Tania Pryputniewicz: In your poem, "You Belong," you begin with the following lines: "She gave me a gift / her disclosure / her addiction." Can you tell us about how addiction has been a gift?
Tina Pocha: Well, I was referring more so to disclosure being a gift, but I think it applies equally to addiction. You, see in India, where I was born and raised, we have a tradition where we mark a little black dot (with an eyebrow pencil or kohl stick) on the cheek of little children to "ward off evil." Children, cute and innocent as they are, are thought to be "perfect" and thus the target of evil spirits and negative energy. So we put this little mark on them as if to say to the spirits, "Look, not perfect, go away, find another target!" Addiction, any kind of suffering really, can be like that–a little spot to remind us that we are not perfect, that we have work to do in this life. What work, you might ask. Well, for some it might be to find focus, for others it might be to learn self-containment. For me, it has been to learn compassion and to dissolve the ego. You see, I came up in a time and place (pre-feminist India) where I felt like I had a lot to prove. I had to be smarter than, better than, faster than everyone else. And this served me well in many ways–especially in the achievement-driven culture we live in today. But it also disconnected me from others, even those closest to me, my husband, my children, my friends. I found myself constantly in a hurry, impatient–why can't you do twelve things at once? I do! I separated myself, held myself aloft. Suffering was incredibly grounding. It brought everything into perspective — what was important, what was painful, what was undoing. It returned me to love. This is why I use the word "belong" in the title.
Tania P: When you say, "suffering was incredibly grounding," do you mean the process of recovery? Or reaching rock bottom?
Tania P: Are there parallels between the process of arriving at a final draft of a poem and realizations that come up in the process of recovery?
Tina P: Yes, there are definitely parallels between arriving at a final draft of a poem and recovery. It is that dipping back and back and back, the recursiveness of writing and creating that makes the poem rich and full, just as circling back to a memory or a pain propels you forward, each time you pick up a little more momentum, a little more energy. And sometimes the poem, the recovery, continues to grow and develop long after it is "finished." The words on the page may be fixed, but the meaning, the message continues to live and generate and resonate with each pass. So it is with recovery. Each day, each surrender, brings with it a deepening, an understanding that is new. Even with this interview, it has provoked me to think about the poem anew—what did I mean, what do I mean? And I imagine with each reading the answer will change, evolve.
Tina P: All my poems are, in essence, "disclosure." I know, I know, the confessional poets went out with shag carpets and avocado green appliances, but for me, at least, writing has always been about expression and testimony. It's about saying this is what I think/feel/ believe. It's about exposure, about vulnerability. In fact, that's how I see relationships as well. They are, as you say, built on "disclosure" and the trust that results from it. I think that is what moved me to write this poem. I was so touched by this person's disclosure because I knew it was offered purely as a gift, as a way to include and surround and uplift. I know that seems counter-intuitive—how can someone's disclosure about addiction be uplifting? But because the intent was or seemed to be to say, "Hey, you are not alone, welcome!" and because the "confession" was so matter of fact (here warm your feet on this), I felt uplifted—even on that "cold tile floor." Poetry, too, has that way of including and building relationships—between not only the poet and the reader but between/amongst all the readers as well. Think of how we gather around words—whether in the physical presence of each other or not—and how those words pull us together into community.
Tania P: In a broader sense, what drew you to writing poems? How has poetry served you?
Tina P: The first poem I ever wrote was in response to a moment of crisis—someone else's crisis. My professor's wife was losing her battle with cancer, and he was dying with her, just melting away. And I felt helpless. And I wanted to do something. We had set up a rotation where we each took turns bringing them food, and shopping for them, and driving them places, but we couldn't stop the grief. He was disappearing before our very eyes. So one day I just picked up a pen and wrote a poem. I needed some release. Ever since, poetry—writing in general—has been a way for me to release and get some relief. Poetry has also been a way for me to immerse myself in language and make something. I tend to be a left-brain-dominant person—rational, practical, linear—and have always envied the creatives in my life (my husband, my daughter) and their ability to make something beautiful. Poetry has been a way for me to harness some of my left-brain function (language) to cultivate and integrate my right-brain-function—intuition, emotion, and creativity. In fact, my goal, my intention for this stage of my life is integration—bringing together the polarities of left and right, masculine and feminine, logic and intuition. In Indian tradition, the marriage of Shiva and Parvati is thought to be symbolic of the ultimate integration of the soul, the achieving of enlightenment where we bring together all the (seemingly) disparate parts of our selves into one whole. I'm tired of living divided—head from heart, strength from tenderness—and poetry helps me to bring it all together.
Tania P: What role do you think labels, such as addict, or poet, play in one's life?
Tina P: We use labels to make sense of the world—so and so is such and such. It's a way for us to orient ourselves—North/South/East/West or Good/Bad or Happy/Sad—so I get why we are attached to our labels. Labels are also important in some developmental stages, adolescence for example, where we are trying to situate ourselves in the world and in relation to one another. In my own life, some labels (scholar, for example) have helped me to achieve great success; others (mother) have helped me to stay and persevere, even when I have felt incompetent and out of my element. But labels can also bring us great pain because they derive from ego—the same source of joy (getting an article published, for example) can also be a source of pain (failing to make tenure). The labels are not real. The real you doesn't change from moment to moment. It's just the ego. So another personal challenge for me the last three years has been to dissolve the ego, to rid myself of labels—even the ones that bring me joy. I can now nurture without being a "Mother;" I can write without being a "Scholar." And yes, the highs are not as high, but neither are the lows as low. I recently wrote a blog post, "On Why I Am Not a Poet," which received mixed responses. I think I may have offended some working poets who live the poet's life with great passion and integrity. I think my rejection of the label "Poet" came off as a rejection of them, of all poets, and that was not my intention. I was trying to say that I want to reject all labels. I could equally have written a blog post titled, "On Why I Am Not a Mother" or "On Why I Am Not a Scholar" – both would have been true. I think what I am trying to say is that labels have been useful in my life, but ultimately they have been a way to separate myself.
Tania P: Finally, what does "recovery" mean to you?
Tina P: Recovery means starting anew. The tower has come tumbling down. You are sitting, cross-legged, rubble all around, with nothing and no one on the horizon. It reminds me of one of my favorite lines from the poet Masahide, "My barn having burned to the ground, I can now see the moon." It is that hopeful place from which all things are possible. For me, it began with a period of isolation, of being okay alone, of taking stock, being still, and then slowly putting the pieces back together, one at a time. I had to separate in order to regroup. It was a slow, gradual process. Recovery means you can circle back–to your original self, to the people you left behind–but also move forward, kind of like the gravitational slingshot maneuver used to propel Voyager into space. Recovery means healing–from the inside out. The old triggers, the old provocations find no ingress. The wound has scabbed over.
A graduate of the Iowa Writers' Workshop, Tania Pryputniewicz is a co-founding blogger for Tarot for Two and Mother Writer Mentor. Saddle Road Press published her debut poetry collection, November Butterfly, in 2014. Recent poems appeared or are forthcoming at Extract(s), NonBinary Review, One, Patria Letteratura, and TAB: The Journal of Poetry and Poetics. She lives in San Diego, California with her husband, three children, blue-eyed Husky, and two portly housecats. She can be found online at www.taniapryputniewicz.com.


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Home / Unlabelled / The #1 Song for Summer 2021 is Bubblegum by Groove Kennedy
The #1 Song for Summer 2021 is Bubblegum by Groove Kennedy
Michael 6:50 PM
The official song of the summer has been declared. The winning song is, "Bubblegum" by Groove Kennedy. Bubblegum has over 250,000 thousand sound usages on the music app, Tik Tok, over 1 million views on spotify and youtube, but most importantly it has been declared the hottest song of the summer by everyone from Kanye West to Bob Lefsetz.
Kanye Kardasian West mentioned the song in an interview when talking about his own album, Donda. He also wanted to point out that he isn't saying Bubblegum is better than anything on his Donda album, just that he liked the song, and so far it is the "song of the summer."
Music critic and email blaster/blogger, Bob Lefsetz mentioned the song on his radio show while discussing the reddit stock market phenomenon with Gamestop. Lefsetz has also mentioned other hot songs this summer including the now trending song, Seventeen Going Under by Sam Fender. Lefsetz is known for his music blog in which he takes money from major labels to act as if he "just discovered" hit songs that just happen to be on major labels paying him.
"Bubblegum" is the lead single from the compilation album, Evil, In Diana, an album produced entirely by Groove Kennedy and consisting of 7 artists signed to his label, Jesus Rode a Dinosaur. The song premiered on hip hop's biggest website, AllHipHop in June. The single and entire album are both available at www.JesusRodeaDinosaur.com
Enjoy Bubblegum by Groove Kennedy below
The #1 Song for Summer 2021 is Bubblegum by Groove Kennedy Reviewed by Michael on 6:50 PM Rating: 5

redpajama_set_name: RedPajamaCommonCrawl


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Odd takes on the news
By RICHARD SCHNEIDER on	 March 1, 2008
Not Your Father's BMW Advertisers are masters of the double-entendre, but sometimes the sexual meaning is so obvious that it's hard to figure out what the "clean" interpretation would be. Such was the case for an ad that ran in various American newspapers this winter, a picture of a BMW with the caption "Hard Top. Firm Bottom." (Do cars have "bottoms"?) This is what made it so odd when a spokesman for the ad agency offered a "Shocked, shocked!" response when asked about the campaign. "You're the first person to bring it up," said gsd&m Idea City account director Corey Platt, admitting that "I can definitely see how it can be taken that way." Denying that they had deliberately targeted the gay audience, he then mused that this appeal was an added "bonus" in cities like Miami and L.A., where more gay men are presumably driving BMW's these days. The clincher seems to be the phrase "It's so L.A." (or Miami, etc.; italics mine) that they're pitching to a very special market. But the question remains: what could the words "hard top, firm bottom" possibly mean to a straight car buyer?
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HomeInstrumentationsString orchestraVivaldi Concerto for 4 Violins in F major Op.3 No.7
Vivaldi Concerto for 4 Violins in F major Op.3 No.7
By: Vivaldi
For: String orchestra
Score with full set of eight parts
Full set of eight parts (no score)
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Paul Wood
Mymusicscores.com
L'estro Armonico op. 3 ("Harmonic Inspiration" in Italian) is a collection of twelve concertos for 1, 2 and 4 violins written by Antonio Vivaldi in 1711. It largely augmented the reputation of Vivaldi as Il Prete Rosso; (The Red Priest). The collections were mostly put together in a chronological order.
Photo by Umutcan Günüç on Unsplash
Albinoni Sinfonia in G for String Orchestra, Fux Overture in C major for String Orchestra, Albinoni Concerto in E minor for Strings Op.2 No.2, Vivaldi Violin Concerto in E major Op.3 No.12, Vivaldi Concerto for 2 Violins in D minor Op.3 No.11, Vivaldi Concerto for 4 Violins in D major Op.3 No.10, Vivaldi Violin Concerto in A minor Op.3 No.6, Vivaldi Violin Concerto in D major Op.3 No.9, Vivaldi Concerto for 2 Violins Op.3 No.8 for String Quartet, Handel Concerto Grosso Op.6 No.9 and Vivalid Violin Concerto Op.6 No.3 for String Trio
Reviews of Vivaldi Concerto for 4 Violins in F major Op.3 No.7
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Score: Vivaldi Concerto for 4 Violins in F major Op.3 No.7
Score: Vivaldi Concerto for 4 Violins in F major Op.3 No.7 & full set of eight parts (Show part names)
Cello, Harpsichord, Viola 1, Viola 2, Violin 1, Violin 2, Violin 3 and Violin 4
Full set of eight parts (Show part names)


Grief does not discriminate. Grief affects all of us, irrespective of age, gender, cultural background, income level, etc. At some point, we all will experience grief, and when this happens, we can become thrown off course - and can feel, we will never be able to smile again.


