Implicit Partial Differential Equations (Progress in Nonlinear Differential Equations and Their Applications)

Book Description

This book is devoted to a large class of partial differential equations and systems which are nonlinear in the highest derivatives. The authors present a new functional analytic method based on the Baire category theorem for handling existence of almost everywhere solutions of these equations. Comparison with other methods is discussed: essentially that of viscosity solutions, but also briefly that of convex integration. Results obtained by this new method have important applications to the calculus of variations, geometry, nonlinear elasticity, problems of phase transitions, and optimal design.

The book is divided into four parts. Part I examines first and second order partial differential equations while Part II considers systems. Building on the theory presented, Part III is devoted to applications, including the singular values case, the case of potential wells, and the complex eikonal equation. In Part IV the authors gather some non-classical Vitali type covering theorems, as well as several fine results on approximation of Sobolev functions by piecewise affine or polynomial function. These results have relevance in other contexts, such as numerical analysis.

Book Description

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.

A-B quasiconvexity and implicit partial differential equations (Research report / Carnegie Mellon University. Dept. of Mathematical Sciences. Center for Nonlinear Analysis)

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A-B quasiconvexity and implicit partial differential equations (Research report / Carnegie Mellon University. Dept. of Mathematical Sciences. Center for Nonlinear Analysis)
Bernard Dacorogna
Manufacturer: Carnegie Mellon University, Dept. of Mathematical Sciences, Center for Nonlinear Analysis
ProductGroup: Book
Binding: Unknown Binding

Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines (Report. Centrum voor Wiskunde en Informatica)

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Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines (Report. Centrum voor Wiskunde en Informatica)
J. G Verwer
Manufacturer: Stichting Mathematisch Centrum
ProductGroup: Book
Binding: Unknown Binding

Explicit-implicit methods for time-dependent partial differential equations (Report NM. Centrum voor Wiskunde en Informatica)

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Explicit-implicit methods for time-dependent partial differential equations (Report NM. Centrum voor Wiskunde en Informatica)
E. De Goede
Manufacturer: Centrum voor Wiskunde en Informatica
ProductGroup: Book
Binding: Unknown Binding

Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD (SuDoc NAS 1.26:208435)

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Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD (SuDoc NAS 1.26:208435)
NASA
Manufacturer: National Aeronautics and Space Administration, Langley Research Center National Technical Information Service, distributor
ProductGroup: Book
Binding: Unknown Binding

Implicit degenerate evolution equations and applications (MRC technical summary report)

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Implicit degenerate evolution equations and applications (MRC technical summary report)
Emmanuele Di Benedetto
Manufacturer: University of Wisconsin--Madison, Mathematics Research Center
ProductGroup: Book
Binding: Unknown Binding

An implicit fourth order difference method for viscous flows, (UILU-ENG 72-2233)

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An implicit fourth order difference method for viscous flows, (UILU-ENG 72-2233)
D. S Watanabe
Manufacturer: Coordinated Science Laboratory, University of Illinois
ProductGroup: Book
Binding: Unknown Binding

A note on a diagonally implicit Runge-Kutta-NystroÌÂˆm method (Report NM. Centrum voor Wiskunde en Informatica)

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A note on a diagonally implicit Runge-Kutta-NystroÌÂˆm method (Report NM. Centrum voor Wiskunde en Informatica)
B. P Sommeijer
Manufacturer: Centrum voor Wiskunde en Informatica
ProductGroup: Book
Binding: Unknown Binding

Book Description

The Starship Enterprise™ has embarked on its most ambitious assignment yet: to lead a courageous band of settlers to a far-off planet, to defend the fragile colony from alien threats, and to unravel the mysteries of a brand-new Earth!

