This morning we stopped by TI's power management group to check out what all they had in store, and got to check out some demos of their new second generation wireless power chipsets. The new solutions meet the 5W Wireless Power Consortium (Qi) standard, and have a smaller total package area. TI demoed the BQ51013 second generation small form factor power Rx PCB charging a variety of devices, including a Kindle. In addition, TI has some newer small form factor (BQ5002010 and BQ5002011) charging Tx solutions that further reduce BOM cost and require lower input voltage compared to their first generation counterparts.
TI also briefly teased its upcoming 10W solution charging an iPad 2. Though the current standard is just 5W for smartphones (1A@5V) obviously charging tablets and larger devices is something coming down the road for the Wireless Power Consortium. At present, inductive chargers achieve around 70% efficiency.
At present, inductive chargers for smartphones generally require an external sleeve or accessory battery cover with the inductive coil and charger inside. Newer second-generation Rx solutions will drive down the size of the inductive charging solution, and inductive coils PCB (instead of hand-wound coils) will make it possible to eventually also make including wireless charging support on the boards themselves.
You haven't used a TouchPad or a Pre have you?
Touchstone makes plugging in USB over and over look ridiculous.
I also think touchstone means I use the TouchPad more often - no effort to charge, just drop it on the stand, you don't even have to line it up exactly.
I wish this thing had an edit button.
Further to this, all phones are STILL going to have microUSB, so it's not like that choice is stolen from you.
I completely agree with everything said above. I use my Touchpad a lot more now that I can just grab it, use it and set it back on the Touchstone for charging. Also helps if you have cats or kids who like to tug on cables, of which I have both.
It sounds like we're just lazy and bought a gimmicky product but it really does seem to change the way you use it. I do think $50 (originally $80) is a ridiculous price but I purchase mine for $30 and would do it again in an instant.


text:
News & Media > District News >
Proud to have been a Patriot!
posted Jun 7, 2017, 6:28 AM by Brenda Williams
I have had the distinct honor of serving as the Pequot Lakes High School Principal for the past seven years. As this school year comes to an end, it will also mark the end of my time as a Patriot; at least for now. It's been an incredible opportunity for our family of six, including four school-aged children, to have grown up in a healthy and supportive environment. Our communities are very blessed to have an extremely high-performing school district, which strives to treat each student like their own child.
I want to begin by informing and thanking our entire school community for the growth in achievement and opportunity we have experienced over the past several years. First and foremost, the improvement and investment in facilities has made a significant impact in the access our students have to STEM programming, technology, and significantly improved learning environments. As a result, the Class of 2017 will go down as the highest overall ACT achievement graduating class, with 13 students in the Class of 2017 having scored a 30 or better on the ACT. Furthermore, 12 students will be earning an Associate's Degree in addition to their High School Diploma at graduation because of our awesome partners at Central Lakes College.
I want to personally thank the ISD #186 School Board for the support and investment they have made in the building level, grass roots initiatives undertaken in the last seven years. The seven--period day, the full implementation of PLTW, the investment in programming that allowed 73 students to earn an Associate's Degree in addition to their HS Diploma are just a few of the initiatives we have successfully implemented as a result of the School Board's support. In addition, our students have access to technology to include devices, programs, and curriculum as a direct result of our local School Board's investment. Over the last seven years, we have been allowed to select the very best teachers to fill openings, even when the cost surpasses that of a beginning teacher. I cannot think of a single item, initiative, or proposal that was brought to the Board that didn't receive complete support when it was warranted, and for that I want to say, "Thank you!"
It's critical that I share the admiration, respect, and pride I have in the staff at Pequot Lakes Schools. I have the advantage of working in the district along with having students in the district. It is fairly normal to observe teachers consistently working through lunch, coming in early or staying late, or providing support on weekends, holidays, and evenings to ensure each and every student succeeds. For instance, our Robotics and Trap coaches have volunteered to ensure programming was available to all interested students. Volunteer tutors, weight room supervisors, and chaperones always come forward, because without them, these opportunities would be lost. I can even recall countless times that financial aid was provided to students who were in need without any strings attached. The staff at Pequot Lakes High School truly love the kids they serve.
In closing, I would like to thank our families and communities for the support they have provided to our entire school team. The donations of time, money, and support are so deeply appreciated. I hope we continue to invest in our great schools!
-- Chip Rankin...Proud to have been a PATRIOT!

redpajama_set_name: RedPajamaCommonCrawl


text:
Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat
David A. Bereiter
Administration (DENT)
The importance of cervical spinal pathways on the adrenal secretion of catecholamines was assessed in chloralose-anesthetized cats. Partial transections of the upper cervical spinal cord were made ipsilateral (n = 21) or contralateral (n = 10) to the adrenal vein sampling catheter. Ipsilateral cuts evoked an immediate increase in the adrenal secretion of epinephrine that remained elevated at 60 min (+ 89.7 ± 27.0 ng/min, P < 0.001) and increased the epinephrine/norepinephrine secretory ratio from 1.99 ± 0.4 to 5.02 ± 0.6 by 60 min (P < 0.01) indicating a preferential augmentation of the secretion of epinephrine. The magnitude of the increase in secretion of epinephrine was well correlated with the cross-sectional area of the ipsilateral cut (rs = 0.681, P < 0.01). In contrast, partial transections of similar size made contralateral to the adrenal vein sample evoked significantly smaller increases in the adrenal secretion of epinephrine by 60 min (+ 12.7 ± 4.8 ng/min) and were not correlated with the cross-sectional area of the cut. The region of transection common to those experiments that caused the greatest increase in the secretion of catecholamines included the deep laminae (laminae V-VII) within the central gray matter as well as a portion of the dorsal columns. Transections restricted to the dorsolateral and lateral funiculi caused small and inconsistent changes in the adrenal secretion of catecholamines. Ipsilateral and contralateral cuts evoked similar effects on peripheral concentrations of catecholamines, on plasma adrenocorticotropin and on plasma angiotensin II, suggesting that the facilitatory effect of ipsilateral cuts on the adrenal secretion of catecholamines was not the result of a humoral mechanism. Arterial pressure and heart rate increased equally by 1 min and returned to prestimulus values by 5 min after transections of the ipsilateral or of the contralateral cervical cord. Electrical stimulation of the ipsilateral cervical spinal cord, caudal to the level of transection, decreased the secretion of epinephrine and arterial pressure by 1 min (-30.5 ± 9.0%, P < 0.05) suggesting the presence of an active inhibitory mechanism that persisted after transection. The results indicated that transections of pathways ipsilateral, but not contralateral, to the adrenal medulla that traverse the upper cervical spinal cord evoke a persistent increase in the adrenal secretion of epinephrine, whereas other indices of neuroendocrine or autonomic function do not reflect this tonic influence. The neural mechanism that underlies the apparent tonic inhibition of adrenomedullary function is distributed over a non-compact ipsilateral projection pathway that is not restricted to the dorsolateral or to the lateral funiculi.
Journal of the Autonomic Nervous System
Adrenal medulla
Autonomic nervous system
Cervical spinal cord
Fingerprint Dive into the research topics of 'Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat'. Together they form a unique fingerprint.
Cervical Cord Medicine & Life Sciences
Epinephrine Medicine & Life Sciences
Catecholamines Medicine & Life Sciences
Veins Medicine & Life Sciences
Arterial Pressure Medicine & Life Sciences
Chloralose Medicine & Life Sciences
Adrenal Medulla Medicine & Life Sciences
Bereiter, D. A. (1989). Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat. Journal of the Autonomic Nervous System, 27(3), 181-192. https://doi.org/10.1016/0165-1838(89)90112-4
Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat. / Bereiter, David A.
In: Journal of the Autonomic Nervous System, Vol. 27, No. 3, 08.1989, p. 181-192.
Bereiter, DA 1989, 'Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat', Journal of the Autonomic Nervous System, vol. 27, no. 3, pp. 181-192. https://doi.org/10.1016/0165-1838(89)90112-4
Bereiter DA. Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat. Journal of the Autonomic Nervous System. 1989 Aug;27(3):181-192. https://doi.org/10.1016/0165-1838(89)90112-4
Bereiter, David A. / Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat. In: Journal of the Autonomic Nervous System. 1989 ; Vol. 27, No. 3. pp. 181-192.
@article{167a1e5d44dd4ca993ae5fb3c2b1320a,
title = "Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat",
abstract = "The importance of cervical spinal pathways on the adrenal secretion of catecholamines was assessed in chloralose-anesthetized cats. Partial transections of the upper cervical spinal cord were made ipsilateral (n = 21) or contralateral (n = 10) to the adrenal vein sampling catheter. Ipsilateral cuts evoked an immediate increase in the adrenal secretion of epinephrine that remained elevated at 60 min (+ 89.7 ± 27.0 ng/min, P < 0.001) and increased the epinephrine/norepinephrine secretory ratio from 1.99 ± 0.4 to 5.02 ± 0.6 by 60 min (P < 0.01) indicating a preferential augmentation of the secretion of epinephrine. The magnitude of the increase in secretion of epinephrine was well correlated with the cross-sectional area of the ipsilateral cut (rs = 0.681, P < 0.01). In contrast, partial transections of similar size made contralateral to the adrenal vein sample evoked significantly smaller increases in the adrenal secretion of epinephrine by 60 min (+ 12.7 ± 4.8 ng/min) and were not correlated with the cross-sectional area of the cut. The region of transection common to those experiments that caused the greatest increase in the secretion of catecholamines included the deep laminae (laminae V-VII) within the central gray matter as well as a portion of the dorsal columns. Transections restricted to the dorsolateral and lateral funiculi caused small and inconsistent changes in the adrenal secretion of catecholamines. Ipsilateral and contralateral cuts evoked similar effects on peripheral concentrations of catecholamines, on plasma adrenocorticotropin and on plasma angiotensin II, suggesting that the facilitatory effect of ipsilateral cuts on the adrenal secretion of catecholamines was not the result of a humoral mechanism. Arterial pressure and heart rate increased equally by 1 min and returned to prestimulus values by 5 min after transections of the ipsilateral or of the contralateral cervical cord. Electrical stimulation of the ipsilateral cervical spinal cord, caudal to the level of transection, decreased the secretion of epinephrine and arterial pressure by 1 min (-30.5 ± 9.0%, P < 0.05) suggesting the presence of an active inhibitory mechanism that persisted after transection. The results indicated that transections of pathways ipsilateral, but not contralateral, to the adrenal medulla that traverse the upper cervical spinal cord evoke a persistent increase in the adrenal secretion of epinephrine, whereas other indices of neuroendocrine or autonomic function do not reflect this tonic influence. The neural mechanism that underlies the apparent tonic inhibition of adrenomedullary function is distributed over a non-compact ipsilateral projection pathway that is not restricted to the dorsolateral or to the lateral funiculi.",
keywords = "Adrenal medulla, Autonomic nervous system, Cervical spinal cord, Epinephrine, Norepinephrine",
author = "Bereiter, {David A.}",
journal = "Autonomic Neuroscience: Basic and Clinical",
T1 - Partial transection of the ipsilateral cervical spinal cord evokes a sustained increase in the adrenal section of catecholamines in the cat
AU - Bereiter, David A.
N2 - The importance of cervical spinal pathways on the adrenal secretion of catecholamines was assessed in chloralose-anesthetized cats. Partial transections of the upper cervical spinal cord were made ipsilateral (n = 21) or contralateral (n = 10) to the adrenal vein sampling catheter. Ipsilateral cuts evoked an immediate increase in the adrenal secretion of epinephrine that remained elevated at 60 min (+ 89.7 ± 27.0 ng/min, P < 0.001) and increased the epinephrine/norepinephrine secretory ratio from 1.99 ± 0.4 to 5.02 ± 0.6 by 60 min (P < 0.01) indicating a preferential augmentation of the secretion of epinephrine. The magnitude of the increase in secretion of epinephrine was well correlated with the cross-sectional area of the ipsilateral cut (rs = 0.681, P < 0.01). In contrast, partial transections of similar size made contralateral to the adrenal vein sample evoked significantly smaller increases in the adrenal secretion of epinephrine by 60 min (+ 12.7 ± 4.8 ng/min) and were not correlated with the cross-sectional area of the cut. The region of transection common to those experiments that caused the greatest increase in the secretion of catecholamines included the deep laminae (laminae V-VII) within the central gray matter as well as a portion of the dorsal columns. Transections restricted to the dorsolateral and lateral funiculi caused small and inconsistent changes in the adrenal secretion of catecholamines. Ipsilateral and contralateral cuts evoked similar effects on peripheral concentrations of catecholamines, on plasma adrenocorticotropin and on plasma angiotensin II, suggesting that the facilitatory effect of ipsilateral cuts on the adrenal secretion of catecholamines was not the result of a humoral mechanism. Arterial pressure and heart rate increased equally by 1 min and returned to prestimulus values by 5 min after transections of the ipsilateral or of the contralateral cervical cord. Electrical stimulation of the ipsilateral cervical spinal cord, caudal to the level of transection, decreased the secretion of epinephrine and arterial pressure by 1 min (-30.5 ± 9.0%, P < 0.05) suggesting the presence of an active inhibitory mechanism that persisted after transection. The results indicated that transections of pathways ipsilateral, but not contralateral, to the adrenal medulla that traverse the upper cervical spinal cord evoke a persistent increase in the adrenal secretion of epinephrine, whereas other indices of neuroendocrine or autonomic function do not reflect this tonic influence. The neural mechanism that underlies the apparent tonic inhibition of adrenomedullary function is distributed over a non-compact ipsilateral projection pathway that is not restricted to the dorsolateral or to the lateral funiculi.
AB - The importance of cervical spinal pathways on the adrenal secretion of catecholamines was assessed in chloralose-anesthetized cats. Partial transections of the upper cervical spinal cord were made ipsilateral (n = 21) or contralateral (n = 10) to the adrenal vein sampling catheter. Ipsilateral cuts evoked an immediate increase in the adrenal secretion of epinephrine that remained elevated at 60 min (+ 89.7 ± 27.0 ng/min, P < 0.001) and increased the epinephrine/norepinephrine secretory ratio from 1.99 ± 0.4 to 5.02 ± 0.6 by 60 min (P < 0.01) indicating a preferential augmentation of the secretion of epinephrine. The magnitude of the increase in secretion of epinephrine was well correlated with the cross-sectional area of the ipsilateral cut (rs = 0.681, P < 0.01). In contrast, partial transections of similar size made contralateral to the adrenal vein sample evoked significantly smaller increases in the adrenal secretion of epinephrine by 60 min (+ 12.7 ± 4.8 ng/min) and were not correlated with the cross-sectional area of the cut. The region of transection common to those experiments that caused the greatest increase in the secretion of catecholamines included the deep laminae (laminae V-VII) within the central gray matter as well as a portion of the dorsal columns. Transections restricted to the dorsolateral and lateral funiculi caused small and inconsistent changes in the adrenal secretion of catecholamines. Ipsilateral and contralateral cuts evoked similar effects on peripheral concentrations of catecholamines, on plasma adrenocorticotropin and on plasma angiotensin II, suggesting that the facilitatory effect of ipsilateral cuts on the adrenal secretion of catecholamines was not the result of a humoral mechanism. Arterial pressure and heart rate increased equally by 1 min and returned to prestimulus values by 5 min after transections of the ipsilateral or of the contralateral cervical cord. Electrical stimulation of the ipsilateral cervical spinal cord, caudal to the level of transection, decreased the secretion of epinephrine and arterial pressure by 1 min (-30.5 ± 9.0%, P < 0.05) suggesting the presence of an active inhibitory mechanism that persisted after transection. The results indicated that transections of pathways ipsilateral, but not contralateral, to the adrenal medulla that traverse the upper cervical spinal cord evoke a persistent increase in the adrenal secretion of epinephrine, whereas other indices of neuroendocrine or autonomic function do not reflect this tonic influence. The neural mechanism that underlies the apparent tonic inhibition of adrenomedullary function is distributed over a non-compact ipsilateral projection pathway that is not restricted to the dorsolateral or to the lateral funiculi.
KW - Adrenal medulla
KW - Autonomic nervous system
KW - Cervical spinal cord
KW - Epinephrine
KW - Norepinephrine
JO - Autonomic Neuroscience: Basic and Clinical
JF - Autonomic Neuroscience: Basic and Clinical