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Concordia University, St. PaulAcademic Catalog, 2022-2023 Edition
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INNOVATION is paving the future of Gippsland's city centres as ReActivate Latrobe Valley continues connecting the community with new projects.
Latrobe Valley residents may have noticed a technician scanning the buildings of Morwell's central business district over the past fortnight.His name is Greg Afflick and he has been busy using terrestrial scanners to digitally map the area from the western end of Commercial Road to Hazelwood Drive.
It is all part of preparations for the "bigger and better" 2015 Winter Night Festival, which will see a range of artwork projected onto Commercial Road shopfronts and infrastructure.
ReActivate Latrobe Valley co-directors Rosalea Monacella and Craig Douglas said the group's intent was to build upon past projects, which they hoped could reconnect people with their town centres.
first go at doing projections onto buildings," Mr Douglas said. "We had a lot of fun with that and got a really good response from the public. "This time we'd like to do it again and do it better," he said.
ReActivate has asked artists to respond to each of the buildings' specifics, where even windows and doors can be used for more interactive displays.
The 26 scans were taken in three days and come with 100 million points of information, which Mr Douglas said would provide local artists with more scope for innovation. Artists who plan to submit their pieces by Monday, 23 March, can also attend a workshop on Friday, 20 March, to better understand the projectionist's tools.
"So for someone who might be creating artwork or organic candles, it's actually profiling that innovation that's going on at a local level," Ms Monacella said. "Ideally we're profiling Gippsland artists, but we're trying to draw in a range of responses to the area."
This year's Winter Night Festival - to be held in June - will have events in Moe, Traralgon and Morwell. Mr Douglas said the festival, along with other initiatives such as 'Get Sunflowered', was mainly a "celebration" of the people and their towns. ReActivate Latrobe Valley and other community groups will join Latrobe City Council to sign a Memorandum of Understanding next week.
"In a funny way, part of what we're doing is describing back to people what's good about living and working here," Mr Douglas said. "Because, you know, you forget. You drive past something everyday and it becomes normal and you forget what's special about it."
If your interested in taking part in this years 2015 projection festival please contact us, or go to the the ReactivateLatrobeValley Facebook Page >>>> https://www.facebook.com/ReactivateLatrobeValley. to find out more, plus other Latrobe projects that you can be involved in!


Getting off the beaten path and onto roads less traveled is becoming increasingly popular as the gravel discipline grows and adventure bikes abound. The cyclocross bike used to be the ideal bike for multi-surface endeavors, but many cyclocross machines have tight geometry, higher bottom brackets and tighter gear ranges.
The growth of gravel and adventure events inspires a bike for the long haul over rough roads. In the past we called these "touring" bikes, but the new breed are more sport bikes than load carriers.
Montreal's Opus Bikes is one of the bike companies embracing adventure riding. Opus' Spark is a gravel/adventure bike designed to provide a relatively affordable ticket to roads less traveled. The Spark 1 starts at less than $1,200 USD with mechanical brakes and goes for under $2,000 with a Shimano 105 drivetrain and hydraulic disc brakes.
We have been riding roads, gravel and more on the Shimano 105 Spark 1 for the past several months. Read on to find out if it answers the call of the wild for budget-conscious gravel and off-road adventurers.
The core of the Opus Spark is a 6061 aluminum TIG welded frame of hydroformed triple-butted tubes. The Spark frames are attractive with a gently arcing top tube combined with arced seatstays. Our Spark 1 review bike has an eye-catching silver anodized look. The frameset has a full carbon tapered steerer fork is 12x100mm thru-axle, flat mount disc and painted to match the frame.
The rear end is 12x142mm thru-axle with a replaceable axle nut. The rear brake caliper is flat mount on the chainstay set for a 140mm minimum rotor diameter.
The BSA standard threaded bottom bracket drops 68mm from axle height and the chainstays run almost parallel to the ground with a curve up to the dropouts at the end, which is intended to reduce chain slap. All rear control lines run through the large down tube and exit at an opening just in front of the bottom bracket. The front brake line also runs internally through the left fork blade.
All this makes for a frame with curb appeal, complete with mounts for fenders and a rear rack, as well as two bottle cages.
The geometry on the Spark 1 falls somewhere between a slack gravel and steeper all-road frame. For our size medium review bike, the effective top tube is 55.5cm with a 72-degree head angle and 73-degree seat tube angle. The bottom bracket drop is 68mm, a typical choice on a cyclocross bike, but as much as 7mm higher than a typical road bike. The stack is 582mm with a 377mm reach. The 43.5 cm chainstays are longer than a 'cross bike, but that will aid tire clearance, comfort, stability and load carrying.
The Spark 1 is the top of the Spark model line with Shimano 105 components except for the FSA Omega aluminum crank with 48/32t "adventure" chain rings and FSA Mega-Exo bottom bracket. The shift/brake levers are Shimano RS505 hydraulic 11-speed with a long body that houses the hydraulic master cylinder and a large bulbous end that houses the shifting mechanism. Our bike came with a short cage Shimano 105 rear derailleur and an 11-28t 11-speed cassette. Rotors on the bike are 160mm in the front and 140mm in the rear.
Other components are an unlabelled aluminum bar and stem. The handlebar has a compact bend and a bit of flare to the drops. The seatpost is a 27.2mm diameter aluminum two-bolt model topped with a Selle Italia Q-Bik saddle.
A relatively lightweight addition to the build is the 1,560 gram Alex Rims A-Class CXD4 wheelset with aluminum tubeless ready rims. Vittoria Revolution 32mm road tires came mounted to the wheels. The tires have a reflective sidewall stripe which is great if you are riding in the dark.
All-told, the Spark 1 weighs 21 pounds without pedals and 14 pounds without wheels. This is a reasonable weight at the price point. For comparison, the Kona Major Jake retails for $1,200 more and only weighs 0.2 pounds less.
The Spark has an entry price of less than $1,200 USD and our flagship Spark 1 is a mere $600 more with hydraulic brakes and solid componentry. That price provides an entry point to the drop bar, disc brake gravel bike market that is relatively accessible to the masses.
The Spark's hydroformed aluminum frame and all carbon tapered fork with flat mount brakes and 12mm thru-axles make the Spark frameset ready for any upgrade, and the multitude of mounting fixtures and clearance for 42mm tires makes it ready for almost any adventure.
Our Spark 1 review bike came with commuter-style 32mm road tires, so that is where we put it to its paces first. The Spark has nice pavement manners with the 32mm tires at 60 psi. At 80 psi road buzz was very apparent unless on newly paved asphalt. Hit a small pothole or ridge in the pavement with that tire pressure and it is a bit jarring. The aluminum Opus frame does not soak the hit much, but it is certainly much better than aluminum race frames of the mid-1990's which gave aluminum a bad reputation for ride quality.
The geometry and hydroformed frame help with the Spark's ride quality and the stiffness in the bike is not objectionable. The bike's cornering is relatively neutral, steering where you lean it, and the Spark 1 is responsive to input, if not lively.
Tires with narrow, smooth treads and stiff sidewalls are not ideal for off-road riding, so for much of my time testing the Spark 1, I swapped in other wheels with 33-40mm tires. (The Spark 1 is now spec'd with 33mm Vittoria Terreno Dry tires, which is more in line with the bike's adventure billing.) These tires were all tubeless run at pressures between 23-30, depending on tire size. The goal was to assess the Spark as a gravel and cyclocross bike as we would normally ride it.
The Alex A-Class CDX4 wheelset run with both tubed and tubeless tires proved a reliable mid-weight, low-price set that is truly tubeless ready. The other wheelsets I ran with the Spark 1 were high-end sets that did not significantly change the bike weight. Interestingly, the biggest changes in ride quality I observed were primarily due to tire and pressure changes.
With tubeless tires at the stated pressures, the bike feels like some aluminum bikes we raced just a few years ago, except with the improved control of hydraulic disc brakes. The road manners in cornering and tracking transfer to the dirt. Admittedly, so does the frame stiffness, which is not a bad thing. It just takes some time to adapt to.
The Spark 1 feels fast in the dirt and a bit chattery in the rough. I'm not sure it's the best choice for a long gravel adventure, but it is fun to ride for shorter mixed terrain rides, and of course, on pavement.
The Opus Spark 1 is a great value as a Shimano-105-equipped bike with hydraulic disc brakes. It is versatile and makes for a great all-weather commuter that can be quickly coaxed into weekend mixed terrain and off-road adventures. The aluminum frame provides a solid ride that will not hold you back from going hard on most terrain.
It is encouraging to see Opus now specs the Spark 1 with Vittoria Terreno Dry tires that are in line with its adventure billing. The Spark 1 has a versatile build that allows for experimenting with different setups, so it is definitely worth trying different tire pressures and even tires if you choose the Spark as your new gravel bike.
For more on the Opus Spark 1, see the specifications and photo gallery below.
See our archives for more gravel bike reviews.


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The all new TrailMaster Turino 50A scooter brings retro scooter styling to everyone! The Turino 50A features a tough little 50cc engine and smooth running automatic CVT transmission with enough power to handle quick trips around the neighborhood and local city streets at speeds up to 30 miles per hour! Not only do you get big, 12 inch mag style steel wheels for great handling, but the Turino also comes standard with a front disc brake for effortless stopping power. But this little scooter is not just all mechanics. It sports some pretty neat design features, too, like a luxury leather seat, LED turn signals, and even a handy USB adapter inside the lockable dash storage area for charging your phone on the go! Stylish color-matched rear view mirrors and generous chrome trim give this moped that extra touch! Comes fully assembled! Electric start. Several colors!