Belle Terre

A six-month distance from the Federation, the planet Belle Terre offers a new life to more than 30,000 families, pioneers, scientists, expatriates, go-getters, loners, and entrepreneurs, all under the watchful eye of Captain Kirk and his crew. But the would-be colonists have barely settled in the untamed wilderness of their new home when Spock makes a startling discovery: not only does the planet's moons contain a rare ore of almost inestimable value, that same moon is also violently unstable. Within months, it will inevitably explode -- destroying all life on Belle Terre!

Customer Reviews:

ST #90 Belle Terre - The story gets a lot better!.......2003-10-27

After trudging my way through the first book in this series, Star Trek #89 "Wagon Train to the Stars," I found "Belle Terre" to be somewhat of a welcome relief. As stated in my review for the first book in the New Earth series, the whole concept of the New Earth series is a very interesting and intriguing one but "Wagon Train to the Stars" just didn't execute on this extremely interesting premise very well. "Belle Terre" does pick up on the pace of the story quite nicely though. There are points in which the pace still seems to drag, thus causing the novel one star.

The cover art for this novel is much better than previous novels and it lends to the story quite well.

The premise:

At the conclusion of Star Trek #89 "Wagon Train to the Stars," Captain Kirk has successfully guided the colony and its sixty two thousand members and ships through treachery and attack from outsiders to Belle Terre.

As "Belle Terre" begins we learn that the Quake Moon, which had been focused on during the first novel of this series, is a moon that contains a large quantity of Quantum olivium which is an extremely rare and valuable substance to the Federation and other civilizations. Captain Kirk is elated to find this out as this rare substance will greatly help the new colony but those hopes are quickly dashed as Spock reveals that the moon is under so much internal pressure that it is going to explode and destroy Belle Terre in the process.

Captain Kirk, the crew of the Enterprise and the colonists must now find a way to stop this massive explosion or be prepared to evacuate the colony and hope to make it back to Federation space before they run out of supplies.

What I found even more interesting about this novel was the subplot in which Captain Kirk asked one of the pathfinder ships and its captain to find a suitable planet that the colonists can be taken to in the event that they cannot prevent the destruction of Belle Terre. Captain Sunn and hid small crew take their pathfinder ship, the Rattlesnake and an extremely intriguing jaunt and find a very interesting world that was once populated but is now approximately one hundred years barren.

What follows from there is a Star Trek numbered novel that far outweighs the leadoff book in this series. The one unfortunate thing about it is that the subplot is much more interesting than the main plot.

I would recommend this novel and New Earth series more as a collectors/completists type read. While they are by far not the best in Trek fiction, they're not the worst either. {ssintrepid}

The Wagon Has Arrived.......2001-06-20

Finally, the wagon train to the stars got there. They're established in their new planet and out of nowhere comes a new menace to the colonists, which the Enterprise must try to avert. Taking into account that this is a TOS book, I'd say they do OK. It's true that many clichés pop up, but I guess that's the way some of us fans like it. I found this book entertaining and the story line kept me hooked. Taking into account that this is the second book of the series and that further developments will come to pass, my recommendation is "keep on reading"

Star Trek hackwork.......2000-08-15

Here's a question: Why, unlike the first book in the New Earth series, is BELLE TERRE written as if the target reader is a 9-year-old? The vocabulary and sentence structure are barely up to the standards of a YA (young adult) novel, and the story itself is a simple-minded meet-the-deadline crisis that ends exactly the way one thinks it will.

The book is needlessly divided into four arbitrary "parts"; the natural assumption here is that it was done for padding, a fair conclusion when one sees a countdown ("Four. Three. Two....") divided into separate paragraphs. The dialogue is straight from the cliche encyclopedia, with enough "one-quarter impulse, Mr. Sulu"s and "course plotted and laid in sir"s to fill three or four bad novels. And the author's idea of a scare? "Skeletons." That's right: skeletons.

My advice: skip directly to Part Three and a different author, where there should be enough background to discern the essentials of this piece of hackwork.