There are 16 top-rated car paint shops in your area and 35 to avoid.
Business Description: At Auto Paint Pros LLC, we understand your car is a personal investment, and that you want to maintain that investment by keeping your car looking and feeling new for as long as possible. That is why we deliver the cost effective solutions that your car needs to keep it looking good for years to come. We are based in North Naples, and provide service to Cape Coral, Fort Myers, Naples, Bonita Springs, and Estero. Accidents happen, even to the most meticulously cared for automobiles. You can trust our technicians to exceed all of your expectations.
Business Description: Serving Customers Since 1982. Collision repair and painting on all makes and models. All auto insurance companies accepted. Free Estimates.
Business Description: Full Service Collision Repair utilizing state of the art equipment and processes. AAA Approved facility. We use auto maker approved envronmentally safe waterbourne paint systems by Spies-Hecker. Lifetime Warranties. Insurance Claims Specialists. Factory Certified for Mercedes Benz, Porsche, Nissan, Infiniti, GM, Ford, Chrysler, and others.
Business Description: The owner of Naples Body & Fender in Naples, FL, Robin D. Shrock, has years of experience in collision repair and auto painting. Our team of technicians know the ins and outs of all major makes and models of automobiles. In fact, we do the job immediately if it is difficult. If it's impossible, it takes a little longer. We are locally owned, registered and insured for our clients' protection. We are also an authorized Accushade & PPG facility. Our services are guaranteed or warrantied depending upon the exact work done on your vehicle. Read below what one of our customers had to say about us. Award winning. Additional DBA - Robin Shrock Inc.
Business Description: We have been serving the Lehigh Acres area since 1988. Our state-of-the-art facility is conveniently located at the corner of Lee Blvd. and Sunshine Blvd. We work with all major insurance companies. We also offer 24-hour towing service.
Business Description: Our Columbia, SC auto body repair center specializes in minor collision repairs. We use a special auto body repair process called Paintless Dent Repair (PDR). This PDR process eliminates the need for painting your vehicle and dramatically speeds up the repair process. Since our process doesn't remove your paint, you're able to keep your factory finish as well as your factory paint warranty. Collision repair | Paintless dent repair | Bumper repair | Hail repair service. All work is satisfaction guaranteed and all technicians are certified and insured.
The insurance appraiser who handled our claim strongly Supreme Auto Collision of Naples. The shop is a Traveler���s Insurance authorized repair center. They advertise that they keep customers fully informed with emails, photos and phone calls. They were also recommended by the Naples Lexus dealership. My experience with this company was terrible. They continually misled me about their ability to repair my car in a timely fashion and the status of the repair work. I received no photos or emails and phone calls to them were of no use. I finally had to go back to them in person to learn the actual situation. I can���t hold them responsible for the significant additional expenditures I had but I can and do hold them responsible for lying to me. Because they consistently misrepresented the status of my car repair, I was forced to make expensive out-of-pocket last minute changes in important personal plans. In short, it was as bad a customer experience I have ever had.
Someone backed into my car and scraped the paint. I got several quotes...Naples Body and Fender made me feel most comfortable. They were able to schedule me at a convienient time, removed the rear bumper and repainted it. I took the car in and had it back the next day. It looks like new!
I took my 2003 Lexus IS300 to Supreme for a complete paint job and couldn't be happier with the results...and I'm picky. It is a very low mileage car that got the paint beat up in the hot FL sun. They fixed a few minor door dings, repainted the entire car, cleared the foggy headlights and detailed the entire car including under the hood. The car honestly looks like brand new. The paint is completely flawless, lays totally flat, no overspray and looks like a factory job. They even resprayed the black plastic grille and plastic cover around the windshield wipers. The job took about a week and cost me $2000 which is pretty much in line with other local estimates. The reviews here on AL and other places along with the lifetime guarantee cinched the deal for me. Go see JR, he does excellent work.
After, going to two national chains here in town, was disgusted with the quotes. It was like you drive a Mercedes, you must be made of money!!! Went on Angieslist found Naples Body and Fender, because of their and quot;Aand quot; rating and great reviews. . A LOCAL owner, acting as a local company!!! Quote was 1/3 of the National chains. The Mercedes came back looking as though nothing had happened!!! Beautiful condition!!! Timely, as promised and would recommend this local company to anyone and any model of car that you need body work on!!! Fabulous job!!! Professional, fare, honest and great down home people to work with!!!!
They even had Enterprise Rental Car pick me up for a day rate of $35.00 a day, while my car was repaired over two days!!! That is service!!!!
On 6/30/13, I was rear-ended in my Honda Odyssey. Our insurance agency recommended Collex. When I took the vehicle in they attended to me quickly and professionally. They gave me an estimate and an expected delivery date. Long story short: they finished ahead of time and did a fantastic job. The workmanship was the best I've seen and carried a lifetime warranty. Jason, the manager, explained exactly what they did (even painting parts underneath you cannot see) and their goal: to return the vehicle to original condition. Mission accomplished! This is the second time I've used Collex and I'm completely satisfied. The experience previous to Collex was an absolute nightmare. The body shop kept making mistakes-chipped paint, misplaced emblems, a cracked interior panel and overspray-and every time I would return the vehicle to repair the damage they had done they seemed to make new mistakes or cause new damage. Never again. Thanks Collex.
We couldn't have been happier with the service and repair. They were the lowest bid, repairing the damaged parts instead of ordering new ones. But to look at the car, you would never know. Both sides of the car look like new, with no differences between the right and left sides. He even touched up (with paint) small dings around the car that were not damaged in the accident. Very honest and professional. Repairs were even completed faster than expected. We will recommend him to all of our family and friends!
Everything went extremely well. Supreme Auto's estimate was the lowest and the staff was friendly and polite. The car was only in the shop for 2 days and it truly looked better than ever when the work was completed.
I would use Supreme Auto Collision again and highly recommend their services to others.
They quoted a price that was half of what everyone else quoted and the quality was great. It was a custom paint job where I could choose the style and color I wanted. Other body shops did not want to do the job because it was a little out of the ordinary. They replaced two doors and some other body work and the custom paint job all turned out great.
We took the car in after the insurance company made out the estimate.�� Their estimator said they could do the repair work for the estimate.����We requested an estimate on repainting the entire car.�� The estimate seemed reasonable, so we had it painted too.
All Superior Auto Works, Inc.
721 S. Dixie Hwy E.