**** Others may be added in the future! For now, the above items guide the site's content focus.
Where did the site name and URL come from?
Inspiration to work until all the rhetoric becomes removed, so the root cause stands on its merit. In the world of investing, the amount rhetoric reaches epidemic levels. StreetRhetoric.com comes from connecting the nickname of Wall Street with all the rhetoric generated from the activities enabled by its patrons. Now the beautiful simplicity of removing rhetoric to understand merit and unveil knowledge creates a lasting motivation.
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For Winthrop parents, a long basketball journey from Australia to Milwaukee
Bill Glauber
They came from Ames, Iowa, and Reno, Nev., from Minnesota and Indiana, South Carolina and Tennessee.
But by far, the longest journey to Thursday's NCAA men's basketball tournament in Milwaukee was taken by Josie and Eric Cooks of Wollongong, Australia.
They hopscotched 34 hours from Sydney to Los Angeles to Seattle to Milwaukee to see their son Xavier play for Winthrop University.
And after all of that, Winthrop was one and done, losing to Butler University, 76-64.
But for the Cooks family, the journey was perhaps a once-in-a-lifetime chance to see their son perform at the highest college level. Xavier Cooks, a 6-foot-8-inch junior, led Winthrop with 23 points.
"When you live on the other side of the world, it's hard for Australian kids to get scholarships much less make the NCAA Tournament," Josie Cooks said.
For Eric Cooks, traveling to Milwaukee was about as close he could get to coming full circle in his life. Born and raised in Gary, Ind., he played at St. Mary's College in California, then had a long pro career in Australia, where he met his wife, started a family and put down roots. He is currently an assistant coach for the Wollongong Hawks.
RELATED: Butler 76, Winthrop 64: Avery Woodson's threes lead way
BRACKETS: USA Today Bracket Challenge | Printable bracket
MORE COVERAGE: NCAA Tournament section
An older son, Dominique, played basketball at Chaminade University in Hawaii and settled in North Carolina. He attended the game with his parents and told them, "Just make the most of it."
Despite the loss, Eric Cooks savored every moment of the game.
"It's worth it, regardless," he said when asked if a defeat would spoil the trip.
In a way, that's the beauty of March Madness. For a lot of teams, just landing a spot in the tournament can make or break the season.
"It's great for the institution, great to elevate the atmosphere" said Doug Presley, who oversees the Winthrop pep band. "There are many of our kids who hadn't even been on a plane before this trip."
The band and cheer squad made a lot of noise, but it wasn't enough to lift the Eagles.
Winthrop's March Madness was a short one. Done before dinner.


Well what an exciting and jazzy week! (and I am not just talking about the wild prints I am lusting after) We've seen the nation come together with pride and joy over the arrival of our future king so I guess the time has come for me to announce that I, like Kate Middleton (just probably not as glamourously) will be having a baby in 2013 :) The blog will continue as normal other than the fact I will just get bigger each week! If anything style wise has changed, it is only that I have developed a dangerous taste for items I couldn't have afforded even before my life changing news - mainly a new obsession with everything Topshop Boutique! Of course I have to think differently as to how I dress, but I'm still young, still very fashion conscious and will always stay true to my own style but am looking forward to this new wardrobe challenge!
You may have seen this stunning print in Naomi's Week In Style and quite rightly neither of us can get enough! In this classic Topshop Boutique style dress (also in black and burgundy, also adore) this dress is the perfect statement on its own on a hot summers day but I cannot wait to start layering this in the colder months.
You may also have seen this jumper in our review of MinkPinks AW13 collection but I cannot stop thinking about this jumper. We met in the window of UO at Marble Arch and it was definitely love at first sight. Each Autumn that comes around sees my knitwear addiction get worse and worse and seeing as its July and 30oC and all I want is this jumper, I have reason to believe it's started again.
This beautiful dress is exactly the same shape as the pink leopard print one from last week and I am glad I've held out as this print is a lot more me. Again, it's the perfect balance between summer and Autumn with all the collar and layering potential I enjoy from a statement dress. This has gone straight to the top of the wishlist!
Big florals are making a come back for A/W in rich autumnal colours and oversized prints! You don't have to tell us twice to sport big and clashing florals so we decided to try it out but in a summery spin on it!
For this look I wore my Topshop floral dress which I love the shape of! It's so summery and flattering and I always feel super girly in it which I love for summer! I wore a sleeveless shirt underneath to smarten it up and put a different spin on the dress for a sophisticated summery look. I wore my favourite zara necklace which picked out the colours in the dress and a skinny vintage belt.
A simple look but I felt summery and confident in the outfit. I can't wait for A/W where I can full on clashing florals and all the rich colours and layers. How bad is that, I'm longing for winter so I can start layering! After all winter is so more chic!
Florals are perfect all year around, you just need to get your colour palette and textures right! Inspired by a double age spread in this months Vogue, it seems blush pinks and autumnal oranges, rusts and darker greens are this AW's floral friends.
Get some rawr! back into your wardrobe, and the best thing is you don't even need to wait for the weather to settle down. Leopard print will always be around, especially in late summer through to Christmas but seems to be taking on a sleeker and sexier feel for AW13, so get Kat Slater out of those fashion police brains.
This dress is a super old topshop one that just seems to never go out of fashion. The buttons and mini collar detail make it perfect for day wear but the sheer material gives it that dressier edge.
What leopard print gems have you gotten hidden away from past seasons? Get them out and give them the 2013 make over!


We want the Nursery to be a fun, safe place for our little ones, and we are committed to helping children become comfortable with us here.
Parents & other caregivers: you are always welcome to stay with your child(ren) to reassure yourselves and them that all is well here. You are also welcome to leave your child(ren) and attend the service for your own spiritual nourishment. We will do our best to engage children in play and comfort them as needed (but we will come and get you if anyone is inconsolable.
Families with babies and toddlers (or older kids) who are able to sit quietly are always welcome in the service as well, and those with 'wanderers' who would prefer not to be in the Nursery are encouraged to seat themselves in the Social Hall area.
The nursery is staffed on Sunday mornings and at some other times by paid care providers. There is no charge for using the nursery, although families attending regularly are encouraged to register for the RE program and make a pledge to the congregation.
At other times, families are welcome to supervise their own infants & toddlers in the nursery.
The nursery is for children ages birth – 3 years old. There are rooms downstairs with play space and toys appropriate for older children – please use them if your children are over the age of 3!
NO food or drink in this room (other than labeled bottles for infants as needed.) Some children have serious food allergies or sensitivities and we can protect them by keeping crumbs and such out of their reach in this space.
PLEASE clean up after yourself and your child if you use this room after the staff has gone home. Nobody else is going to, and then the staff will have to clean up before service on Sunday. That's not fair to them when they left it clean!
Our regular nursery staff person is Stacy Mahon. Stacy has a degree in education from Chestnut Hill College in Education and has worked in childcare in a variety of settings since 2007. She has provided weekly care to the youngest BuxMont UUs since 2010.
Stacy is assisted each week by a teen or young adult from our Fellowship. These workers, like Stacy, are familiar with our little ones, kind, caring, and competent.
Any questions? Please contact the DRE.