Why sequel writers should read the series.......2000-08-13

I'm only part way through the book but had to stop and share my frustration. In "Belle Terre", Kirk orders the Starfleet cutter Impeller of Captain Merkling to aid in the search for some lost children. Apparently, Kirk is senile because in "Wagon Train to the Stars," the Impeller, severly damaged by the Orions, was sent limping back to Federation space with a blinded Captain Merkling on board. The only possible explanations are that 1) Q made an early appearance and helped out, 2) transwarp was developed, used ot get the Impeller back to Belle Terre quickly, or 3) the author and the editor screwed up royally. Sorry, but I have to go with option 3 as my final answer. This bodes ill for the rest of the book.

A Miserable Start.......2000-07-25

I was afraid the push would be toward these multi-book stories. The last time I saw this I bought the entire VECTORS series of Star Trek books all at once -- a decision I regret to this day. At least this time all I am out is the price of one new book (selling cheap). This book just drags. Too much detail, too many characters. I am a stalwart fan of the series and I was just bored to tears with this one.

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"...a great deal of hard work to produce a great deal of poverty."
Sex! Incest! Murder! and...Farming! and...Flatulence?!
The second best novel of all time?
Zola's favorite; but brutishness can overwhelm the humor
Vive la Terre!

The Earth: La Terre (Penguin Classics)
Émile Zola
Manufacturer: Penguin Classics
ProductGroup: Book
Binding: Paperback

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ASIN: 0140443878

Customer Reviews:

"...a great deal of hard work to produce a great deal of poverty.".......2006-04-27

The connection to the Rougon - Macquart series is Jean Macquart (the brother of Gervaise from "L'Assommoir"), but even though he is the main character in that respect "The Earth" is about so much more. Mainly the human condition told through the lives of the townsfolk and farmers of Beauce. Jealousy, murder, rape, farting, love, blasphemy, birth, longing, violence, cursing, sex it's all here...even a belligerent puking donkey! Yes, Zola's storytelling can sometimes be shocking bordering on vulgar, but so is life. A masterpiece.

Sex! Incest! Murder! and...Farming! and...Flatulence?!.......2005-08-08

You'll find all five in abundance in this book, I kid you not!

I love Zola, and I'm trying to get through all the Rougon-Macquart series. For those of you that don't know, Zola wrote a 20-novel saga about a family under the Second Empire. So far I have read about six. They are all thrilling, exciting, lurid, and wonderful. This one is no exception. It is amazing and I loved it, although it was my least favorite so far among the Zola books I have read so far. (However, in its defense, it was undoubtedly the dirtiest!) The main character is one Jean Macquart, really a very nice and ordinary guy (later to fight in the Franco-Prussian war in Zola's The Debacle, the penultimate of the Rougon-Macquart, which I'm reading now) who becomes a farm hand in the most perverse, twisted peasant village you could ever imagine.

Why is this my least favorite Zola novel so far? Because it's very hard to care about the characters, whereas in some of his other books, such as "L'Assommoir", featuring Jean Macquart's sister Gervaise, or "Germinal", featuring Gervaise's son and Jean's nephew Etienne, the characters were sympathetic and the stories tragic. But almost no one was sympathetic in this book except for Jean. The evil characters were so awful you could barely read about them. I can't give away all the plot twists, but you will delight in the larger than life and humorous characters. They are so wretched!

Everyone is obsessed with one thing-land. (Except the characters that run a brothel and claim they're better than their poor relatives). But land's the thing. How to hold on to it, how to keep from losing it through marriage or disinheritance. The entire family is presided over by a hideous, cruel, and rich matriarch, called La Grande, who is in her late eighties and was born during the Terror, in 1793. She often smiles to herself about how much she enjoys setting her family at each other's throats and inciting their murderous rage. She's deliberately designed her will to cause countless lawsuits between her benefactors! But the major plot centers around the Fouan family, La Grande's brother's family.

Jean falls in love with La Grande's great-niece, Francoise, but there are problems. I can't give anything serious away in case you read this book, which you should if you haven't! You'll love it. It's as exciting as anything from our own time. Don't read the intro, by the way, until AFTER you read the book because the introduction gives away all the major plot points. I truly regret having read it. Read my introduction instead!