text:
Rendezvous Rye 2014 – Sample Vault Review
Sláinte! – Paddy
Originally located in Park City, UT, The High West Distillery became operational as the first legal distillery in the state since 1870 in 2007 with a small 264-gallon still and Saloon in an historic livery stable and garage. Since then, it has grown into a internationally recognised brand with four locations, including a state-of-the-art distillery which opened in Wanship, UT in 2015 and features a 1,585 gallon Forsyths copper pot still that's 25 feet tall and has capacity to produce 3,000 barrels a year. When High West first became operational, they built their reputation on blending whiskies they had sourced from distilleries such as MGP Indiana, Barton 1792 Distillery in Kentucky, Four Roses Distillery in Kentucky, and several other undisclosed distilleries whilst their own operation developed in the background. Unlike several other craft producers at the time, High West have always been open and honest about this business model and the sources of the whiskies where they could legally divulge this information.
As High West's flagship product, Rendezvous Rye was the not only the first product produced by the distillery but it was also their first blend of their sourced stocks. The backstory for this particular label is that it commemorates the first recorded whiskey festival in the West during a period spanning 1825 to 1840. The whiskey itself is a blend of two straight rye whiskeys with high rye mashbills with the constituent parts changing over the years as barrels from particular sources have dried up. Originally, Rendezvous Rye used 6 y.o. barrels of MGP rye whiskey from the 95% rye, 5% malted barley mashbill, and blended it with 16y.o. Barton rye whiskey which supposedly used a 53% rye, 37% corn and 10% malted barley mashbill. Since 2018, however, High West have started adding their own mature distillate into the blend and now the blend consists of what High West call "A blend of older straight rye whiskeys ranging in age from 4 to 7 years" on their website. The two mashbills now are 6y.o.+ 95% rye, 5% malted barley rye whiskey from MGP and rye whiskey from High West Distillery made using a 80% rye, 20% malted mashbill. This whiskey is also non chill-filtered or carbon treated before bottling.
Today I'll be reviewing the old Barton/MGP blend thanks to a 50ml sample from my friend @JHKBourbon.
Name: Rendezvous Rye (Batch 14K06)
Age: 6y.o.
Proof: 92 Proof (46% ABV)
Type: Straight rye whiskey
Mashbill: 95% rye, and 5% malted barley, blended with 53% rye, 37% corn and 10% malted barley.
Producer: High West Distillery, UT
Website: https://www.highwest.com/products/rendezvous-rye.php
Nose: The nose opens with big grassy rye notes and bright red fruit with faint maple syrup and baking spices. The rye becomes increasingly herbaceous and earthy the deeper you nose with a touch of barrel influence also becoming apparent.
Palate: The palate opens with red apples and cinnamon before a wave of peppery and tannic spice moves across the palate. As you continue to chew, the rye becomes herbaceous and gains a savoury edge as the rye and tannic oak build on the palate.
Finish: The finish is packed with lingering rye spice, tannins, and baking spices which fade to a herbaceous rye-driven aftertaste.
If you're a big rye fan, then this is the rye whiskey for you. Drinking this I get the clear impression that when High West promises a blend of two rye whiskies the end product is always going to be a big, bold, grassy rye whiskey. It's jam-packed with flavour elements from both its constituent parts coming through as you move from the nose to the palate. The younger MGP rye whiskey is right at the front with all those typical MGP notes before what I imagine is the older Barton rye whiskey showing its age with herbaceous and oak-driven notes. There's very little caramel or maple syrup notes which leads me to believe that the percentage of Barton rye in the blend couldn't be very high. I can see why fans of these earlier releases weren't happy when the recipes in these bottlings changed as the older rye really brings a lot of those mature earthy rye and barrel notes to the blend that balance out the young, bright, MGP rye notes. A true rye lover's rye.
These still appear at auction from time to time and offer fans of High West an opportunity to taste a piece of the brand's history. If you can find this at a bar even better!
Posted in Reviews, Sample Vault ReviewsBy Bourbon Paddy
Previous PostPrevious Ezra Brooks Rye Whiskey Review
Next PostNext Pikesville 110 Proof Rye Review


Night of the Arts will be held from 5 to 8 p.m. April 5 at Southeast High School.
The event will feature an art show, band and choir concert, and a bake-off open to students and community members. The secret ingredient is coconut. The winner will receive a $25 gift card to Applebee's.
A spaghetti dinner will be served at $7 per adult and $5 for senior citizens and students.
The event is sponsored by Southeast Music Boosters.


The global monetary providers trade has generated a very robust demand for economists with specialised knowledge of economic methods and markets. It's of equal benefit to these starting out on their profession as it is to those already working in a business, management or finance role. Northumbria University is in the business of unlocking worth in a approach that is distinctive to your small business, no matter measurement or sector. Our content material goes beyond the quantitative parts of personal finance to steering on key monetary selections from college to retirement. It's designed to familiarise college students with the major theoretical developments and practices in the areas of company finance and danger administration. You'll examine further specialist programs in business and finance and can full a dissertation on a topic carefully linked to your programme.
Chancellor Harold Martin Sr. is known as among the Triad's Most Admired CEOs by the Triad Business Journal. Yr 1 provides you a agency grounding in key areas of worldwide business and finance through compulsory modules. Saving courses mean you can evaluate them, it additionally lets you create a everlasting listing of 'favourites' that may at all times be there once you go to our site.
Each of the courses on this framework will provide you with those vital core skills, in addition to providing more specialist options depending on the pathway you select to pursue. Our specific three-year Finance Programme will introduce you to numerous businesses by way of three 12-month rotations. They do not know concerning the deal taking place between the lending firm and your small business and so they make their outstanding payments to your company only. The Smeal College of Enterprise has recently determined to permit college students majoring in Vitality Business and Finance to enter their Certificates in Enterprise Fundamentals program. Combined with our machine-readable news archive, our data gives traders and researches the advantage when the minutiae and microseconds make all of the difference.
Our teaching and research in International Business are ranked 3rd on the planet by the 2015 Financial Times Masters in Management rankings, that means you'll examine amongst main lecturers to realize the data and expertise to thrive in your future profession.


The St Mary Parish Council on Aging participates in the second Annual Trunk n Treat. The seniors made treats as well as passing them out.
A 23-year-old Amelia man has died after being shot Tuesday night in Amelia, according to a St. Mary Parish Sheriff's Office news release. The investigation into his death continues.
St. Mary Parish's unemployment rate dipped below 8 percent in September for the first time in 20 months, while the total number of people in the workforce declined slightly.
A man sustained moderate injuries Tuesday after he lost control of the vehicle he was driving near Amelia, and the vehicle rolled over several times, according to state police.


"The younger the driver, the higher the rates" could be the motto of auto insurance. Young, novice drivers have statistically shown to be immature behind the wheel, easily distracted and to crash - a lot - so they are the riskiest category of drivers to insure. Rates decrease at different times with different insurers, but generally your rates can drop as much as 20 percent when you turn 25.
The Insurance Institute for Highway Safety (IIHS) found that drivers ages 30 to 69 are much less likely to crash. If you keep a clean record, auto insurance rates typically stay fairly flat for drivers until they become a senior driver. Young and elderly drivers are typically found to pose the most risk and pay more as a result.


text:
Home News BLOODY HEELS : 'Ignite The Sky' – new album by Latvian hard rock act / out 10.07.20 via Frontiers
BLOODY HEELS : 'Ignite The Sky' – new album by Latvian hard rock act / out 10.07.20 via Frontiers
Comments Off on BLOODY HEELS : 'Ignite The Sky' – new album by Latvian hard rock act / out 10.07.20 via Frontiers
Frontiers Music Srl is proud to announce the release of a new album by Latvian hard rockers Bloody Heels. 'Ignite The Sky' will be released on 10th July, with a first single and video from it entitled 'Criminal Masterminds' out today (29th April).
In describing the album, singer Vicky White states that "it has some pretty heavy songs, but at the same time there's plenty of melodic stuff, harmonies and big choruses. I like to call this album 'Dark AOR', haha! We managed to blend everything we love about music, to be honest. But one thing is for sure, we've never felt such a strong connection with the songs before."
[youtube https://www.youtube.com/watch?v=9CpLlfhLBm0&w=560&h=315]
Discussing the first single, White continues: "'Criminal Masterminds' is definitely one of our heaviest songs to date. It was also one of the last that we wrote for the album. It's one of those songs that came together in just a couple of hours. We wanted to release it as the first single because I think it captures what Bloody Heels is about now. It's a bit heavier and more in your face, but still quite melodic, with a big chorus and lots of harmonies. It's quite different from anything that we've done before, but doesn't abandon who we are."
In regard to its video, White explains that "it was filmed in one day right before our European tour last October. A magical day for us, really, although we filmed it outside in quite cold weather, while the water poured on us was freezing! Luckily, we didn't get sick because we had to leave on tour 48 hours later.
Concluding with a comment about current events, White ends: "I also want to say that of course we all know what's happening right now in the world. Hopefully we can cheer some people up with this song and video. We have to remember that we are all one in spirit and the only way we're gonna crawl out of this mess is together. Stay home, stay healthy, and keep up the positive vibes!"
Latvian hard rockers Bloody Heels recently joined the rapidly expanding pool of young talent at the Frontiers label and one listen to their 2017 debut album 'Through Mystery' will explain why the label simply had to sign them. With nods to the best of the classic 80's hard rock scene, but also bordering on heavy metal (just listen to the kick drums on the new single), the band is a delightful mix of catchy and driving rock. With a great whisky-soaked voice, singer Vicky White provides the perfect accompaniment for the musical fire and brimstone that guitarist Harry Rivers, bassist Gunn Everett and drummer Gus Hawk rain down upon listeners to the band.
Formed in Riga in 2012, Bloody Heels have a musical style that can perhaps be described as a missing link between Crashdïet and Crazy Lixx, with additional heavier elements akin to early W.A.S.P. and Kissin' Dynamite. The band have already made a name for themselves in mainland Europe via a 2014 EP and aforementioned debut album and have toured in Scandinavia, Germany, Slovakia, Czech Republic, Poland, the Benelux and the Baltic States.
IGNITE THE SKY
1 Ignite The Sky
2 Criminal Masterminds
3 No Matter
4 Sugar & Spice
5 Farewell To Yesterday
6 Black Swan
7 Stand Your Ground
8 Thin Line
9 Silhouette
10 Healing Waters
11 Streets Of Misery
album pre-order link
orcd.co/ignitethesky
BLOODY HEELS
Valts Berzins (Vicky White) – vocals
Haralds Avotins (Harry Rivers) – guitars
Gunars Narbuts (Gunn Everett) – bass
Gustavs Vanags (Gus Hawk) – drums
Erna Daugaviete – cello on 'Silhouette'
Dagnis Rozins – saxophone on 'Healing Waters'
facebook.com/bloodyheelsband
instagram.com/bloodyheelsband
Previous article Five Finger Death Punch" BLUE ON BLACK "Feat. Kenny Wayne Shepherd, Brantley Gilbert And Brian May – #1 Hit That Keeps On Giving To First Responders
Next article Single Review : Evanescence – 'Wasted On You


There are a few other VBA components you'll use often within your code. These are comments, constants, and to a lesser extent, enums. This section provides a brief introduction to each and shows you how these components can be helpful within your code.
VBA programming consists of writing statements and comments. While comments are not explicitly required, uncommented code is hard to read and very difficult to understand, especially if someone else needs to work with your code. When working with the VBA Editor in Access, comments are prefaced with an apostrophe and appear in green. Comments are ignored during code execution. You can have one or many lines of comments in a procedure, and VBA will ignore them all. Comments don't slow down the execution of your code; so don't be afraid to use them liberally. At a minimum, your comments should list what the procedure is for and when it was written. Figure 4.2 shows a typical procedure with detailed comments.


text:
\section{Introduction}\label{sec:intro}

The problem of understanding scattering near the unitarity limit in perturbative
QCD has received a lot of attention over the past ten years. In the Regge limit
of perturbative QCD, {\em i.e.} when the centre-of-mass energy in a collision is
much bigger than the fixed hard scale of the problem, parton densities inside the
projectiles grow with increasing energy, leading to the growth of the scattering
amplitudes. As long as the densities are not to high, this growth is described
by the BFKL equation~\cite{bfkl}. But as the parton density becomes higher and
the scattering amplitude approaches the unitarity limit, one enters in a regime
called saturation~\cite{glr, glr+}, where BFKL evolution breaks down.

