, 58 and fat, insists he is still the legal head of the Norwegian government. He complains constantly about his prison treatment. Two tough guards with tommy-guns stand over the puppet premier while he goes to work with a brush and a bucket of water."
ON THIS DAY IN 1948, the Eagle reported, "Tel Aviv, May 15 (U.P.) – Arab planes bombed Tel Aviv three times today and one Egyptian air force pilot was taken prisoner when his plane was forced down just north of the new Jewish capital. The Egyptian government in Cairo announced officially that Egyptian planes raided the newborn State of Israel in the forefront of an Arab attack from all sides, including one raid on a Jewish airdrome outside Tel Aviv … Egyptian troops driving into Palestine have 'wiped out' a Jewish settlement on the road to Beersheba, an official communique in Cairo said today … Jewish sources said direct Arab-Jewish negotiations for a truce in Jerusalem were started after Jews captured virtually all strongpoints abandoned by the British in the Holy City … Egyptian troops spearheaded the Arab assault, attempting an amphibious landing 21 miles south of Tel Aviv and crashing across the southern Palestine border at two points. Syrian and Lebanese troops roared down across the northern frontier several hours before the midnight deadline, riding into battle in 150 armored trucks."
ON THIS DAY IN 1963, Eagle sports columnist Steve Solomon wrote, "Mama Throneberry just didn't pick the name 'Marvin Eugene' out of a hat when she gave identity to her bouncing baby boy back on September 2, 1933 in the town of Collierville, Tennessee. Something inside of her told her that the baby with the round full face and the long legs had to have the initials M.E.T. Possibly she didn't realize why, but 29 years later the answer was clear as the mud on her son's uniform. If Albert Einstein was born with the brain of a mathematical genius; if Babe Ruth was born to be the king of swat, then Marvin Eugene Throneberry was born to be a Met. Why are men set aside, given certain unquestionable abilities and then sent on [their] way to fulfill their life's purposes? Who can say? But it was in the cards that Marvelous Marv would become the living legend of a ballclub who would bring the National League back to New York."


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Tournaments > 2010 > Austria > European Poker Tour - EPT Vienna
Tournament: European Poker Tour - EPT Vienna
Date: Oct 25 - 31, 2010
Venue: Kursalon Vienna, Austria
Event: No Limit Hold'em II (Oct 30 - 31, 2010)
Buy-in: €1,000 + €100
Prize: €79,000
Oct 25, 2010 No Limit Hold'em - Turbo €300 + 30
Oct 26 - 31, 2010 PSLIVE No Limit Hold'em - EPT Main Event €5,000 + 300
Oct 26, 2010 No Limit Hold'em - Bounty €400 + 30
Oct 27, 2010 No Limit Hold'em - Bounty €1,000 + 100
Oct 28 - 29, 2010 No Limit Hold'em €2,000 + 150
Oct 28 - 29, 2010 Pot Limit Omaha €1,000 + 100
Oct 29 - 30, 2010 No Limit Hold'em - Heads Up €3,000 + 200
Oct 29, 2010 No Limit Hold'em €1,000 + 100
Oct 29, 2010 8 Game €1,000 + 100
Oct 30 - 31, 2010 No Limit Hold'em €10,000 + 300
Oct 30 - 31, 2010 No Limit Hold'em II €1,000 + 100
Oct 30, 2010 No Limit Hold'em - Women's Event €300 + 30
Oct 30 - 31, 2010 H.O.R.S.E. €1,000 + 100
Oct 30, 2010 No Limit Hold'em - Turbo Bounty €400 + 30
1st Dylan Linde $14,302 €10,250 — —
2nd Jae Kim $40,185 €28,800 — —
3rd Josua Eich $24,278 €17,400 — —
4th Igor Salomasov $10,465 €7,500 — —
5th Dennis Goebel $7,716 €5,530 — —
6th Colaiemma Nunzio $5,511 €3,950 — —
7th Vitaliy Wolov $4,423 €3,170 — —
8th Berthold Winz $3,349 €2,400 — —