text:
REGISTRATION, ACCOMMODATION & TOURS
Professor, Department of Plant
& Environmental Sciences
Faculty of Biochemistry,
Weizmann Institute of Science,
Prof. Asaph Aharoni
Speaker's Bio
Senior Researcher, Department of Ornamental Plants and Agricultural Biotechnology, Institute of Plant Sciences, ARO, Volcani Center, Rishon LeZion, Israel
Dr. Tzahi Arazi
Doctor, Laboratory of Plant Breeding,
Department of Plant Sciences,
Wageningen University & Research,
Wageningen, The Netherlands
Dr. Christian W.B. Bachem
Regius Professor of Botany,
University of Cambridge,
Prof. David Charles Baulcombe
Director, C.M. Rick Tomato Genetics Resource Center,
University of California Davis,
California , U.S.A.
Dr. Roger T. Chetelat
Department of Immunology,
Prof. Eran Elinav
Professor, Faculty of Life
and Environmental Sciences;
Director, Tsukuba Plant Innovation Research Center, University of Tsukuba,
Tsukuba, Japan
Prof. Hiroshi Ezura
Professor of Biochemistry;
Head of Plant and Microbial Sciences,
School of Biological Sciences,
Royal Holloway University
of London, Egham Hill, Egham,
Prof. Paul D. Fraser
Research Director,
Italian National Agency for New Technologies (ENEA),
Energy and Sustainable Development),
Dr. Giovanni Giuliano
Department of Cell
and Metabolic Biology,
Leibniz Institute of Plant Biochemistry,
Halle, Germany
Prof. Bettina Hause
Horticultural Sciences,
University of Florida,
Gainesville Florida, USA
Prof. Harry Klee
Doctor, Head of Algae, Fungi and Plants Division, Department of Life Sciences, Natural History Museum, London, UK
Dr. Sandra Knapp
Doctoral Supervisor, College
of horticulture, Agricultural University,
Prof. Ping Leng
Researcher, Department of Vegetables and field Crops, The Institute of Plant Sciences, Agricultural Research Organization (ARO), The Volcani Center, Rishon LeZion, Israel
Dr. Michal Lieberman-Lazarovich
HHMI Investigator,
Cold Spring Harbor Laboratory,
Cold Spring Harbor,
Prof. Zachary B. Lippman
School of Integrative Plant Science,
Cornell University, Ithaca,
Prof. Gregory Martin
Prof. Lucas Mueller
Head of the School of Plant Sciences and Food Security,
Tel Aviv University, Tel Aviv, Israel
Prof. Guido Sessa
Professor, Institute of Plant Breeding, Genetics & Genomics,
University of Georgia,
Athens, Georgia, USA
Prof. Esther van der Knaap
Group leader, Institute of Genetics and Developmental Biology (IGDB), Chinese Academy of Sciences,
Prof. Cao Xu
Max-Planck-Institute of Molecular Plant Physiology,
Potsdam, Germany
Dr. Saleh Alseekh
Professor, School of Plant Sciences
and Food Security,
Prof. Adi Avni
Director, Max Planck Institute
for Chemical Ecology,
Department of Molecular Ecology,
Jena, Germany
Prof. Ian Thomas Baldwin
Professor and Head, INRA/INPT laboratory "Genomics and Biotechnology of Fruits", University of Toulouse, Institut National Polytechnique - ENSA Toulouse, France
Prof. Mondher Bouzayen
Professor, Faculty of Agriculture,
Institute of Plant Sciences,
The Hebrew University,
Dr. Idan Efroni
Plant and Environmental Science, Weizmann Institute of Science,
Dr. Yuval Eshed
Proffesor, Max-Planck-Institute
of Molecular Plant Physiology,
Potsdam-Golm, Germany
Prof. Alisdair Fernie
Professor, USDA-ARS Robert W. Holley Center and Boyce Thompson Institute, Cornell University Campus, Ithaca NY USA
Prof. James J. Giovannoni
Professor, IBMCP (CSIC-UPV),
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Professor, Director General
Agricultural Genomics Institute, Shenzhen, Chinese Academy of Agricultural Sciences, Shenzhen, China
Prof. Sanwen Huang
Seoul National University,
College of Agriculture and Life Sciences,
Department of Plant Science,
Prof. Byoung-Cheorl Kang
Barnett Rosenberg Professor, Department of Biochemistry and Molecular Biology and Department
of Plant Biology, Michigan State University, East Lansing, Michigan USA
Prof. Rob Last
Research Geneticist, Department
of Vegetable and Field Crop Research, The Institute of Plant Sciences,
Agricultural Research Organization (ARO), The Volcani Center,
Rishon LeZion, Israel
Dr. Ilan Levin
Frances Brody Chair in Life Sciences,
Department of Biology, Technion,
Haifa, Israel
Prof. (Emer.) Eliezer Lifschitz
Project Leader,
Department of Metabolic Biology,
John Innes Centre,
Prof. Cathie Martin
Professor of Biology, Department
of Biology, Indiana University, Bloomington, Indiana, USA
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Escola Superior de Agricultura
"Luiz de Queiroz"
University of São Paulo - USP,
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Research Scientist, Department of Vegetable and Field Crop Sciences,
Plant Science Institute, Volcani Center, Rishon LeZion, Israel
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Institute of Plant Sciences and Genetics in Agriculture, The Robert H. Smith Faculty of Agriculture, Food and Environment, The Hebrew University of Jerusalem, Rehovot, Israel.
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text:
Jeff the Gatekeeper Caught in a Fib
by News Division · November 29, 2017
It's not a "radio show," Jeff. It's a podcast. There is a difference.
[Jeff Dornik] seems to have made it his mission to single-handedly tweet-storm Phil Johnson to death. It may be that he resembles what I imagine the Lance Bass of discernment would look like. It could be the newness of him. It could be because Howse pulled Dornik out of his sleeve like a cheating gambler pulls out an Ace of Spades, right when he decided to flush two of his best podcasters down the Worldview Weekend toilet (if ever there was an appropriate metaphor, that is it) for not aggressively defending him well enough. Perhaps it's because Dornik hit the ground running on Howse's network with all the enthusiasm a lap dog has for its master, I don't know. But, watching Dornik relentlessly attack Phil Johnson with a steady flock of two or three angry, heckling women has me moderately annoyed.
That's how we began the post, Jeff the Gatekeeper, On Maybe Keeping it Shut. Jeff is so not keeping it shut. Bless his heart.
The first thing you need to know about Jeff Dornik is that he's a hatchet man for Brannon Howse. Howse lost his first-string podcast hosts in the summer of 2017 because of his handling of White's Interfaith Dialogue with Yasir Qahdi. To fill the noticeable void, he reached out to a couple guys in a desperate attempt to find a rag-tag group of yes men to follow him around like Chester does to Spike in the old Looney Toon cartoons. Jeff was – and still is – thrilled to talk into his $24.95 PC mic for the great and honorable cause of Brannon Howse.
More than a month has gone by since we left Jeff the Gatekeeper (or @JefftheGK as he is known on Twitter) and he is still on Twitter pecking at people over the James White Contra Mundum of 2017 affair. Apparently, some things are hard to let go. Heck, he just posted an article about James White's IFD twenty minutes ago over at his blog (Alexa Rank is zero in case you were wondering).
The thing is, we very clearly do not agree with the concept of a game of two-hand hug played between a Pastor and Imam instead of debating or disputing. What we also don't like is the endless molotov-throwing at anyone Brannon Howse tells you to twitter bomb. There are vultures and other carions who eat the dead. And then there are parasites that live in the stomachs of carions. Then there are viruses that live in the body of those parasites. That is Jeff Dornik, refusing to let go of the righteous white knight twitter jousting for the honor of survivor blog gals type thing he's been doing for four or five months now. Let it go, son. Seriously.
They're not radio programs. They're podcasts. But do you know who's missing from this list? Justin Peters. Mike Abendroth. Susan Heck. Jesse Johnson.
Jeff the GK is a lesson in doing whatever it takes to bring down a theological opponent, in this case, Phil Johnson. Playing on the cues of Brannon Howse, Jeff began to attack everyone who wouldn't attack James White for his IFD (if this sounds like third grade, it's understandable). However, when you begin to bend and warp the bounds of personal integrity, your righteous battle becomes unrighteous…and pathetic.
This tweet from Phil Johnson demonstrates the point.
So Jeff the Gatekeeper says, "As a lifelong supporter of [Grace to You] and someone who has attended their Shepherds Conference multiple times, I'm not allowed to ask where my money is going?"
The inference seems clear. Jeff is a supporter of GTY. What kind of supporter? He's a financial supporter. After all, he's "allowed to ask where [his] money is going." So, Phil Johnson – being the director of Grace to You – apparently has access to such information (go figure). Phil then calls him out on the fib, and points out that Jeff had "NEVER" been a donor to GTY.
Jeff's response was, "If I never claimed to be a donor, how am I lying about being a donor?" The only way Jeff could not have claimed to have been a financial donor is if (A) by calling himself a "lifelong supporter" he meant to support in terms of well-wishes and positive thinking and by "I'm not allowed to ask where my money is going" he meant only his conference registration fees for ShepCon. At which point, the obvious answer would be, "Your conference registration fees for ShepCon are going to…you know, ShepCon.
It would be best if Brannon Howse kindly and discreetly let Jeff the GK go. Or maybe it's best that Jeff the GK let Brannon go. Or maybe it's best that they both just go.
[Editor's Note: Posts coming soon include, "Dismantling the Worldview Weekend Newsletter" and "Where is Brannon Howse a Church Member?"]
Dr. Sproul Goes To Heaven: Five Videos to Remember Him
by News Division · Published December 14, 2017
Robots Are Taking Over the World: Jim Bakker Gives New Reason to Buy Survival Slop Buckets
by News Division · Published January 18, 2018
Listen to this Sermon! The Pope is AntiChrist
by News Division · Published October 11, 2017
Next story Michael Brown is More Dangerous to Christianity than a Jihadi: We Release Emails with Brown
Previous story Jim Bakker and John Shorey Give Prophecies from Random Guy They Know
California Legislature Blames Religious People for LGBTQ Suicides
Gay Priest Says He's More Concerned About People Reading Pulpit & Pen Than Watching Adult Entertainment


Microsoft Publisher makes it easy to create advertising and marketing materials for your business without extensive training or practice. You do not even have to design common types of materials from scratch, because Publisher includes ready-made templates. You can either use these templates without changes and just add your text, or use them as a basis for your own design. Use Publisher to create postcards that you can mail to clients to announce events or sales, or to remind them of appointments or payments due.
Launch Publisher. Click the "File" menu and choose "New."
Click "Postcards" at the farthest right of the "Most Popular" category of templates on the page that appears to the right of the File menu. A page of postcard templates appears. Select "Installed and Online Templates" from the pull-down menu at the top left of this page.
Look through the thumbnails and choose among the postcard templates. Click on the "All Marketing" or "All Real Estate" folders if you want to see more templates in those categories. Click on the thumbnail of the postcard template that you decide on to open it in the main Publisher window.
Delete the filler text on the information pane of the postcard and type your own text in its place, or leave rows blank if you wish. Import pictures using the "Insert" toolbar and the "Pictures" or "Clip Art" icon if you want to add images to your postcard. Position and size these images with your mouse. Click on any nontext windows to change their size or color using your mouse and the menus that appear when you right-click the fields.
Scroll down to view and edit the address pane. Delete the filler text in the Return and Recipient address fields, and type your business address in the Return address box. Right-click on any nontext fields you want to edit, and import images and position them with the "Pictures" or "Clip Art" icons.
Save your work by clicking "File" and "Save As," then specifying the file name and save location on your computer.
Print a copy on regular paper and take it to your local post office to make sure it meets postal regulations if you intend to send it by mail.
Click on the text box to the right of your work and delete it before you send your file to a commercial printer or print it on postcard stock.
Save the postcard in PDF format, if need be, by using Adobe Acrobat. Click "Save as Adobe PDF" if you want to prepare your postcard for sending as an email file attachment.
DeMerceau, John. "How to Make Postcards in Microsoft Publisher." Small Business - Chron.com, http://smallbusiness.chron.com/make-postcards-microsoft-publisher-50290.html. Accessed 21 April 2019.


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Centrally located for Suffolk's tourist attractions.
Doves Barn Cottage is a 'Quality in Tourism' 4 star rated, 2 bedroom holiday rental property situated on the outskirts of the picturesque but well served village of Needham Market, in the heart of rural Suffolk. It is available for rental throughout the year.
The tastefully furnished living room includes a flat screen TV with DVD player. The property has a fully fitted kitchen including a dishwasher, washing machine and a breakfast bar. The bathroom is located on the first floor of the property with a bath and overhead shower. The master bedroom has a large walk in wardrobe and both bedrooms are equipped with TVs. The inside of property is non smoking.
The exterior of the house consists of a private garden and patio area with gas barbecue and seating.
The owner of the property resides on site in a separate detached dwelling and is on hand to help with any enquires but is always unobtrusive.
There are pubs, takeaways and local shops located in the village, and the larger market town of Stowmarket is only a few miles away which has mainline train service to London.
Outdoor Facilities: Yes. private seating area and gas barbeque to the rear of property.Private enclosed garden to the front of the property with decked seating area.
Local Services: Needham Market is situated off the A14 between Stowmarket and Ipswich. It is served by a local railway station and has a regular bus service (Numbers 87, 88 and 88A).