To study scattering amplitudes in the Regge limit, the $q\bar q$-dipole model
\cite{dipole,mueller} has been developed. This formalism constructs the
light-cone wavefunction of a dipole (a quark-antiquark pair in the colour singlet
state) in the leading logarithmic approximation. The size of the dipole provides
the hard scale that justifies the use of perturbation theory. As the energy
increases, the dipole evolves and the wavefunction of this evolved dipole is
described as a system of elementary dipoles. When this system of dipoles
scatters on a target, the scattering amplitude has been shown to obey the BFKL
equation.

Interestingly enough, the dipole formalism was shown to be also well-suited to
include density effects and non-linearities that lead to saturation and
unitarization of the scattering amplitudes. Indeed, Kovchegov~\cite{kov} derived
an equation for the dipole scattering amplitude that reduces to the BFKL
equation when the amplitude is small and that contains high-energy unitarity
effects as the amplitude reaches unity. Although this equation is
not exact, as it is a mean field approximation of the more complete infinite
hierarchy of equations established by Balitsky~\cite{bal}, it has the advantage
of being a closed equation for the scattering amplitude. This equation, which is
usually referred to as the BK (Balitsky-Kovchegov) equation, is propably
the simplest and most accurate equation one can consider to describe the saturation
regime of QCD.

The BK equation is an evolution equation for ${\cal{N}}(\mathbf{r},\mathbf{b},Y),$ the imaginary
part of the scattering amplitude of a dipole of transverse size $\mathbf{r}$ at
impact parameter $\mathbf{b}$ and where the rapidity $Y$ is the logarithm of the
centre-of-mass energy. It is a non-linear equation that resums QCD fan diagrams
in the leading-logarithmic approximation~\cite{kov}. Many interesting features
of this equation have been understood analytically~\cite{bk+,Munier1} for the $\mathbf{r}$
and $Y$ dependences. In particular, it was shown that the asymptotic
solutions have the so-called geometric scaling \cite{geomsc} property
${\cal{N}}(\mathbf{r},\mathbf{b}\!\sim\!0,Y)\!=\!{\cal{N}}(|\mathbf{r}|Q_T\Omega_s(Y)),$ where $Q_T$ is a
scale characterising the target and $\Omega_s(Y)\!=\!\exp(vY)$ is the dimensionless
saturation scale. One has not been able however to extract any useful information on
the $\mathbf{b}$ dependence. The analysis of the BK equation in impact-parameter space
(see {\em e.g.} ~\cite{conf,bknum}) even shows a contradiction with confinement as the
large-$\mathbf{b}$ dependence of the solutions develops a power-law tail with increasing
rapidity.

It was recently proposed~\cite{us} to analyse the equation in momentum space, by
Fourier transforming ${\cal{N}}(\mathbf{r},\mathbf{b},Y),$ into $\tilde{{\cal{N}}}(\mathbf{k},\mathbf{q},Y)$ where
$\mathbf{k}$ can be interpreted as the incoming transverse momentum of the dipole and
$\mathbf{q}$ as the momentum transfer. It was shown in~\cite{us} that the three
variables $\mathbf{k},$ $\mathbf{q},$ and $Y$ give information on the approach to the unitarity
limit. In particular, it was predicted that the geometric scaling property should
also be present in momentum space when $|\mathbf{k}|\!\gg\!|\mathbf{q}|$ as one should have
asymptotically $\tilde{{\cal{N}}}(\mathbf{k},\mathbf{q},Y)\!=\!\tilde{{\cal{N}}}[|\mathbf{k}|/(|\mathbf{q}|\Omega_s(Y))].$
The goal of this paper is to formulate and analyse the BK equation in momentum space,
to solve it numerically and compare our results with those predicted. The equation in
momentum space has already been studied numerically in the $\mathbf{b}$-independent situation
\cite{bknumimp}. Our purpose here is to extend those analysis to full
momentum space including the transfer momentum dependence.

The plan of the paper is as follows. In section \ref{sec:bdep}, we write the BK
equation in momentum space and derive some analytical properties.
In section \ref{sec:trav}, we briefly explain the properties of asymptotic solutions
and how they translate into geometric scaling. In Section \ref{sec:numsol}, we give
details about the numerical techniques used to solve the equation and present our
results. Section \ref{sec:ccl} concludes.

\section{The BK equation in momentum space}\label{sec:bdep}

The BK equation in coordinate space reads
\begin{equation}\label{eq:bkspace}
\partial_Y {\cal{N}}(\mathbf{x},\mathbf{y}) = \frac{\bar{\alpha}}{2\pi}\int d^2z
\frac{(\mathbf{x}\!-\!\mathbf{y})^2}{(\mathbf{x}\!-\!\mathbf{z})^2(\mathbf{z}\!-\!\mathbf{y})^2}
\left[{\cal{N}}(\mathbf{x},\mathbf{z})+{\cal{N}}(\mathbf{z},\mathbf{y})-{\cal{N}}(\mathbf{x},\mathbf{y})-{\cal{N}}(\mathbf{x},\mathbf{z}){\cal{N}}(\mathbf{z},\mathbf{y}) \right]
\end{equation}
where $\bar\alpha\!=\!\alpha_sN_c/\pi.$ The two-dimensional vectors $\mathbf{x}$ and
$\mathbf{y}$ are the transverse positions of the quark and antiquark composing  the
dipole of transverse size $\mathbf{r}\!=\!\mathbf{x}\!-\!\mathbf{y}$ at impact parameter
$\mathbf{b}\!=\!(\mathbf{x}\!+\!\mathbf{y})/2.$ The rapidity $Y$ is not mentioned explicitly in the
amplitude but ${\cal{N}}(\mathbf{x},\mathbf{y})$ always carries a $Y$ dependence. Let us define the
following Fourier transformation:
\begin{equation}\label{eq:fourier}
\tilde{{\cal{N}}}(\mathbf{k},\mathbf{q})=\f1{(2\pi)^2}\int d^2x\,d^2y\: e^{i\mathbf{k}.\mathbf{x}}e^{i(\mathbf{q}-\mathbf{k}).\mathbf{y}}
\,\frac{{\cal{N}}(\mathbf{x},\mathbf{y})}{(\mathbf{x}\!-\!\mathbf{y})^2}\ .
\end{equation}
Then the equation verified by $\tilde{{\cal{N}}}(\mathbf{k},\mathbf{q})$ can be written as
\begin{equation}\label{eq:fullbk}
\partial_Y \tilde {\cal N}(\mathbf{k},\mathbf{q})
 = \frac{\bar{\alpha}}{\pi} \int \frac{d^2k'}{(\mathbf{k}\!-\!\mathbf{k}')^2}
 \left\{ \tilde {\cal N}(\mathbf{k}',\mathbf{q})-\f1{4} \left[
   \frac{(\mathbf{q}\!-\!\mathbf{k})^2}{(\mathbf{q}\!-\!\mathbf{k}')^2}+
   \frac{\mathbf{k}^2}{\mathbf{k}'^2}
   \right]\tilde {\cal N}(\mathbf{k},\mathbf{q})
 \right\}
 -\frac{\bar{\alpha}}{2\pi}\int d^2k'\
\tilde {\cal N}(\mathbf{k},\mathbf{k}')\tilde {\cal N}(\mathbf{k}\!-\!\mathbf{k}',\mathbf{q}\!-\!\mathbf{k}').
\end{equation}
This equation involves three contributions. The first integration contains the
linear terms corresponding to real and virtual gluon emissions (see
Fig.\ref{fig:linterms}). The last term is the nonlinear correction which, as
represented in Fig.\ref{fig:nonlin}, arises from the resummation of fan diagrams.
\begin{figure}
  \subfigure[]{\includegraphics{lin-real.eps}}\hspace{2.0cm}
  \subfigure[]{\includegraphics{lin-virt.eps}}
\caption{Linear contributions to the evolution of the dipole density in momentum
space: (a) real gluon emission, (b) virtual gluon emission.}\label{fig:linterms}
\end{figure}
\begin{figure}
\includegraphics{nonlin.eps}
\caption{Non-linear contribution to the evolution of the dipole density in
momentum space. This correspond to the resummation of fan
diagrams.}\label{fig:nonlin}
\end{figure}
A trivial change of variable in the virtual correction term in Eq.
\eqref{eq:fullbk} can put the evolution equation under a form emphasizing more
clearly the cancellation of divergences between the real and virtual gluon
emissions. We get
\begin{eqnarray}
\partial_Y \tilde {\cal N}(\mathbf{k},\mathbf{q})
 & = &\frac{\bar\alpha}{\pi}\int \frac{d^2k'}{(\mathbf{k}-\mathbf{k}')^2}
   \left\{
   \tilde {\cal N}(\mathbf{k}',\mathbf{q}) - \frac{1}{2} \left[
     \frac{\mathbf{k}^2}{\mathbf{k}'^2+(\mathbf{k}-\mathbf{k}')^2} +
     \frac{(\mathbf{q}-\mathbf{k})^2}{(\mathbf{q}-\mathbf{k}')^2+(\mathbf{k}-\mathbf{k}')^2}
     \right] \tilde {\cal N}(\mathbf{k}, \mathbf{q})
   \right\} \nonumber \\
 & - & \frac{\bar\alpha}{2\pi} \int
d^2k'\,\tilde {\cal N}(\mathbf{k},\mathbf{k}')\,\tilde {\cal N}(\mathbf{k}-\mathbf{k}',\mathbf{q}-\mathbf{k}').
\label{eq:bk}
\end{eqnarray}