Without getting into too much detail, suffice to say a bunch of land disputes come into play, because the nastiest and scariest member of the Fouan family has married Lise, Francoise's sister. He doesn't want Francoise to get married to Jean or anyone for that matter because A., he would lose some of the land he inherited from Francoise's late father, and B., he is obsessed with Francoise and believes his numerous attempts to rape her will eventually succeed.

Meanwhile, everyone is sleeping with everyone, from cousin to cousin to brother and sister; people are slaughtered for their land, everyone is terribly cruel to everyone, and you find out a lot of things you didn't know about the nineteenth-century. For instance, did you know that people found flatulence as funny then as we do now?! Quite the history lesson.

One of the best characters in the book, the eldest Fouan son (called Jesus Christ because of his long hair and beard) can fart at will and always has some stashed up no matter what the occasion. You can't hope to win if you bet him that he can't fart, let's say, six times in a row. He can, no matter what time of day, and keeps getting free drinks on account of it.

There are a lot of graphic sexual scenes. This is foreshadowed by the opening scene, where Francoise mates a bull and cow! Later, animal stories are symbolically repeated with the people. They are "of the earth" and it's "all natural". Here, some of Zola's metaphors were a bit heavier handed than in his other works, and while elsewhere he made me feel terrible and shed tears about the plight of the working class in 19th century France, here he made peasants sound very unsympathetic.

Although one can understand their fears over foreign competition and their desire to have the government protect their produce, it's still hard to understand how that translated into the nastiest people I can ever remember reading about. In Zola's other books he somehow made the poverty more vivid, he made me feel it was directly responsible for people losing their dignity and their ability to live decently.

Here, it's not clear what is going on or how on earth family members would be driven to rape each other, kill each other, and steal from each other. At first their bickering is realistic, then it turns insane. Apparently Zola based his account on reports by priests from the time in these villages, and peasants who had read the book, according to Zola's son in law, tended to recognize their neighbors in the book! (If not themselves, he added, the introduction tells us.) But it still seems exaggerated to me. I still think most peasants wouldn't do what the main characters in this book did. It's an extreme example.

Don't get the wrong idea. You will still love this book although I think if you're going to read one Zola book only read Germinal or l'Assommoir. This book will keep you both laughing and reeling from how crazy and disgusting these peasants are, but it's highly unsympathetic, although I'm not sure Zola intended it to be.

I think, based on what I've read, that he felt that these were the people who were the lifeblood of France, and tried to "naturalize" their lives and make them somehow outside bougeois morality. I'm not sure it quite worked, despite his genius, but it's a great story. I think I'll read more about what he was trying to do later, because it's not always clear. As fans of his novels know, he tries to put forth "scientific" explanations for human behavior but ultimately he is a great artist and his work transcends his pretenses.

Despite the problems with the book, he's still one of the best writers ever: Vive Zola!

The second best novel of all time?.......2005-05-04

This book is a masterpiece. Had Zola not written the awe-inspiring Germinal, this would clearly be his greatest work. Zola does his best writing when he focuses not on Parisian society but rather on the lower classes: the laborers, the peasants, the working stiffs. In this case, his subject matter is the farmers of the Beauce, an agricultural region between Chartres and Orleans. Here, families have cultivated the same plots of land for generations. In fact, land itself is everything to these people, and they will do whatever they can to protect the earth they have, and to acquire as much more as they can before they die. When Old Fouan decides to divide up his holdings among his three children, no one is happy with the portion they receive. Their avarice of earth leads to mutual animosity and eventually to treachery. Jean Macquart, an affable, hard-working farmhand, is, like us, an outsider in this hermetic world, until he falls in love with a farmer's daughter and becomes a participant in their private war.
The scope of the book is wide, and looks beyond the Fouan family to examine political and social issues of the time, including the effect of the impending Franco-Prussian War, the triumphs and failures of modern scientific farming methods, and how the market's regulation of prices damns the farmers to eternal poverty. Zola's description of the agricultural life, its rewards and its hardships, is vivid and moving. He neither romanticizes nor denigrates the farmer's relationship to the land, but rather paints a realistic picture of dirty, exhausting toil that nonetheless has its physical and spiritual rewards.
The book achieves a tremendous range of mood. It's like an emotional roller coaster. There are passages in the book which are downright terrifying. Elsewhere there are moments which are laugh-out-loud funny. Zola obviously had a lot of fun writing the more light-hearted scenes in the book. He includes everything from a farting contest to a vomiting donkey. Overall, however, this novel is a dark portrayal of human greed and selfishness, and the brutal lengths to which people will go to satisfy their hunger for property. This book should be read by all.