Designed to make books look irresistible, the Rainbow Box in a natural birch finish is a flexible portable wooden storage box for kids books, toys and more. A natural, handmade alternative to a traditional children's bookcase.
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text:
\section*{ON JUSTIFICATION OF GIBBS DISTRIBUTION\footnotemark}
\footnotetext{REGULAR AND CHAOTIC DYNAMICS, V. 7, No. 1, 2002

{\it Received January 10, 2001

AMS MSC 37H10, 70F45}}

\begin{centering}
V.\,V.\,KOZLOV\\
Department of Mechanics and Mathematics\\
Moscow State University\\
Vorob'ievy gory, 119899 Moscow, Russia\\
\end{centering}

\begin{abstract}
The paper develop a new approach to the justification of Gibbs canonical distribution
for Hamiltonian systems with finite number of degrees of freedom. It uses the condition of
nonintegrability of the ensemble of weak interacting Hamiltonian systems.
\end{abstract}

\paragraph{1. Gibbs distribution.}

We consider the probability distribution in the phase space of Hamiltonian
system with the density
\begin{equation}
\rho=ce^{-\frac H{k\tau}},
\end{equation}
where $H$ is a Hamiltonian, $\tau$ is an absolute temperature, $k$ is the
Boltzmann constant, $c$ is a normalized factor. It plays the key role in
the equilibrium statistical mechanics. Gibbs show in~[1] that the
averaging with respect to probability measure with density~(1) give rise
to the fundamental relations of equilibrium thermodynamics.

To deduce the canonical Gibbs distribution one usually consider the
ensemble of Hamiltonian systems with Hamiltonian function of the following
form
\begin{equation}
\mathcal{H}=\mathcal{H}_0(P,\,Q)+\varepsilon\mathcal{H}_1(P,\,Q),
\end{equation}
where\vspace{-6mm}
\begin{gather}
\mathcal{H}_0=\sum\limits_{s=1}^n H_0(p^{(s)},\,q^{(s)}),\notag\\
p^{(s)}=(p^{(s)}_1,\,\ldots,\,p^{(s)}_m),\qquad
q^{(s)}=(q^{(s)}_1,\,\ldots,\,q^{(s)}_m).
\end{gather}
Thus at $\varepsilon=0$ the system with Hamiltonian~(2) is decomposed
on~$n$ identical systems with~$m$ degrees of freedom and
Hamiltonian~$H_0$. The canonical variables~$P$,~$Q$ are the
momenta~$p^{(1)},\,\ldots,\,p^{(n)}$ and
coordinates~$q^{(1)},\,\ldots,\,q^{(n)}$ of separate subsystems. The
perturbing function~$\mathcal{H}_1$ is the energy of interaction of
$n$~subsystems; it usually depends on their coordinates~$Q$. Small
parameter~$\varepsilon$ is the characteristic of intensity of subsystems'
interaction.

We consider the case, when the Hamiltonian~$\mathcal{H}$ is sufficiently
smooth with respect to variables~$P$,~$Q$. However, in application we
often see cases with singular interaction. The classical example is the
Boltzmann-Gibbs gas, the assembly of rigid balls in cube that elastically
collide with each other (see [1,\,2,\,3]).

The traditional approach to the deduction of Gibbs distribution suggested
by Fowler and Darwin ([4], the rigorous exposition see in~[5,\,6])
essentially uses the ergodic hypothesis: for all small~$\varepsilon>0$ the
Hamiltonian system with Hamiltonian~(2) is ergodic on fixed energy
manifolds~$\mathcal{H}=const$. With some additional conditions some
systems with Hamiltonian~$H_0$ are distributed in accordance with
formula~(1) as~$\varepsilon\to0$ and~$n\to\infty$.

But the proof of ergodic hypothesis for specific Hamiltonian systems is
usually pretty difficult problem. Moreover the ergodic hypothesis often
contradicts with results of KAM theory. In particular if the Hamiltonian
system with Hamiltonian~$H_0$ is completely integrable and the energy
surfaces~$H_0=const$ are compact, then the ergodic property is not
present with certainty.

In view of this remark we can set the following interesting problem: prove
that in analytical (or even in infinitely differentiable) case if the
energy surfaces~$H_0=const$ are compact, then the Hamiltonian system with
Hamiltonian~(2) never satisfy ergodic hypothesis.

We can try to modify the Fowler--Darwin method assuming that
$\varepsilon\ne0$ and~$n$ depend on~$\varepsilon$ in such way
that~$n(\varepsilon)\to\infty$ as~$\varepsilon\to0$. We can assume that
for some functions~$\varepsilon\mapsto n(\varepsilon)$ the system with
Hamiltonian~(2) is ergodic on the surfaces~$\mathcal{H}=const$ as a
result of huge number of its degrees of freedom. This somewhat weakened
version of ergodic hypothesis is closely related to the unsolved problem
of estimation of small parameter in KAM theory, when the ``last'' Kolmogorov
torus disappears. The weaker conjecture on transitivity of system with
Hamiltonian~(2) on energy surfaces~$\mathcal{H}=const$ for large values
of~$n$ and small~$\varepsilon$ is not proved yet. If this problem has the
positive answer, then we can assert the presence of diffusion in
Hamiltonian systems with many degrees of freedom (see [7--9]).

\paragraph{2. Probability density as an integral of Hamiltonian equations.}

A different approach to the deduction of canonical Gibbs distribution was
proposed in the paper [10]. This approach is based on the fact that the
stationary density of probability distribution is the integral of
Hamiltonian differential equations uniquely defined in the whole phase
space. In this case the number of interacting subsystem~$n\ge2$ is fixed.

More exactly in [10] we consider the case, when the subsystems have one
degree of freedom:~${m=1}$. Under some natural condition we can proceed to
the angle--action variables in each subsystem, and using the well-known
Poincar\'{e} method we can obtain the constructive condition of
nonexistence of new integrals (see [11,\,12]). The results of paper~[10]
can be easily converted to the more general case, when~$H_0$ is a
Hamiltonian of completely integrable system. We are going to find out the
sufficient conditions (constructive if possible) of nonintegrability of
systems~(2)--(3).

We study the conditions of existence of an integral
$\mathcal{F}(P,\,Q,\,\varepsilon)$ of the canonical differential equations
\begin{equation}
\dot{P}=-\frac{\partial\mathcal{H}}{Q},\qquad
\dot{Q}=\frac{\partial\mathcal{H}}{P}
\end{equation}
with a Hamiltonian $\mathcal{H}$ of the form~(2)--(3). We emphasize
that the integral~$\mathcal{F}$ depends on the parameter~$\varepsilon$.
Poincar\'{e} considered the analytical case; in particular we can
construct the integral~$\mathcal{F}$ as a power series with respect
to~$\varepsilon$. We suppose that $\mathcal{F}$ is a function of
class~$C^2$ with respect to all the variables~$P$,~$Q$ and~$\varepsilon$.
Hence we can suppose
\begin{equation}
\mathcal{F}=\mathcal{F}_0(P,\,Q)
+\varepsilon\mathcal{F}_1(P,\,Q)+o(\varepsilon),
\end{equation}
where $\mathcal{F}_0$ and~$\mathcal{F}_1$ are functions of class~$C^2$
and~$C^1$ with respect to~$P$ and~$Q$ correspondingly. Probably we can
weaken the requirements to the class of smoothness of
integral~$\mathcal{F}$, and the following arguments still will be correct.
But this is a separate problem and we are not going to discuss it here.

\paragraph{3. Non-perturbed problem.}
Suppose $\varepsilon=0$. Then we have a system of~$n$ independent
subsystems. It is strongly nonergodic: at~$\varepsilon=0$ system of
differential equations~(4) has~$n$ independent first integrals
\begin{equation}
H_s=H_0(p^{(s)},\,q^{(s)}),\qquad 1\le s\le n.
\end{equation}
It is clear that the function $\mathcal{F}_0$ from expansion~(5) is a
first integral of this unjointed system. Let's show that under the
specific conditions the function~$\mathcal{F}_0$ depends only
on~$H_1,\,\ldots,\,H_n$. In particular these conditions will imply that
any separate subsystem with~$m$ degrees of freedom does not nave first
integrals independent on the integral of energy. The ideas of our
arguments follows Poincar\'{e} method~[11].

Let $M$ be a phase space of Hamiltonian system with Hamiltonian
function~(6). Certainly for all~$s$ these spaces are identical. A phase
space of new system is the direct product
$$
\mathcal{M}=M\times\ldots\times M,\qquad \dim\mathcal{M}=2nm.
$$
Let $h_s$ be a value of total energy of system with number $s$, and
$$
\sum(h_s)=\{p^{(s)},\,q^{(s)}:H_s(p^{(s)},\,q^{(s)})=h_s\}
$$
is the a energy surface. If the value of~$h_s$ is uncritical, then $\sum$
is a smooth $2m-1$-dimensional manifold. At fixed values
of~$h=(h_1,\,\ldots,\,h_n)$ and~$\varepsilon=0$ unjoined Hamiltonian
system~(4) is reduced to the direct product of dynamical systems defined
on
$$
S(h)=\sum(h_1)\times\ldots\times\sum(h_n)\subset\mathcal{M}.
$$

The ergodic property of system with Hamiltonian~$H_s$ on~$\sum(h_s)$ does
not necessarily imply the constancy of integral~$\mathcal{F}_0$ on the
invariant set~$S(h)$. Consider the following simple example

{\it EXAMPLE.}
Suppose the following dynamical system
\begin{equation}
\dot{x}_i=\omega_i,\qquad \dot{y}_j=\omega_j;\qquad
i,\,j=1,\,\ldots,\,k
\end{equation}
with constant incommensurable systems
$\omega=(\omega_1,\,\ldots,\,\omega_k)$ is defined on direct product of
$k$-dimensional tori $\mathbb{T}^k\{x\bmod
2\pi\}\times\mathbb{T}^k\{y\bmod 2\pi\}$. According to the Weyl theorem,
each separate subsystem is ergodic on~$\mathbb{T}^k$. But equations~(7)
have single-valued nonconstant integrals $\sin(x_i-y_i)$\, ($1\le i\le
k$).