Let us now look at the properties of this equation in some particular cases.
If the amplitude (in coordinate space) only depends on the size of the dipole
{\em i.e.} ${\cal{N}}(\mathbf{x},\mathbf{y})\!=\!{\cal{N}}(\mathbf{x}\!-\!\mathbf{y})$, then
$\tilde {\cal N}(\mathbf{k},\mathbf{q})\!=\!2\pi\delta^{(2)}(\mathbf{q})\tilde {\cal N}(\mathbf{k})$, where
\begin{equation}
\tilde {\cal N}(\mathbf{k})=\int\frac{d^2x}{2\pi\mathbf{x}^2}\ e^{i\mathbf{k}.\mathbf{x}}{\cal{N}}(\mathbf{x})
\end{equation}
obeys
\begin{equation}\label{eq:bkbindep}
\partial_Y \tilde {\cal N}(\mathbf{k}) = \frac{\bar{\alpha}}{\pi} \int \frac{d^2k'}{(\mathbf{k}\!-\!\mathbf{k}')^2}
\left[ \tilde {\cal N}(\mathbf{k}')-\frac{\mathbf{k}^2}{\mathbf{k}'^2+(\mathbf{k}-\mathbf{k}')^2}\tilde {\cal N}(\mathbf{k}) \right]
-\bar{\alpha}\,\tilde {\cal N}^2(\mathbf{k}).
\end{equation}
One recovers the usual equation \cite{glr} discussed for $\mathbf{b}$-independent
situations.\\
Let us now look at the equation in the forward limit $\mathbf{q}\to 0$. Due
to the fact that the non-linear term in \eqref{eq:bk} is off-diagonal, the
equation for the forward dipole amplitude involves non-forward contributions.
However, if we assume that the amplitude is peaked around $|\mathbf{q}|=0$ and has the
factorised form
\begin{equation}\label{eq:facto}
\tilde {\cal N}(\mathbf{k}, \mathbf{q}) = \phi(|\mathbf{q}|)\,\tilde {\cal N}_0(\mathbf{k}),
\end{equation}
the non-linear term can be simplified
\[
\int d^2k'\:\tilde {\cal N}(\mathbf{k},\mathbf{k}')\,\tilde {\cal N}(\mathbf{k}-\mathbf{k}',\mathbf{q}-\mathbf{k}') \approx 2\pi\,\tilde {\cal N}_0^2(\mathbf{k})
\int_0^\infty k'\,dk'\:\phi^2(k').
\]
If we normalize the $\mathbf{q}$-dependent factor in \eqref{eq:facto} in such a way that
\[
\phi(0) = \int_0^\infty k'\,dk'\:\phi^2(k'),
\]
we obtain a closed equation for the rapidity evolution of $\tilde {\cal N}_0(\mathbf{k})$ of the form
\[
\partial_Y \tilde {\cal N}_0(\mathbf{k}) = \frac{\bar{\alpha}}{\pi} \int \frac{d^2k'}{(\mathbf{k}\!-\!\mathbf{k}')^2}
\left[ \tilde {\cal N}_0(\mathbf{k}')-\frac{\mathbf{k}^2}{\mathbf{k}'^2+(\mathbf{k}-\mathbf{k}')^2}\tilde {\cal N}_0(\mathbf{k}) \right]
-\bar{\alpha}\,\tilde {\cal N}_0^2(\mathbf{k}),
\]
which is equivalent to the equation \eqref{eq:bkbindep} obtained in the
$\mathbf{b}$-independent situation. It is however important to realize that, while the
simplification is exact for $\mathbf{b}$-independent amplitude, it requires assumptions
on the small-$\mathbf{q}$ dependence of the amplitude in the forward limit.

\section{Traveling waves and geometric scaling}\label{sec:trav}

In this section, we briefly summarize the properties of the asymptotic solutions of the BK equation and replace this in the context of the new form \eqref{eq:fullbk}.

Let us start with the case of the $\mathbf{b}$-independent equation \eqref{eq:bkbindep}. It has been shown~\cite{Munier1} that, in the diffusive approximation, the equation for $\tilde {\cal N}(k\!=\!|\mathbf{k}|)$ is equivalent to the Fisher-Kolmogorov-Petrovsky-Piscounov (F-KPP) equation~\cite{KPP}. This equation, well known in statistical physics, admits traveling-wave solutions at large rapidities and momentum $k$, which means that the solution is a function of $Y\!-v_c\!\log(k)$ only, where $v_c$ is the speed of the wavefront.
More generally, if the evolution equation satisfies the following conditions:
\begin{itemize}
\item $\tilde {\cal N}=0$ is an unstable fix point and the equation contains a linear term, leading to a growth of the amplitude, and a non-linear damping term; this is realized in \eqref{eq:bkspace}
and \eqref{eq:fullbk},
\item the initial condition is steep enough, which in the QCD case is ensured by colour transparency,
\item the linearised equation admits a superposition of waves as solution
\begin{equation}\label{eq:waves}
\tilde {\cal N}_{\text{lin}}(k,Y) = \int_{c-i\infty}^{c+i\infty} \frac{d\gamma}{2i\pi} a_0(\gamma) \exp\left[\omega(\gamma) Y - \gamma \log(k^2/k_0^2)\right],
\end{equation}
\end{itemize}
then the asymptotic solution of the full equation takes the form
\begin{equation}\label{eq:travwaves}
\tilde {\cal N}(k,Y) \underset{Y\to\infty}{\sim} \left[\frac{k^2}{Q_s^2(Y)}\right]^{-\gamma_c},
\end{equation}
for $k\gg k_0$ where the saturation scale $Q_s^2(Y)$ grows as $k_0\ e^{v_c Y}$. The critical exponent $\gamma_c$ and the critical speed $v_c$ are given by
\[
v_c = \frac{\omega(\gamma)}{\gamma} = \omega'(\gamma),
\]
meaning that the group velocity is equal to the phase velocity.

In the case of the BK equation, the corresponding linear equation is the BFKL equation, whose solutions have been extensively studied~\cite{Lipatov86,NP,Navelet:1997tx,LipatovReview}. For the impact-parameter-independent case, Munier and Peschanski have proven~\cite{Munier1} that the three conditions for traveling waves are fulfilled. In a recent study, we have shown~\cite{us} that this can be extended to the full BK equation including momentum transfer. In this case, the reference scale $k_0$ becomes proportional to the typical scale of the target $Q_T$ or to the momentum transfer $|\mathbf{q}|$ whether $|\mathbf{q}|$ is smaller or larger than $Q_T$. Before going into the numerical studies, we recall the important points concerning geometric scaling at non-zero momentum transfer.

In the previous work~\cite{us}, one of the key points was to show that the BFKL solutions can be put under the form \eqref{eq:travwaves} when $|\mathbf{k}|\!\gg\!|\mathbf{q}|$. Since the definition \eqref{eq:fourier} of the Fourier-transformed amplitude introduces an additional $(\mathbf{x}\!-\!\mathbf{y})^2$ w.r.t. the usual one, the solution is slightly different to the one we used in~\cite{us}. However our conclusions are unchanged as we shall see now. Let us start with the well-known result~\cite{Lipatov86,NP,Navelet:1997tx,LipatovReview} that
\[
{\cal{N}}_{\text{lin}}(\mathbf{x},\mathbf{y})=
\int_{\frac{1}{2}-i\infty}^{\frac{1}{2}+i\infty}
\frac{d\gamma}{2i\pi}\ e^{\bar\alpha\chi(\gamma)Y}
\left(\frac{\abs{\mathbf{x}-\mathbf{y}}}{\abs{\mathbf{x}}\abs{\mathbf{y}}}\right)^{2\gamma}\phi_0(\gamma)
\]
is solution of the BFKL equation in coordinate space with
\begin{equation}\label{eq:bfklchi}
\chi(\gamma) = 2\psi(1)-\psi(\gamma)-\psi(1-\gamma).
\end{equation}
and where $\phi_0(\gamma)$ is a function that specifies the initial condition. Note that we kept only the dominant component at high energy which corresponds to vanishing conformal spin $n=0.$
If we now Fourier transform this solution according to \eqref{eq:fourier}, one obtains
\[
\tilde {\cal N}_{\text{lin}}(\mathbf{k},\mathbf{q})=\int_{\frac{1}{2}-i\infty}^{\frac{1}{2}+i\infty} \frac{d\gamma}{2i\pi}\ e^{\bar\alpha\chi(\gamma)Y}
f^\gamma(\mathbf{k}, \mathbf{q})\phi_0(\gamma,\mathbf{q})
\]
with
\begin{equation}\label{eq:linvpr}
f^\gamma(\mathbf{k}, \mathbf{q}) = \frac{\Gamma^2(\gamma)}{\Gamma^2\left(\frac{1}{2}+\gamma\right)} \frac{2}{\abs{k}} \left|\frac{q}{4k}\right|^{2\gamma-1}{}_2{\rm F}_1\left(\gamma,\gamma;2\gamma;\frac{q}{k}\right){}_2{\rm F}_1\left(\gamma,\gamma;2\gamma;\frac{\bar q}{\bar k}\right) - (\gamma\to 1-\gamma).
\end{equation}
A factor antisymmetric under the replacement $\gamma \to 1-\gamma$
and as been absorbed in $\phi_0(\gamma,\mathbf{q}).$ Note that in \eqref{eq:linvpr} we use the complex representation of vectors: $x\!=\!x_1\!+\! ix_2$ and $\bar x\!=\!x_1\!-\!ix_2$ for the vector $\mathbf{x}=(x_1,x_2);$ however from now on, we shall use $x$ to denote the modulus of the vector. Although this is not straightforward, one can explicitly check (see Appendix \ref{app:lin}) that \eqref{eq:linvpr} is an eigenfunction of the linear kernel of eq. \eqref{eq:fullbk} with the correct eigenvalue \eqref{eq:bfklchi}. When $k\gg q$, the hypergeometric functions go to 1 and $f^\gamma(\mathbf{k},\mathbf{q})$ becomes a simple power of $q/k$. The full solution of the linear part of \eqref{eq:fullbk} thus becomes
\[
\tilde {\cal N}_{\text{lin}}(\mathbf{k},\mathbf{q}) = \int_{\frac{1}{2}-i\infty}^{\frac{1}{2}+i\infty}
 \frac{d\gamma}{2i\pi} \phi_0(\gamma,\mathbf{q}) \, \exp\left[\bar\alpha\chi(\gamma) Y - \gamma \log(k^2/q^2)\right],
\]
where irrelevant factors have again been absorbed in the initial condition $\phi_0(\gamma,\mathbf{q}).$
This expression proves that the conditions for obtaining traveling waves and geometric scaling are fulfilled. More precisely, including all the terms common to each evolution equation of this universality class~\cite{Munier1}, it predicts
\begin{equation}\label{eq:newqs}
Q_s^2(Y) = q^2 \Omega_s^2(Y) \underset{Y\to\infty}{\sim} q^2
\exp\left[\bar\alpha\frac{\chi(\gamma_c)}{\gamma_c}Y-\frac{3}{2\gamma_c}\log(Y)
-\frac{3}{\gamma_c^2}\sqrt{\frac{2\pi}{\bar\alpha \chi''(\gamma_c)}} \frac{1}{\sqrt{Y}}
+{\cal{O}}(1/Y)
\right],
\end{equation}
together with the leading edge of the traveling front
\begin{equation}\label{eq:newfront}
\tilde {\cal N}(\mathbf{k},\mathbf{q}) \underset{Y\to\infty}{\sim}
\phi^{\gamma_c}(\mathbf{q})\,\log\left(\frac{k^2}{q^2\Omega_s^2(Y)}
\right)\,\abs{\frac{k^2}{q^2\Omega_s^2(Y)}}^{-\gamma_c}\,
\exp\left[-\frac{1}{2\bar\alpha\chi''(\gamma_c)Y}\log^2\left(
\frac{k^2}{q^2\Omega_s^2(Y)}\right)\right].
\end{equation}
When $q$ becomes smaller that the typical size $Q_T$ of the target, one can show that $Q_T$ substitutes to $q$ in the saturation scale. $Q_s$ is thus expected to be proportional to $q$ only at large $q$. The value of $\gamma_c$ is 0.6275. Note that those behaviours are the same as the ones predicted by the forward analysis.

Let us also point out that all these results have been studied in terms of the momentum transfer $q$ and could not be derived in terms of the impact parameter $b$. One way to understand this is to look at the BFKL equation. One clearly sees that the equation in momentum space (see \eqref{eq:fullbk}) is local in $q$ while the equation in coordinate space (see \eqref{eq:bkspace}) couples different values of the impact parameter $b$. In the following section, we shall explicitly check that these predictions are observed by numerical simulations of the full equation \eqref{eq:fullbk}.

\section{Numerical analysis}\label{sec:numsol}

\subsection{Description of the method}

Instead of working directly with the momentum $\mathbf{k}$, we shall use the
variable $\mathbf{p}=\mathbf{k}-\mathbf{q}/2$, which is the canonical conjugate of $\mathbf{r}$.
The Fourier transform of the dipole amplitude
then becomes
\[
\tilde {\cal N}(\mathbf{p};\mathbf{q}) = \frac{1}{(2\pi)^2} \int \frac{d^2r}{r^2}\,d^2b \,e^{i\mathbf{r}.\mathbf{p}}
\,e^{i\mathbf{b}.\mathbf{q}} {\cal{N}}(\mathbf{r};\mathbf{b}),
\]
and the BK equation in momentum space takes the form
\begin{eqnarray}\label{eq:fullbk_pq}
\partial_Y \tilde {\cal N}(\mathbf{p};\mathbf{q}) & = &
\frac{\bar\alpha}{2\pi}\int\frac{d^2p'}{(\mathbf{p}'-\mathbf{p})^2}
\left\{ 2\tilde {\cal N}(\mathbf{p}';\mathbf{q})
  - \left[\frac{\left(\mathbf{p} +\frac{\mathbf{q}}{2}\right)^2}
               {\left(\mathbf{p}'+\frac{\mathbf{q}}{2}\right)^2 + (\mathbf{p}'-\mathbf{p})^2}
        + \frac{\left(\mathbf{p} -\frac{\mathbf{q}}{2}\right)^2}
               {\left(\mathbf{p}'-\frac{\mathbf{q}}{2}\right)^2 + (\mathbf{p}'-\mathbf{p})^2}
    \right] \tilde {\cal N}(\mathbf{p};\mathbf{q})
\right\} \nonumber\\
 & - & \frac{\bar\alpha}{2\pi}\int d^2p'\,
  \tilde {\cal N}\left(\mathbf{p}-\frac{\mathbf{p}'}{2}+\frac{\mathbf{q}}{4};\frac{\mathbf{q}}{2}+\mathbf{p}'\right)
  \tilde {\cal N}\left(\mathbf{p}-\frac{\mathbf{p}'}{2}-\frac{\mathbf{q}}{4};\frac{\mathbf{q}}{2}-\mathbf{p}'\right).
\end{eqnarray}
Although this formulation seems more complicated, it emphasises more clearly the
symmetry properties of the BK equation under the transformation $\mathbf{k} \to
\mathbf{q}-\mathbf{k}$ which simply becomes $\mathbf{p} \to - \mathbf{p}$ in the new variables.
Let us notice that the solution of the linear problem can be seen as depending
only on the ratio $\mathbf{p}/q$. Also, the limit $k \gg q$ we are interested
in is equivalent to $p \gg q$.

For numerical studies, we shall therefore use $L=\log(Rp)$, $L_q = \log(Rq)$, where $R$ is the typical target size, and
$\phi$, the angle between $\mathbf{p}$ and $\mathbf{q}$. It is obvious from
\eqref{eq:fullbk_pq} that we have
\[
\tilde {\cal N}(L, L_q, \phi) = \tilde {\cal N}(L, L_q, -\phi) = \tilde {\cal N}(L, L_q, \pi-\phi) = \tilde {\cal N}(L, L_q,
\pi+\phi),
\]
provided the same equality holds for the initial condition. In practice, we have computed the amplitude $\tilde {\cal N}(L, L_q, \phi)$ on a lattice
of $n_p \times n_q \times n_\phi$ points regularly spaced with
$L_{\text{min}}\le L \le L_{\text{max}}$, $L_{q,\text{min}}\le L_q \le
L_{q,\text{max}}$ and $0\le \phi \le \frac{\pi}{2}$.
We have then discretised the integral in the r.h.s. of \eqref{eq:fullbk_pq} and
solved the resulting set of differential equations by a Runge-Kutta method.

\subsection{Results}

In this section, we shall study the properties of the numerical solutions of equation \eqref{eq:fullbk_pq}. We have studied two choices of initial distribution:
\begin{equation}\label{eq:init_exp}
\left.\tilde {\cal N}(\mathbf{p};\mathbf{q})\right|_{Y=0} = \frac{1}{p^2+R^{-2}}\,e^{-Rq},
\end{equation}
and
\begin{equation}\label{eq:init_pert}
\left.\tilde {\cal N}(\mathbf{p};\mathbf{q})\right|_{Y=0} = \frac{1}{p^2+R^{-2}}\frac{1}{1+q^2R^2}.
\end{equation}
Although the first choice seems more natural, the exponential damping at large $q$ leads to very small amplitudes producing numerical results difficult to handle. Therefore, in order to make the study at large $q$ easier, we shall also consider the less-steep behaviour \eqref{eq:init_pert}. The value of the coupling $\bar \alpha$ has been fixed to 0.2. We shall not consider the effect of the running of the strong coupling constant in this paper.
Before presenting the results, let us notice that the dependence of $\tilde {\cal N}$ on the angle $\phi$ is not really interesting for our purposes, hence, we shall concentrate on the amplitude averaged over $\phi$. Concerning the choice of the discretisation parameters, we have used 101 values of $L$ between $-5$ and 20, 53 values of $L_q$ between $-5$ and $8$ and 9 values of $\phi$ between 0 and $\pi/2$.

To begin with, we shall check if the traveling waves predicted for $k \gg q$ in~\cite{us} are indeed observed in numerical simulations. This is done by plotting the rapidity evolution of the dipole amplitude as a function of $k$ (or, equivalently, $p$) for different values of $q$. As clearly seen in Figure \ref{fig:qbins}, as the rapidity increases, a traveling wave is formed at large values of $p$. For these results, the initial condition used is \eqref{eq:init_pert}.

To observe this more precisely, it is interesting to study the properties of the saturation scale $Q_s$. In~\cite{us}, it was predicted that $Q_s$ should evolve asymptotically like a $q$-independent power of the energy, and, at fixed rapidity, should grow linearly with $q$ when $q$ becomes larger than the inverse size of the target. Let us first check the high-energy dependence of the saturation scale. Due to the $q$-dependence of the initial condition \eqref{eq:init_pert}, one cannot simply extract the saturation scale by solving $\tilde {\cal N}(p=Q_s(Y,q);q)=\bar N_0$ since, for sufficiently large values of $q$, the amplitude will always be smaller than $\bar N_0$. To fix this problem, we rely on the fact that the asymptotic behaviour of $\log(Q_s)$ is expected to be insensitive to the choice of $\bar N_0$. We shall thus use a $q$-dependent threshold $\bar N_0(q)$, taking into account the damping at large $q$ introduced by the initial condition. This leads us to solve
\begin{equation}\label{eq:qsdef}
\tilde {\cal N}(p=Q_s(Y,q);q)=\bar N_0(q)=\frac{\bar N_0(0)}{1+R^2 q^2},
\end{equation}
for different values of $Y$ and $q$. In Figure \ref{fig:qs}(a), where we have chosen $\bar N_0(0)=0.05$, we show that whatever $q$ is, $\log(Q_s(Y)/Q_s(Y_0))$, with $Y_0$ fixed to 1, goes to a constant value at asymptotic rapidities. In fact, one can even check that our numerical results are consistent with the expansion
\[
\partial_Y \log\left[Q_s^2(Y,q)\right] = \bar\alpha\frac{\chi(\gamma_c)}{\gamma_c} - \frac{3}{2\gamma_c}\frac{1}{Y}+\frac{3}{\gamma_c^2}\sqrt{\frac{2\pi}{\bar\alpha\chi''(\gamma_c)}}\frac{1}{Y^{3/2}}+\frac{c_2(q)}{Y^2},
\]
valid at large $Y$. Notice that, in this expression, the $q$-dependent non-universal term $c_2 Y^{-2}$ is required in the rapidity range under consideration.

The extraction of the $q$-dependence of the saturation scale is more tricky since the definition \eqref{eq:qsdef} is obviously not sufficient. Basically, one has to obtain the position of the wavefront in a way that does not depend on any threshold $\bar N_0$ at all. Our method consists in studying the so-called {\em reduced front} $p^{2\gamma_c} \tilde {\cal N}(p,q)$ which is expected to show a maximum in $p$ in the region where geometric scaling holds~\cite{Munier1}. However, since the violations of geometric scaling in the ultra-violet appear outside of our lattice, we shall define $Q_s$ as the maximum of a {\em modified version} of the reduced front $p \tilde {\cal N}(p,q)$ {\em i.e.} replace $\gamma_c=0.6275$ by 0.5. Physically, the maximum of this quantity can be considered as a measure of the momentum for which the saturated regime is replaced by the traveling front. We have applied this method to extract the average\footnote{We average over an interval of rapidity in order to minimise numerical uncertainties.} saturation scale for $20\le Y \le 25$ and checked that the result does not change if one replace 0.5 by another value close to it. The result is shown in Figure \ref{fig:qs}(b) and we see that the saturation scale obtained from this method is constant for small momentum transfer and shows a linear increase as $q$ becomes larger than $R^{-1}$. For very high values of $q$ ($\log(Rq) \gtrsim 2$), the results start to diverge from this proportionality. We attribute this feature to the fact that the asymptotic traveling-wave behaviour is not yet reached, and at those high values of $q$, we are not extracting the true saturation scale.

\begin{figure}
\subfigure[$\log(Rq)=-5$]{\includegraphics[scale=0.75]{q-5.eps}}\hspace{1.5cm}
\subfigure[$\log(Rq)=-1$]{\includegraphics[scale=0.75]{q-1.eps}}
\subfigure[$\log(Rq)=0$]{\includegraphics[scale=0.75]{q0.eps}}\hspace{1.5cm}
\subfigure[$\log(Rq)=1$]{\includegraphics[scale=0.75]{q1.eps}}
\subfigure[$\log(Rq)=2$]{\includegraphics[scale=0.75]{q2.eps}}\hspace{1.5cm}
\subfigure[$\log(Rq)=4$]{\includegraphics[scale=0.75]{q4.eps}}
\caption{Rapidity evolution of the dipole density as a function of $p$ for different values of $q$. For each plot, we show the amplitude for $Y$ varying between 0 and 25 by steps of 2.5.}
\label{fig:qbins}
\end{figure}

\begin{figure}
\subfigure[]{\includegraphics[scale=0.9]{qs.eps}}
\subfigure[]{\includegraphics[scale=0.9]{qred.eps}}
\caption{This figure presents the results concerning the saturation scale: (a) shows that the evolution of the saturation scale with $Y$ has the predicted behaviour and (b) represents the $q$-evolution of the saturation scale (see text for details).}
\label{fig:qs}
\end{figure}

\begin{figure}
\includegraphics{y.eps}
\caption{This figure shows the $Y$ dependence of the amplitude $\tilde {\cal N}(\mathbf{p};\mathbf{q})$. In the left plot we have fixed $\log(Rq)=-3$, while $\log(Rq)=0$ in the centre plot and $\log(Rq)=3$ in the right one.}
\label{fig:ydep}
\end{figure}

\begin{figure}
\includegraphics{y-bfkl.eps}
\caption{This figure shows the $Y$ dependence of the amplitude $\tilde {\cal N}(\mathbf{p};\mathbf{q})$ compared to the amplitude obtained by BFKL evolution. In each pair of curves, the upper one is obtained from BFKL evolution and the lower one includes nonlinear effects. In the left plot we have fixed $\log(Rq)=-3$, while $\log(Rq)=0$ in the centre plot and $\log(Rq)=3$ in the right one.}
\label{fig:vsbfkl}
\end{figure}

\begin{figure}
\includegraphics{k.eps}
\caption{Rapidity evolution of the dipole density as a function of $q$ for different values of $p$. In the left (resp. centre, right) plot we have set $\log(Rp)=-3$ (resp. 0, 3).}
\label{fig:kbins}
\end{figure}

Let us say a few words about the evolution in the regime $k\!\sim\!q$. As shown in Figure \ref{fig:ydep}, this region presents oscillations and the amplitude seems to saturate to a constant value at large $Y$. To see more precisely the effect of the nonlinear term in \eqref{eq:fullbk}, we can compare the $Y$-evolution of the amplitude presented in figure \ref{fig:ydep}, with the results obtained from BFKL evolution {\em i.e.} keeping only the linear term in \eqref{eq:fullbk}. The comparison of these two evolutions is presented in Figure \ref{fig:vsbfkl}. This figure shows interesting features. First, one clearly sees the damping due to the inclusion of the nonlinear effects. Then, one observes the exponential growth of the BFKL amplitude with rapidity. Finally, we see that at high energy and for a given value of $q$, the BFKL amplitude becomes degenerate for $k\ll q$. This feature, closely related to the plateau observed in the infrared region in Figure \ref{fig:qbins}, shows that $q$ acts like an infrared cut-off \cite{mueltri}.