{\bf Remark.} {\it
However, if Hamiltonian systems are weakly mixing (mixing) systems
on~$\sum(h_s)$, then their direct product also has weakly mixing (mixing)
property on~$S(h)$. In particular in these cases the
function~$\mathcal{F}_0$ is constant on any connected component of
manifold~$S(h)$.}

Let $\mathbb{T}^1$ be a nondegenerate periodic trajectory of system with
number $s$ with energy~$h_s$, $T_s$ its period, and~$\omega_s=2\pi/T_s$
its frequency. According to Floquet--Lyapunov theorem, in a neighborhood
of this trajectory on~$\sum(h_s)$ we can express the
coordinates~$\varphi_s\bmod 2\pi$,\,$z_1^{(s)},\,\ldots,\,z_{2m-2}^{(s)}$,
so that in the new variables the motion equation obtain the following
form:
\begin{equation}
\dot{\varphi}_s=\omega_s+f_s(\varphi_s,\,z^{(s)}),\qquad
\dot{z}^{(s)}=\Omega_sz^{(s)}+g_s(\varphi_s,\,z^{(s)}).
\end{equation}
Here $f_s=O(|z^{(s)}|)$, $g_s=o(|z^{(s)}|)$, and~constant square
matrix~$\Omega_s$ of order~$2m-2$ is nondegenerate. Assuming in~(8)
$z^{(s)}=0$ we obtain the equation of periodic trajectory:
\begin{equation}
\dot{\varphi}_s=\omega_s\qquad (1\le s\le n).
\end{equation}

According to the assumption on non degeneracy of periodic
trajectory~$\mathbb{T}^1$, nondegenerate periodic trajectories with
similar period are situated on close energy surfaces~$\sum(h_s)$; periods
and frequencies continuously depend on energy~$h_s$.

It is clear that the direct product
$\mathbb{T}^1\times\ldots\times\mathbb{T}^1=\mathbb{T}^n$ is
$n-$dimensional invariant torus of canonical system of differential
equations~(4) at~$\varepsilon=0$ situated on~$S(h)$. In the neighborhood
of this torus the equation of motion have form (8). Hence, such torus is
reducible and nondegenerate (see, for example, [12]). On the torus the
equation are reduced to a conditionally-periodic form (9). As usually,
we call an invariant torus nonresonance if the frequencies
$\omega_1,\,\ldots,\,\omega_n$ are independent on the ring of integers. In
the further analysis the following condition is essential

\hangindent=40pt\hangafter=1 A) For almost all admissible values of
$h\in\mathbb{R}^n$ nonresonance tori are everywhere dense on the manifold
$S(h)$.

{\it EXAMPLE.}
Let separate subsystems describe the inertial motion on the manifold
$\mathcal{N}$ of negative curvature. Energy $h$ is non-negative. All
periodic trajectories with positive energy are hyperbolical; hence they
are not degenerate. Periodic trajectories are the motions on closed
geodetics on $\mathcal{N}$ with different speed. If $l$ is a length of
closed geodetic, then the period is equal to $\frac{l}{\sqrt{2h}}$. Hence
the frequency $\omega$ is defined by the formula\vspace{-3mm}
$$
2\pi\frac{\sqrt{2h}}{l}.
$$
Since the lengths of $n$ geodetics $l_1,\,\ldots,\,l_n$ are fixed, then
for almost all positive values of energy $h_1,\,\ldots,\,h_n$ the
frequencies $\omega_1,\,\ldots,\,\omega_n$ are incommensurable.
It is possible to show (and this is a separate problem) that in a
considered situation condition A is fulfilled.

{\bf Proposition 1.} {\it
If condition A is fulfilled, then for all $h\in\mathbb{R}^n$ the
function $\mathcal{F}_0$ is constant on any connected component of $S(h)$.}

{\it Proof.} Since $\mathcal{F}_0$ is an integral of system of equations (4)
at $\varepsilon=0$, then (according to the Kronecker theorem)
$\mathcal{F}_0$ is constant on any nonresonance torus $\mathbb{T}^n$.
Since this torus is reducible and nondegenerate, then $d\mathcal{F}_0=0$
in points $\mathbb{T}$ (see [12], ch. IV). According to condition A, for
almost all values of $h\in\mathbb{R}^n$ nonresonance tori are everywhere
dense on $S(h)$. Hence, $d\mathcal{F}_0=0$ on such manifolds $S(h)$.
Therefore $\mathcal{F}_0$ is constant on their connected components. For
other values of $h$ the conclusion of proposition 1 follows by continuity.

{\bf Remark.} {\it
The proof shows that in condition A instead of ``for almost all admissible
values of $h\in\mathbb{R}^n$'' we can say ``for everywhere dense set of
values of $h\in\mathbb{R}^n$''. However, such weakening of condition A
practically does not give anything new.}

In further analysis we will use the proposition on everywhere density of
the set of maximum resonance tori (when all frequencies are rationally
expressed through one frequency). This condition together with condition A
produces ``an alternation'' of resonance and nonresonance invariant tori
and replaces the condition of nondegeneracy of non-perturbed completely
integrable system in the Poincar\'{e} theory.

\paragraph {4. Energy surfaces.}

Let us consider a case, when function the $H_0:M\to\mathbb{R}$ has a
finite number of critical values $a_1<a_2<\ldots<a_r$, and $a_1=\min H_0$.
Such situation is common in applications. When the total energy $h_0$
passes through the critical value, the continuous dependence of energy
surface $\sum(h_0)$ on $h_0$ is lost. In that moment its topology
generally changes.

In fig. 1 we present the plot of Hamiltonian $H_0$ with three critical
values. The points $a_1$ and $a_3$ are stationary values of $H_0 $, and
the critical point $a_2$ is not a stationary value. The presence of the
nonstationary critical points is the characteristic property of potentials
describing gravitational or Coulomb interaction.

Let's denote as $K_{i_1 i_2\,\ldots\,i_n}$ an open parallelepiped in
$\mathbb{R}^n=\{h_1,\,\ldots,\,h_n\}$. This parallelepiped is a
direct product of the intervals
\begin{equation}
a_{i_1}<h_1<a_{i_1+1},\,\ldots,\,a_{i_n}<h_n<a_{i_n+1}.
\end{equation}
If number $i_s+1$ is larger than $r$, then we replace $a_{i_s+1}$ with a
symbol $\infty$. In fig. 2 these domains are shown for $n=2$ and $r=3$.
Each point $h\in K_i$,\,$i=(i_1,\,\ldots,\,i_n)$ corresponds to a smooth
regular manifold, which may consist of several connected parts. The
quantity of connected components of $S(h)$ does not depend on a point
$h\in K_i$; we denote this number by symbol $\varkappa_i$.

Let us introduce in the phase space $\mathcal{M}$ open areas
$\mathcal{K}_i$ defined by the inequalities similar to (10):
$$
a_{i_1}<H_1(p^{(1)},\,q^{(1)})<a_{i_1+1},\,\ldots,\,a_{i_n}<
H_n(p^{(n)},\,q^{(n)})<a_{i_n+1}.
$$

It is clear that the closure of these domains in the whole covers all
$\mathcal{M}$. Also each $\mathcal{K}_i$ has exactly $\varkappa_i$
connected components.

{\bf Proposition 2.} {\it
For any connected component of domain $\mathcal{K}_i$ there exists the
continuously differentiable function}
$$
f_i:K_i\to\mathbb{R},
$$
{\it such that the following equality is fulfilled in this domain}
\begin{equation}
\mathcal{F}_0=f_i(H_1,\,H_2,\,\ldots,\,H_n).
\end{equation}

{\bf Remark.} {\it
Actually function $f_i$ belongs to the class of smoothness $C^2$. However
it is not essential for the further analysis.}

{\it Proof.} It is clear that the domain $\mathcal{K}_i$ is foliated to the
regular surfaces $S$. The function $\mathcal{F}_0$ is constant on these
surfaces (more exactly on their connected components) (the proposition 1).
Hence, on any connected component $\mathcal{K}_i$ the function
$\mathcal{F}_0$ has natural representation (11). By definition in any
point $\mathcal{K}_i$ functions $H_1,\,\ldots,\,H_n$ are independent.
Therefore we can introduce locally new coordinates so that
$H_1,\,\ldots,\,H_n$ will appear as $n$ of new variables. The transition
to such coordinates is carried out with certainty with the help of
continuously differentiable reversible transformation. In new variables
the function $\mathcal{F}_0$ is continuously differentiable and depends
only on $n$ variables $H_1,\,\ldots,\,H_n $. The proposition is proved.

\paragraph{5. Resonances.}
Let us consider again an invariant torus $\mathbb{T}$ of non-perturbed
system. The equations of motion on the torus are reduced to form (9).
This torus we call completely resonance if there exist $n-1$ linearly
independent integer vectors
$$
u=(u_1,\,\ldots,\,u_n),\quad v=(v_1,\,\ldots,\,v_n),\,\ldots, \quad
w=(w_1,\,\ldots,\,w_n),
$$
such that
\begin{equation}
(u,\,\omega)=u_1\omega_1+\ldots+u_n\omega_n=0,\quad
(u,\,\omega)=0,\,\ldots, \quad (w,\,\omega)=0.
\end{equation}
In other words all frequencies $\omega_s$ are rationally expressed through
one of them. This is equivalent to the proposition that all solutions of
differential equations (9) on the torus $\mathbb{T}^n$ are periodic with
the same period.

Let $\Phi$ be a restriction of perturbing function
$\mathcal{H}:M\to\mathbb{R}$ on the invariant torus $\mathbb{T}^n$. It is
clear that $\Phi$ is $2\pi-$periodic function of
$(\varphi_1,\,\ldots,\,\varphi_n)=\varphi$. We associate it with multiple
Fourier series
\begin{equation}
\Phi=\sum_{k\in\mathbb{Z}^n}\varphi_k\exp i(k,\,\varphi).
\end{equation}

A nonresonance torus we call the Poincar\'{e} torus if the factors of
Fourier decomposition (13) with numbers $u,\,v,\,\ldots,\,w$ are nonzero.
Since the Poincar\'{e} tori consist of the separate closed trajectories,
they have no ``rigidity'' property and collapse after the addition of
perturbation. We can not exclude the possibility that the family of
degenerate periodic trajectories, components of the Poincar\'{e} torus, at
perturbation give rise to the finite number of nondegenerate periodic
trajectories with close transition.