Finally, let us see how the $q$ behaviour of the amplitude evolves with rapidity. In Figure \ref{fig:kbins}, we show how the initial condition \eqref{eq:init_exp} evolves with rapidity for different values of $p$, as a function of $q$. First of all, it appears that the extension in $q$ remains roughly constant as the rapidity increases. Then, we see an increase of the amplitude for small values of $q$. As noticed in~\cite{us}, the fact that the $q$-behaviour of the amplitude does not develop a power-law tail when the energy increases as it is the case with impact parameter, is one of the main advantage in studying the BK equation in momentum space.

\section{Conclusion}\label{sec:ccl}

Let us summarize the main results of this paper. First, we have proposed a Fourier transform of the dipole scattering amplitude which leads to a new form of the BK high-energy evolution equation. This new form involves the amplitude in momentum space instead of coordinate space (see equation \eqref{eq:fullbk}). We have shown that the momentum-transfer-dependent equation reduces to the usual momentum-space evolution in the $b$-independent case. This equation is also obtained in the forward case $q=0$, assuming a steep $q$ dependence of the amplitude.

We have then checked numerically the properties of the asymptotic solutions of the proposed $q$-dependent BK equation. We have shown that all the properties predicted theoretically in~\cite{us} are indeed reproduced by numerical simulations. More precisely, one obtains traveling waves at large rapidities, leading to geometric scaling in the region $k \gg q$. The speed of the traveling front converges to the $q$-independent value predicted by previous analysis. Concerning the saturation scale, we have shown that it goes from a constant behaviour to a linear increase with momentum transfer when $q$ goes from values smaller than the target typical scale to larger values. While the coordinate-space version of the BK equation leads to a diffusion in impact parameter already at the level of the linear kernel, the corresponding equation in momentum space remains local in $q.$ This means that, to the contrary of what happens in impact-parameter space where the evolution generates a perturbative tail at large $b$, the $q$ behaviour does not show an increase at large values of $q$. This important property is also the reason for which momentum space is the natural frame to discuss traveling-wave solutions and geometric scaling.

In addition to these results, the possibility to solve the full BK equation allows for various extensions. From the phenomenological point of view, it can help to test saturation effects in many processes including {\em e.g.} diffractive photoproduction of vector mesons. On more theoretical grounds, one may be tempted to analyse the odderon equations Ref.\cite{Hatta:2005as}. Due to the parity of the odderon, this contribution cannot be introduced at the level of the $b$-independent BK equation. In all these cases, it would be interesting to introduce the effect of the running coupling. Finally, this equation can also serve as a basis for studies of fluctuation effects and the corresponding Langevin equation derived very recently~\cite{stoc}.

\begin{acknowledgments}
We would like to thank R. Peschanski for fruitful discussions and suggestions. G.S. is funded by the National Funds for Scientific Research (Belgium).
\end{acknowledgments}

\begin{appendix}

\section{Solutions of the linearised equation}\label{app:lin}

In this appendix, we write down the main lines that show that \eqref{eq:linvpr} is a solution of the linear part of equation \eqref{eq:fullbk} with the correct eigenvalue. We start by going to the complex representation and use the integral representation of $f^\gamma(\mathbf{k},\mathbf{q}),$ see Appendix B of~\cite{us}. One has, up to a $\gamma$-dependent factor:
\[
f^\gamma(x) = \abs{x}^{2\gamma}\int d^2v\,\abs{v}^{2\gamma-2} \abs{1-v}^{2\gamma-2} \abs{1-\bar x v}^{-2\gamma},
\]
with $x=q/k$. If we perform the change of variables $k' \to v=k'/k$ in (the linear part of) \eqref{eq:fullbk}, we are left with the integral
\[
I^\gamma(x) = \frac{\bar\alpha}{2\pi} \int\frac{d^2v}{\abs{1-v}^2}\left[ 2f^\gamma(x/v)-\frac{1}{\abs{v}^2}f^\gamma(x)\right] + \frac{\bar\alpha}{4\pi} \int\frac{d^2v}{\abs{1-v}^2}\left(\frac{1}{\abs{v}^2}-\frac{\abs{1-x}^2}{\abs{v-x}^2}\right) f^\gamma(x).
\]
The second integral can be computed, {\em e.g.} by dimensional regularisation. We also perform the change of variables $v\to u=1/v$ in the first integral, leading to
\[
I^\gamma(x) = \frac{\bar\alpha}{\pi} \int\frac{d^2u}{\abs{1-u}^2}\left[ \frac{1}{\abs{u}^2} f^\gamma(ux)-\frac{1}{1+\abs{1-u}^2}f^\gamma(x)\right] + \frac{\bar\alpha}{2} \log\left(\frac{1}{\abs{1-x}^2}\right) f^\gamma(x).
\]
Inserting the integral representation of $f^\gamma(x)$, one obtains
\begin{eqnarray*}
I^\gamma(x) & = & \frac{\bar\alpha}{\pi} \abs{x}^{2\gamma}
\int d^2v\,\abs{v}^{2\gamma-2} \abs{1-v}^{2\gamma-2}
\lim_{\varepsilon\to 0} \left(
\int\frac{d^2u}{\abs{1-u}^{2-2\varepsilon}} \abs{u}^{2\gamma-2}\abs{1-\bar vxu}^{-2\gamma}
-\int\frac{d^2u}{\abs{1-u}^{2-2\varepsilon}}\frac{\abs{1-\bar v x}^{-2\gamma}}{1+\abs{1-u}^2}
\right)\\
& + & \frac{\bar\alpha}{2} \log\left(\frac{1}{\abs{1-x}^2}\right) f^\gamma(x).
\end{eqnarray*}
where we have explicitly regularised the divergence at $u=1$.

Performing the integration over $u$ and taking the limit $\varepsilon\to 0$, we get
\[
I^\gamma(x) = \bar\alpha\chi(\gamma)f^\gamma(x) + \bar\alpha R^\gamma(x),
\]
with
\begin{eqnarray*}
R^\gamma(x) & = & \frac{1}{2} \log\left(\frac{1}{\abs{1-x}^2}\right) f^\gamma(x) \\
& + & \abs{x}^{2\gamma}\int d^2v\,\abs{v}^{2\gamma-2}\abs{1-v}^{2\gamma-2}
\left[
(1-\bar x v)^{-\gamma} \partial_\varepsilon\, {}_2F_1(\gamma,\gamma;\gamma+\varepsilon;\bar v x)
+
(1-x \bar v)^{-\gamma} \partial_\varepsilon\, {}_2F_1(\gamma,\gamma;\gamma+\varepsilon;v \bar x)
\right]_{\varepsilon=0}.
\end{eqnarray*}
The derivative of the hypergeometric function can be explicitly computed and we are finally left with the integration
\[
R^\gamma(x) = \frac{\abs{x}^{2\gamma}}{2}
\int d^2v\,\abs{v}^{2\gamma-2}\abs{1-v}^{2\gamma-2}\abs{1-\bar xv}^{-2\gamma}
 \log\left(\frac{\abs{1-\bar xv}^4}{\abs{1-x}^2}\right).
\]
Finally, the conformal transformation $v=\frac{1-u}{1-\bar x u}$ gives
\[
R^\gamma(x) = \frac{\abs{x}^{2\gamma}}{2}
\int d^2u\,\abs{u}^{2\gamma-2}\abs{1-u}^{2\gamma-2}\abs{1-\bar xu}^{-2\gamma}
 \log\left(\frac{\abs{1-x}^2}{\abs{1-\bar xu}^4}\right)= -R^\gamma(x).
\]
Therefore, $R^\gamma(x)=0$ and $f^\gamma(x)$ is an eigenfunction of the linear kernel with $\chi(\gamma)$ as associated eigenvalue.

\end{appendix}

redpajama_set_name: RedPajamaArXiv


John Running, celebrated for the humanity that was showcased in his photographs of people across the Colorado Plateau and the world, has died at his Flagstaff home.
The photographer was known for intimate portraits of Navajos and Hopis who were displaced from their land.
FLAGSTAFF – An Arizona man celebrated for the humanity that was showcased in his photographs of people across the Colorado Plateau and the world has died.
John Running died Sunday of complications from a brain tumor at his Flagstaff home, said his daughter, Raechel Running. He was 77.
His love of people, places and their cultures took him down the Colorado River through the Grand Canyon, to Mexico to photograph the Tarahumara and across the U.S. to highlight what he saw as injustices against Native Americans. He photographed children near the sea in Trinidad and honored another photographer with pictures of farmers, fishermen, homemakers and children in Scotland.
Running briefly aspired to be a geologist before pawning a 12-gauge shotgun his father gave him on his 12th birthday to buy a camera while working in the New Mexico oil fields. He honed photography while serving in the U.S. Marine Corps, developing photos under the cover of a blanket in his bunk. He analyzed lunar images with the U.S. Geological Survey, produced training films for astronauts and in 1967, won a photography contest in Flagstaff, where he had moved with his first wife, Helen. The two met while Running was stationed in Trinidad and had two children — Raechel and John Paul.
Throughout decades, Running mentored aspiring photographers at his downtown Flagstaff studio, which closed a few years ago. He was known for intimate portraits of Navajos and Hopis who were displaced from their land in one of the largest relocation efforts in U.S. history. He saw a similar story line in the Israel-Palestinian conflict and traveled there with Sue Bennett, a photographer who became his romantic partner, to document people's lives.
Running's photos also became album covers for Canyon Records, an independent label specializing in Native American music. Owner Robert Doyle said Running was the only photographer he would hire for more than 15 years because he was confident Running understood tribal culture and reservation life, he was generous and people felt comfortable around him.
Born in Buffalo, New York, in 1939, Running made his first trip to the Southwest as a Boy Scout in his teenage years. He later graduated from Northern Arizona University in 1969 with an anthropology degree.
His photos of cowboys, women body builders, corporate executives and pow wows landed in annual reports, calendars, advertisements, magazines and books. Running donated his collection to Northern Arizona University's Cline Library in 2014 — some 20 million images, archivist Jonathan Pringle said. Some of the collection is digitized, including a timeline of Running's life and journal entries.
The library is hopeful the collection will give people a glimpse of the work that went into Running's photos.
Navajos from Big Mountain who have resisted efforts to relocate from Hopi land were among Running's most consistent subjects. Percy Deal grew up there and said Running and his first wife were interested in Navajo women's connection to sheep, wool and weaving.
But as they learned more about an inter-tribal land dispute that forced thousands to be displaced, Running photographed the families through generations — some of whom would show up in Running's downtown Flagstaff studio looking for him or images of relatives — and became family. The studio also hosted Navajo weaving workshops.
Raechel Running said her mother's own heritage, gentle nature and a shared vision for cultural diversity, environmental stewardship and understanding helped her father in tribal communities. The couple split when Running became involved with Bennett, who died in 2003.
John Running married jeweler and rock climber, Shelley Claude, in 2012.
No formal memorial services are planned. Doyle said he plans to honor Running's work by adding it to a traveling museum exhibit on Canyon Records.
"In death we get to reclaim his light," she said.


Gingerbread cake is flavorful and easier to make than gingerbread men. A fresh loaf of gingerbread will last five to seven days. It can be served as a breakfast or spicy desert. A fresh loaf of gingerbread will last five to seven days.... A simple and delicious recipe for classic Gingerbread Men! These Gingerbread Cookies are made with all butter (no shortening!) for the best flavor. Perfectly spiced with molasses, ginger, cinnamon, cloves, and nutmeg, and decorated with a sweet and simple ( not royal icing!) frosting.
Homemade Gingerbread Play Dough Recipe is beautifully scented and coloured to mimic freshly baked gingerbread cookies. The smell of gingerbread is generally associated with Christmas time, making this play dough recipe perfect to introduce to children around �... Place your scrummy gingerbread men biscuits on oven trays and bake in batches 12-15 minutes until golden. Cool 5 minutes on tray before cooling on a wire rack. Once cooled spoon melted nestle bakers choice white melts into a piping bag and decorate according to picture and attach 2 nestle bakers choice milk choc bits as buttons. Serve.
These are the best gingerbread men I've ever eaten. This gingerbread recipe doesn't call for all the treacle common in many recipes. They have a nice light flavour with a hint of orange. how to make a particle system in unity 10/01/2015�� However the piece de resistance for me was the amazing (if I may say so myself) salted caramel icing. It did catch a bit in the pan, but I think the caramelised sugar flecks give it an even more authentic gingerbread man look.
I've had this batch of salt dough mixed up (only the dry ingredients just waiting for a great day to make some ornaments. I wanted to try Gingerbread Scented Salt Dough for an added Christmas-y smell.


Softball player for almost 8 years. Fast pitch. I was a pitcher, 2nd and short. But mostly just pitched all games. My dad was my coach. My life was centered around softball, if I wasn't on the field, I was in my back yard practicing or at the winter clinics.


text:
Resume - David Landers DVM Library
Drought (Fiction - Young Adult)
Format: Print Length
Rurouni Kenshin - Rated: T - English - Adventure/Romance - Chapters: 4 - Words: 15,565 - Reviews: 73 - Favs: 30 - Follows: 27 - Updated: 4/3/2005 - Published: 7/17/2004 - Kenshin, Kaoru This is a Jason and Courtney fanfic. It's a Harlequin Presents from back in the late 70's or early 80's. I got three books that I need help finding (one is driving me "bonkers" 'cause I didn't like it the first time around, but message #21 sounds like it and I thought I knew the name, and the more I try to remember ahh...) 1ST: The title of the book is JEWEL.
Publisher: Carolrhoda Lab TM (January 1, 2011)
ISBN: B00WZWTN4A
Prada and Prejudice
The Infernal Devices, the Complete Collection: Clockwork Angel; Clockwork Prince; Clockwork Princess
Catherine and the Pirate
The Blind Wish (Jinni Wars)
She got away from them, naked, hid and then returned to the spot she was raped and put all her clothes, and wig, on. She found a ship called The Hague and snuck onto it and hid. A guy named Karl van Buskirk found her and believed her to be male due to her disguise The Infernal Devices, the Complete Collection: Clockwork Angel; Clockwork Prince; Clockwork Princess. When he sees the baby I think it finally hits him that the baby is his. Evil cousin comes back and abducts the child and goes psycho - I think because she is preggers from back-home beau but they have no money and hero is rich. Anywho Hero saves the day and finally sees evil cousin for what she is EVIL Scotland Destiny: Sweetly Romantic Time Travel Mini-Adventures (Eternal Time Shadows Book 4). Gregory Maguire, Mirror, Mirror (2009), a retelling of the Snow White story, about a young woman in 1502 Tuscany who grows up under the influence of Lucrezia Borgia pdf. She started another quilt, using the original quilt top as a practice piece read Drought (Fiction - Young Adult) online. He is trying to get a business deal from his ex new husband. The first night she is at his house the business men shows up and the little girl cuddles him. He says as a thought "keep that up and i will by you a horse" The ex shows up...bad guy.. Emily and the Scot. Twilight - Rated: M - English - Romance/Hurt/Comfort - Chapters: 20 - Words: 165,561 - Reviews: 5368 - Favs: 3,449 - Follows: 3,165 - Updated: 4/15/2014 - Published: 11/18/2011 - Bella, Edward - Complete Serena is enjoying her tour of England when she is suddenly transported to the past, where her knowledge of history must keep her alive while she searches for the way home and tries not to fall in love with the man she will have to leave behind Forbidden. When Edward proposes an unconventional business deal to Bella, will it lead to an investment of the heart, or will someone from Bella's past cause a meteor shower of complications The Flappers: Ingenue? The heroine was Norse and thought she was too tall; she was very self conscious and thought she was ugly. The hero captured her and chained her feet together because he thinks she could hurt him or his crew pdf.
Download Drought (Fiction - Young Adult) pdf
Don't quote me but I think it was a Silluette. The cover was red and had a pair of black cowboy boots and badly drawn female toes with red polish. I remember everything but the title and author! There is a book that I have read where this rich young woman leaves her cushy lifestyle to work on a ranch. She changes her name and the rancher that hires her has a girlfriend who turns out to be a klepto online. Chris Scott, Antichthon (1982; titled The Heretic in Britain), a biographical novel about the Italian philosopher and scientist Giordano Bruno, who was burnt at the stake for heresy in 1600. Sir Walter Scott, Quentin Durward (1823), about a naïve young Scot in the fifteenth century court of the French King Louis XI Winterkill. Librivox has over 200 classic novels available for free Newt's Emerald. Lydia held her maid's boots and guided her to the ground. 'We are only a brief ride from the hostelry. If I lead you, do you think you could stay on board Rufus for that short distance?' Martha viewed the animal with disfavour but nodded. 'I reckon even riding that beast is better than standing around here getting frozen to the marrow.' When I was a child I had the most enormous dolls house online.
Ludell
Hello :) I've been wracking my brain to come up with the title and author of a book I'm hoping you all can help me with... Plot: Teacher takes in a student as a foster child (possibly named Carrie? Casey?) who was being neglected by her own mother. The little girl initially has trouble fitting in, breaks her arm, is accused of stealing by rude neighbors, breaks husband Joe's mandolin, and basically gets off to a rough start pdf. Not knowing the title and author of this book is about to drive me bananas. A Historical Romance that takes place after/during the Reign of Terror/French revolution. I believe the heroine is the daughter of French nobility My Faire Lady. The title is More than Perfect by Day Leclaire if anyone's interested. (Also, the business partner was Gabe Moretti not D'angelo and has his own story. - Becoming Dante ) I need help finding a book Ludell! I think there was an epilogue in the future, but that's all I remember, please help me get the name of this book! ^_^ 371 #1 I am sure you mean The Rake by Mary Jo Putney Peril on the Sea. I am looking for this book I read about 8 years ago. I remember some specifics but neither the title nor the author! The book has a royal couple - I believe a duke who doesn't love his wife but married because she had the right breeding and was young. When the book starts the heroine has been denied access to her baby boy because she flouted some rule Find Me Where the Water Ends (So Close to You Trilogy). As a supporter of Indie Authors she is Managing Editor for the Historical Novel Society Indie Reviews, and inaugurated the HNS Indie Award. Contact Jenn for questions about a custom image or photoshoot, or information on licensing a stock image exclusively We Hear the Dead.
A Spark Unseen
Real Fake Princess Volume 4 (v. 4)
The Merchant's Daughter (Fairy Tale Romance Series)
The Katerina Trilogy, Vol. III: The Morning Star
Conspiracy of Blood and Smoke
Manga Classics: Sense and Sensibility
Eight To One
Camp Boyfriend
Salt & Storm
These Ruthless Deeds
Cate of the Lost Colony
The Crown's Game
Raven Queen
Shadows Fall Away
Emma, Vol. 4
She h works for an arrogant (I think some genius, self made) CEO who for some reason does not show her his face The Curse: Touch of Eternity (The Curse Series). A former pastor and English professor, he specializes in historical fiction and historical western romance novels. He won a 2001 Christy Award for the Civil War drama Edge of Honor. Morris lives with his wife in Gulf Shores, Alabama. Popular author Gilbert Morris writes average of 1 book per month: http://clicktotweet.com/ROpce 1 heroine hires ex-prisoner, another hires a drunk download Drought (Fiction - Young Adult) pdf. Her son runs away and while they look for him, the house blows up. He thinks it's the people after him and she thinks it's her husband. One brother owns a bar, one does computers, one is deputy sherriff. Posted this in the other thread before I saw this one... I've been looking for a book I read about ten years ago, and I can't remember the name or author -_- I remember that the author writes a lot of romance, suspense, and damsel in distress type novels Wayfarer (Passenger). Toronto Romance Writers was inaugurated in 1986, and this small chapter has blossomed to over 150 members today. If you're serious about writing romance, and want to meet like-minded writers for discussion, support, advice, feedback or just a chance to get away from your computer and talk with people who understand what drives you to write, Toronto Romance Writers is the place to be Sweet Rebellion. At some point, someone tries to kidnap her sister. The heroine eventually gets married to a reformed rake who is ashamed of his past. The second book is actually the first part of a trilogy Forever . . . (Richard Jackson Book). Can't remember what the story ending was. The heroine decides to go to an inappropriate masked ball with a friend. They get separated and she meets this man. He has black hair with a single streak of white in it. Anyway he assumes she's a prostitue and they have sex. She's a virgin he's surprised, she politely thanks him for the sex and walks away The Flappers: Diva. PLEASE if you know the title let me know. I want to say that there is a woman with black hair on a horse in the cover but i could be wrong pdf. I forgot the author but would like to read it again Everlasting. Twilight - Rated: M - English - Romance/Humor - Chapters: 1 - Words: 13,502 - Reviews: 335 - Favs: 954 - Follows: 473 - Published: 4/25 - Bella, Edward - Complete Anastasia Steele doesn't have the most honorable life. Christian Grey doesn't have the most honorable intentions download. Chiefly performance pieces: screenplays, stage plays and radio plays on Columbus, Cesare Borgia, George and Martha Washington, Poe, Joaquin Murietta (the inspiration for Zorro), Johnny Mitchell (coal mining in 1900) and a nun, Soeur Placide de Poyanne who helped rescue the Belgian National Treasure during WWII Shadow Of The Hawk. The Hero's brother is trying to get the title and wealth from the Hero, and the mistress and brother team up for this purpose The Magic of Inherian: Scepter of Salvation, Book 1. It turns out that he is actually an aristocrat himself and it's not revealed until the end. I'm probably getting the two books mixed up. But the one I'm looking for is from the first description My Bonny Light Horseman: Being an Account of the Further Adventures of Jacky Faber, in Love and War (Bloody Jack Adventures Book 6). I read my first copy to shreds, then got it for the Kindle Dark Triumph (His Fair Assassin).
Category: Historical
Church & State
Civilization & Culture
Cleaning, Caretaking & Relocating
Differential Geometry
Mathematical & Statistical
Medieval Thought
Mothers & Children
Non-Euclidean Geometries
Revolution & Founding
Rituals & Practice
Slang & Idioms
Tropical Agriculture
All rights reserved © Resume - David Landers DVM Library	Powered by WordPress	Theme by SEOS