Let us introduce finally the Poincar\'{e} set
$\mathbb{P}\subset\mathbb{R}^n$. It is a set of points from
$\mathbb{R}^n=\{h_1,\,\ldots,\,h_n\}$, which are the images of the
Poincar\'{e} tori under the ``energy'' mapping
$\mathcal{M}\to\mathbb{R}^n$: a point with coordinates
$$
(P,\,Q)=(p^{(1)},\,\ldots,\,p^{(n)},\:q^{(n)},\,\ldots,\,q^{(n)})
$$
passes to a point with coordinates
$$
h_1=H_1(p^{(1)},\,q^{(1)}),\,\ldots, \quad h_n=H_n(p^{(n)},\,q^{(n)}).
$$

{\bf Remark.} {\it
In the Poincar\'{e}} {\it theory [11,\,12] the usually supposition is that the
non-perturbed system with the Hamiltonian $\mathcal{H}_0$ is completely
integrable and nondegenerate. Therefore the set of its first integrals is
a set of action variables ``numerating'' the invariant tori. The
Poincar\'{e}} {\it set (introduced in [12]) is defined here as a set of points
in space of action variables corresponding to the completely resonance
tori collapsing after the addition of perturbation. In our case functions
$H_1,\,\ldots,\,H_n$ are the set of integrals of the non-perturbed problem
and the Poincar\'{e}} {\it set is a set of points in space of values of these
integrals.}

{\bf Proposition 3.} {\it
In points of the Poincar\'{e} set $\mathbb{P}$} {\it functions}
$$
\mathcal{H}_0=\sum_{s=1}^n\qquad \text{\it and}\qquad
\mathcal{F}_0=f(H_1,\,\ldots,\,H_n)
$$
{\it are dependent.}

{\it Proof.} Let $\{\,\}$ be a Poisson bracket connected with symplectic
structure on $\mathcal{M}$. Since function $\mathcal{F}$ is the first
integral of initial system (4), then $\{\mathcal{H},\,\mathcal{F}\}=0$
for all values of $\varepsilon$. Since
$\{\mathcal{H}_0,\,\mathcal{F}_0\}=0$, then
\begin{equation}
\lim\limits_{\varepsilon\to 0}
\frac{\{\mathcal{H},\,\mathcal{F}\}}{\varepsilon}=0.
\end{equation}
Using decomposition (2) and (5) we receive from (14) the equality
\begin{equation}
\{\mathcal{H}_0,\,\mathcal{F}_1\}=\{\mathcal{F}_0,\,\mathcal{H}_1\}.
\end{equation}
Well known that $\{\mathcal{F}_0,\,\mathcal{H}_1\}$ is a derivative of
$\mathcal{F}_1$ by virtue of the initial system of differential equations
with Hamiltonian $\mathcal{H}_0$. The Poisson bracket
$\{\mathcal{F}_0,\,\mathcal{H}_1\}$ has similar sense. Besides by formula
(11) we obtain
\begin{equation}
\{\mathcal{F}_0,\,\mathcal{H}_1\}=\sum_{s=1}^n \frac{\partial f}{\partial
H_s}\{H_s,\,\mathcal{H}_1\}.
\end{equation}

Now let us restrict equality (15) on the invariant torus $\mathbb{T}^n$.
It is clear that $\{\mathcal{H}_0,\,\mathcal{F}_1\}$ is equal to the
derivative of restriction of function $\mathcal{F}_1$ on $\mathbb{T}^n$ by
virtue of system of differential equations (9). Let
$\Psi:\mathbb{T}^n\to\mathbb{R}$ be a restriction of $\mathcal{F}_1$ on
$\mathbb{T}^n$ and
\begin{equation}
\Psi=\sum_{k\in\mathbb{Z}^n}\psi_k\exp i(k,\,\varphi)
\end{equation}
its Fourier series. In points $\varphi\in\mathbb{Z}^n$ the left part of
(5.4) becomes
\begin{equation}
\sum_{k\in\mathbb{Z}^n} i(k,\,\omega)\psi_k\exp i(k,\,\varphi).
\end{equation}

In view of formulas (13) and (16) the right part of relation (15) in
points of the invariant torus is equal to
\begin{equation}
\sum_{k\in\mathbb{Z}^n}i\left(\frac{\partial f}{\partial H_1}k_1\omega_1
+\ldots+\frac{\partial f}{\partial H_n}k_n\omega_n\right) \varphi_k\exp
i(k,\,\varphi).
\end{equation}

Comparing (18) and (19) we obtain a chain of equalities
\begin{equation}
(k,\,\omega)\psi_k=(\xi k_1\omega_1+\ldots+\xi_n k_n\omega_n)
\psi_k,\qquad k\in\mathbb{Z}^n.
\end{equation}

Now let $\mathbb{T}^n$ be the Poincar\'{e} torus. Setting $k$ equal to
$u,\,v,\,\ldots,\,w$ we obtain that $\omega$ as a vector of
$n-$dimensional space is orthogonal to the hyperplane $\Pi$ generated by
linearly independent vectors $u,\,v,\,\ldots,\,w$. Since
$(u,\,\omega)=\ldots=(w,\,\omega)=0 $, and
$\varphi_u\ne0,\,\ldots,\;\varphi_w\ne0$, then we obtain from
(20) $n-1$ linear relations:
$$
\begin{matrix}
u_1(\xi_1\omega_1)+\ldots+u_n(\xi_n\omega_n)=0,\\
\hdotsfor{1}\\
w_1(\xi_1\omega_1)+\ldots+w_n(\xi_n\omega_n)=0.
\end{matrix}
$$
Hence the vector with components $\xi_1\omega_1,\,\ldots,\,\xi_n\omega_n$
is orthogonal to the hyperplane $\Pi$ and consequently it is collinear to
the vector $\omega=(\omega_1,\,\ldots,\,\omega_n)$. Hence
$\xi_1=\ldots=\xi_n$.

Thus in points of the Poincar\'{e} set the derivatives
$\frac{\partial f}{\partial H_1},\,\ldots,\,\frac{\partial f}{\partial
H_n}$ are equal to each other. It means obviously the dependence of
functions $\mathcal{H}_0$ and $\mathcal{F}_0$.

{\bf Remark.} {\it
Since functions $\Phi$ and $\Psi$ are assumed to be only once continuously
differentiable, then the Fourier series (13), (17)-(19) may diverge. In
this case relations (20) can be deduced in another way. For this purpose
we multiply the derivative with respect to time}
$$
\dot{\Phi}=\frac{\partial\phi}{\partial\varphi_1}+\ldots
+\frac{\partial\phi}{\partial\varphi_n}\omega_n
$$
{\it on $\exp i(k,\,\varphi)$, apply the operation of averaging over}
$\mathbb{T}^n$
$$
\frac{1}{(2\pi)^n}\int\limits_{\mathbb{T}^n}(\,\cdot\,)\,
\partial \varphi_1\,\ldots, d\varphi_n,
$$
{\it and integrate by parts. In result we obtain the left part of relation
(20) up to the factor $-i$. The right part of (20) is obtained
similarly.}

Let us introduce the additional condition

\hangindent=37.5pt\hangafter=1 B) The Poincar\'{e} set $\mathbb{P}$ is
everywhere dense in any parallelepiped $K_i$.

The proposition 3 imply the following corollary

{\bf Corollary.} {\it
If conditions A and B are fulfilled, then the functions $\mathcal{F}_0$
and $\mathcal{F}_0$ are everywhere dependent.}

Hence we immediately obtain the following representation on any
parallelepiped $K_i$:
\begin{equation}
\mathcal{F}_0=F_i(\mathcal{H}_0),
\end{equation}
where $F_i$ is some continuously differentiable function.

Indeed, introducing the new variables
$H_1,\,\ldots,\,H_{n-1}$,\,$\mathcal{H}_0=\sum H_s$ instead of
$H_1,\,\ldots,\,H_n$ we can write down formula (11) in the another form:
$$
\mathcal{F}_0=f_i(H_1,\,\ldots,\,H_{n-1},\;
\mathcal{H}_0-H_1-\ldots-H_{n-1}).
$$
Since functions $\mathcal{F}_0$ and $\mathcal{H}_0$ are dependent, then
the right part of this equality actually does not depend on
$H_1,\,\ldots,\,H_{n-1}$.

\paragraph{6. Deduction of Gibbs distribution.}

Now let $\varepsilon$ tend to zero. At the limit we obtain the $n$
unjoined subsystems moving independently: the change of the initial data
$p^{(l)}$, $q^{(l)}$ for $l\ne s$ does not affect the dynamics of
subsystem with number $s$. In order to be consistent we shall also assume
at $\varepsilon=0$ that the subsystem with number $s$ being in some fixed
state $(p^{(s)},\,q^{(s)})\in M$ is a random event. The following natural
condition plays the main role in the process of deduction of Gibbs
distribution

C) These random events are independent.

If $\rho_s(p^{(s)},\,q^{(s)})$,\,$1\le s\le n$ is a density of probability
distribution of the subsystem with number~$s$, and
$$
\rho(P,\,Q,\,\varepsilon)=\rho_0(P,\,Q)+O(\varepsilon)
$$
is a density of probability distribution in the initial system with
Hamiltonian (2), then using condition C and the rules of multiplication
of probabilities of independent events we obtain as $\varepsilon\to0$ the
following equality:\vspace{-2mm}
\begin{equation}
\rho_0=\rho_1\,\ldots\,\rho_n.
\end{equation}

Equality (22) is also called the Gibbs hypothesis on the preservation of
thermodynamic equilibrium of subsystems at vanishing interaction ([1], see
also [13]). The sense of this term will be explained below.

Our main result is the following theorem

{\bf Theorem.}
{\it Suppose conditions A, B and C are fulfilled. Then}
\begin{equation}
\rho_s=c_s e^{-\frac{H_s}{k\tau}},\qquad c_s=const>0
\end{equation}
{\it for all} $1\le s\le n$.

In particular, according to (22),\vspace{-4mm}
$$
\rho_0=c_0 e^{-\frac{H_s}{k\tau}},\qquad c_0=c_1\ldots\,c_n.
$$
From (22) we see that all separate subsystems have the same distribution.
We compute the factors~$c_s$ using the normalizing condition
$$
\int\limits_M \rho_s\,d^np\:d^nq=1.
$$

{\it Proof of theorem.} First note that $\rho_s$ is a function of Hamiltonian
$H_s$ only, and it is continuously differentiable in all open
intervals\vspace{-3mm}
\begin{equation}
(a_1,\,a_2),\quad (a_2,\,a_3),\,\ldots,\quad (a_r,\,\infty).
\end{equation}
More exactly the number of such functions is equal to the number of the
connected components of level surface $\sum(h_s)$, when the energy $h_s$
changes in each of intervals (24). Some of these functions may coincide.

Indeed, for almost all $h_s\ge a_1$ the Hamiltonian system with
Hamiltonian $H_s$ has everywhere dense set of nondegenerate periodic
trajectories on energy surfaces $\sum(h_s)$. Otherwise condition A is not
fulfilled because of the identity of separate subsystems. Then, according
to Poincar\'{e} [11], the points of nondegenerate periodic trajectories
are stationary for the restriction of any first integral on $\sum(h_s)$.
The continuity imply that the first integrals of Hamiltonian system with
Hamiltonian function $H_s$ are constant on the connected components of
$\sum(h_s)$. At last we should note that $\rho_s$ is the first integral
and use the (simplified) arguments of section 4.

Now let us consider again equation (22) true on any parallelepiped $K_i$:
\begin{equation}
\rho_0(H_1+\ldots+H_n)=\rho_1(H_1)\,\ldots\,\rho_n(H_n).
\end{equation}
This functional equation is easily solved. We differentiate (25)
sequentially with respect to $H_1,\,\ldots,\,H_n$ and divide the result on
the product $\rho_1\,\ldots\,\rho_n$. In result we obtain the following
chain of equations
$$
\frac{\rho_1'}{\rho_1}=\ldots=\frac{\rho_n'}{\rho_n}=-\beta.
$$
Here $\beta$ is some constant independent on the number $s$. Hence
\begin{equation}
\rho_s=c_s e^{-\beta H_s},\qquad c_s=const.
\end{equation}
The dimension of constant $\beta$ is equal to the inverse energy
dimension. Usually one suppose that $\beta=(k\tau)^{-1}$, where
$\tau$ is the absolute temperature, and $k$ is the Boltzmann constant.

We should note that formula (26) may depend on the choice of multiindex
$i=(i_1,\,\ldots,\,i_n)$. More precisely, any connected component of the
set $\mathcal{K}_i\subset\mathcal{M}$ has its own set of the factors
$\beta$ and $c_s$ in (26).

However, we can easily show that the constant $\beta$ has an universal
character. Indeed, suppose the constants $\beta$ in formula (26) are
equal to the values $\beta_1,\,\ldots,\,\beta_n$ on some connected
component of domain $\mathcal{K}_i$ with some index $i$. Then, according
to (6.1), in this domain
\begin{equation}
\rho_0=c_0 e^{\sum\beta_s H_s}.
\end{equation}
If some $\beta_s$ are not equal to each other, then functions (27) and
$\mathcal{H}_0=\sum(H_s)$ are independent. But this statement contradicts
to the corollary of proposition 3.

This argument has the evident physical meaning: at thermodynamic
equilibrium all components of system have identical temperature.

The last remaining possibility is that constants $c_s$ in formula (26)
are different on the different intervals of values of energy (24). But in
reality this possibility is not realized because of the continuity
property of functions $\rho_s:M\to\mathbb{R}$.

The theorem is completely proved.

In conclusion of the work we shall make one important remark. The Gibbs
theory presented in [1] does not imply that the densities of probability
distributions $\rho_1,\,\ldots,\,\rho_n$ should be continuous functions on
$M$. We can consider more general situation and assume, for example, that
functions $\rho_s$ are continuously differentiable only on those domains
of phase space $M$, in which energy is contained between its neighboring
critical values
\begin{equation}
a_r<H_s<a_{r+1}\qquad (r=1,\,\ldots,\,p;\quad a_{p+1}=\infty).
\end{equation}
Naturalness of such assumption is already evident if we consider the
example of mathematical pendulum: the separatrices on phase cylinder
separate the domains with essentially different type of motion
(fluctuations and rotations).

Applying the developed above method we again obtain formula (23), but the
constants $c_s $ have different values in different domains (28).
Moreover, these constants may be different for different connected
components of domains (28). It is quite possible that such generalized
discontinuous Gibbs distribution could be useful for the study of concrete
thermodynamic systems.

Let us assume, for example, that the phase space $M$ has only two domains
$M_+$ and $M_-$ of form (28). In domains $M_\pm$ we have the following
densities of distributions
$$
c_\pm e^{-\frac{H}{k\tau}}.
$$
We calculate the constants $c_+$ and $c_-$ using the normalizing condition
$$
c_+\int\limits_{M_+}e^{-\frac{H}{k\tau}}d^np\,d^nq+
c_-\int\limits_{M_-}e^{-\frac{H}{k\tau}}d^np\,d^nq=1.
$$
If the difference $\Delta=c_+-c_-$ is given, then factors $c_\pm $ are
uniquely defined by this equality:
\begin{gather*}
c_+\int\limits_M e^{-\frac{H}{k\tau}}d^np\,d^nq=1+
\Delta\int\limits_{M_-}e^{-\frac{H}{k\tau}}d^np\,d^nq,\\
c_-\int\limits_M e^{-\frac{H}{k\tau}}d^np\,d^nq=1-
\Delta\int\limits_{M_+}e^{-\frac{H}{k\tau}}d^np\,d^nq.
\end{gather*}
Since $c_\pm>0$, then the right parts of these equalities are positive. It
happens with certainty if the jump $\Delta$ satisfies the following
inequality
$$
|\Delta|< \Biggl[\,\int\limits_M
e^{-\frac{H}{k\tau}}d^np\,d^nq\,\Biggr]^{-1}.
$$

Could we obtain the probability distribution with piecewise smooth
function of distribution using the Fowler-Darwin method?

The paper is prepared with the financial support of RFBR(99-01-0196) and
INTAS.\vspace{-7mm}

redpajama_set_name: RedPajamaArXiv


Dating way back to 1681, the legendary Grand Hotel Les Trois Rois in Basel is one of the oldest luxury hotels in Europe and has remained true to its tradition of excellence. Guests can experience the elegance and charm of bygone days, enhanced by all-out luxury and world-class amenities.
The hotel's premier location on the banks of the Rhine river in the very heart of Basel's beautiful Old Town makes every stay a truly memorable experience.
The city of Basel is situated in the scenic landscape of the Dreiländereck triangle, where the borders of France, Germany and Switzerland meet. Nestling between the Swiss Jura mountains, the rolling hills of Germany's Black Forest and the Vosges mountains of Alsace, this lively town is an all-year-round destination with a wide range of activities to choose from.
An icon of old world charm and historic elegance, the Grand Hotel Les Trois Rois offers superior comfort, opulent guestrooms, refined amenities and time-honored hospitality that will meet and exceed the highest expectations. The 101 rooms and suites feature precious antique furnishings and high-tech amenities, and are tastefully decorated in classic or Art déco style.
The storied 5 star deluxe hotel combines the glory of the past with modern facilities and welcomes guests with an ambience of warmth and sophistication.
The Suite Les Trois Rois is the crown jewel of Basel's finest hotel: extending over 260 sqm, it features authentic Art déco interiors, outdoor sauna and private jacuzzi with fabulous rooftop views Basel and makes you feel truly regal.
Enjoy the hautest of haute cuisine in our two Michelin-starred gourmet restaurant Cheval Blanc. Celebrity chef Peter Knogl – he was named "2011 Chef of the Year " and earned two twinkling Michelin stars and 18 Gault Millau points for his outstanding culinary skills pleases the palates of our guests with traditional French cuisine with a Mediterranean twist.
Chez Donati, the oldest Italian restaurant in Basel, is located only moments away from the Grand Hotel Les Trois Rois and provides you with a fine dining experience in an upscale atmosphere.
The Les Trois Rois Brasserie is a great place to savor creative Swiss and French brasserie. The Bar tantalizes your taste buds with exquisite cocktails and tempting snacks. On balmy summer days, the romantic terrace right on the banks of the Rhine river invites you to linger a while and unwind while taking in fabulous views.


Last Friday, everyone was buzzing about the big werewolf transformation of Hemlock Grove, Netflix's adaptation of the Brian McGreevy novel.
ShockTillYouDrop.com spoke with executive producer Eli Roth (who directed the first episode as well) briefly about this transformation which appears in an episode directed by Deran Serafian.
Serafian is where our conversation with Roth began because, in case the name doesn't jump out at you, Serafian spent the early days of his career on the Italian horror scene before going on to produce shows like House M.D.
Inside, Roth talks about the werewolf transformation, why gore has gone mainstream on television and offers an update on his cannibal film The Green Inferno. All 13 episodes of Hemlock Grove season one will be available exclusively on Netflix beginning April 19th.
Shock Till You Drop: I just got done talking to Deran Serafian – who has a rich history in Italian horror and is now directing Hemlock, too. Did you bring him on board?
Eli Roth: We knew Deran from his experience on House and, of course, his father directed Vanishing Point, so we knew him from that. And he told me, "You know, I shot second unit for Argento." And I was like, "What?" And he's the lead in Zombie 3. He had worked so closely under Fulci and Argento and that's what I loved. We talked about the transformation and it had to be signature. I thought about the average viewers that have watched Twilight and seen the transformation of a shirtless guy walking by a tree and transforms. Our idea of a transformation is Rick Baker and Rob Bottin. So, we've got to do something modern that's in the classic tradition. It has to be a violent birth, I want it to eat its placenta after and Deran was into it. It should shake off all of the blood and goo. And that's how we approached all of the kill scenes. Obviously, we had to adhere to Netflix's guidelines and standards, but in terms of the twists and such, we can go dark with it.
Shock: How many episodes did you direct?
Roth: Just the first one. I wanted to direct more, but the production moved to Toronto and pushed and I had to work on The Green Inferno in Peru. The nice thing about shooting a show that's 13 episodes is you can change things up in the earlier episodes as you go along. You realize in episode five "Oh, we should have set this up better in episode one, so you can go back and shoot it." The werewolf transformation, Deran was able to storyboard out and parcel it out while we're doing ten episodes so we can get it right.
Shock: How's Green Inferno coming along?


If you're about to buy (or have already bought) a sloping site, here are 5 key tips to keep in mind as you head into the building process.
You need a builder who has specific experience with sloping sites. When checking a prospective builder's portfolio, ask to see some houses that were constructed on trickier terrain – this will give you an idea of whether they are confident and skilled enough to build on your sloped block. With this in mind, you'll probably want to lean towards a builder who customises their designs, as templated designs rarely work well with uniquely shaped landscapes.
Orientation is vital to any house build, but this is particularly true when you have a slope or two to consider. For example, you won't want your driveway to turn into a river leading straight to your front door every time it rains. Alternatively, you might find a hill on your land, shelters your home from prevailing winds, which means your living area could benefit from panoramic windows without the chilly trade-off.
Certain layouts complement different types of slopes. For instance, a strong slope up away from the road lends itself to a one-storey home with a garage underneath at the front of the property. However, a strong slope down away from the road can sometimes work well with a house that has a lower half-storey at the back. Talk to your builder about what kind of design will suit your property's natural features.
Since hills are generally made from rock, you can expect the ground of a sloping site to be a bit shallower than usual (i.e. it doesn't take much digging to hit rock). With this in mind, you'll want to minimise the amount of excavation that's performed to keep costs within your budget.
A sloped site might have challenges, but it also has opportunities. By creatively working with the property's layout, a good builder can create a home for you that has a character and charm unlike any other in the neighbourhood. It's all about expressing your desires, keeping an open mind, and making sure you've chosen the right builder for the job!
Building on sloped blocks is a specialty of ours at Shelton Homes. If you'd like to discuss your options or get some personalised advice about this topic, please don't hesitate to get in touch.