Zola's favorite; but brutishness can overwhelm the humor.......2004-12-27

Zola's series of books on life during Napoleon III's reign will probably never be criticized for shying away from readers' sensitivities. La Terre is a very good book, and Zola's declared favorite, but the very brutishness of the acts perpetrated by the characters (other Amazon reviews have summarized them) tend to overwhelm the lighter moments. In fact, the simple humor (dunghill marriage proposals, drunken barnyard animals and the lifestyle of the character named Jesus Christ) is the main current of the story, and suggests that there's not a whole lot that can be done to change the ways of provincial farmers. Like Germinal, the protagonist Jean (a member of the family tree that connects all 20 novels in Zola's series) quickly becomes the character needed to move along the plot - while the other, more colorful beings form Zola's themes.

Like another of the Zola Penguin editions, I found the translation very readable and the translator's introduction useful, but the back cover summary misleading. Though many of the activities featured in the book are seasonal (wine-making, the harvest, etc.), the story of greed, squabbling and murder is a one-way street. "Unremitting hardship" is experienced by the farmers, but much of it is their own doing - they reap in continual poverty what they sowed in short-run greed and mental laziness. Zola would really not have us feel sorry for these characters, where even the most pitiful - Hilarion, for example, carry out grevious crimes.

There's a hostility to innovation, change, religion and outsiders that keeps the people of Beauce at a hardscrabble existence. Change would seem to come anyway, in the form of imports from America (fertile soil and the Homestead act brought about the most rapid liberalization of land ownership in history during this time). I can't help but be reminded of the election year Outsourcing panic that was used in Wisconsin campaign advertisements. Wasn't it just a few years ago that a lot of us were stuck in the Dilbert Zone? If we couldn't take the monotony of cubicle life and abhorred all the infighting and micromanagement, why are we so terrified of India? Would this not be the catalyst for change that we requested back in the 1990's? If there's a contemporary lesson from La Terre, it might be located in Part 5, Chapter 4, where a liqoured-up Lequeu finally vents his feelings to the locals, who cheer the upcoming Franco-Prussian War.

Vive la Terre!.......2004-04-27

As the title implies, this is a story of the earth -- specifically, the land, the soil from which life springs. Zola may mean to conflate this to mean 'mud' -- that is, something unproductive and foul; after all, his characters display some sensationally base attributes and they can be completely gross. But ultimately, this is a novel about the pleasures and passions -- both good and bad -- that come from the love of the land, of making things grow, and of reaping what has been sown.

The book is less concerned with the Rougon-Macquart family than with the peasant-farming community of the great plains of Beauce, France's breadbasket. Jean Macquart represents the family; he comes to the region after military service, first as a carpenter, then as a hired hand. But he functions mostly as a secondary character, only coming to prominence in the last 50 or so pages. Instead, Zola focuses on the Fouan family. The book starts with old man Fouan dividing the land he has slaved over for half a century among his three scheming children. His daughter Fanny is a penny-pincher more concerned with her reputation in the community than her father's (or her husband's) comforts. The youngest son Buteau is a (...) lecher who continually assaults his sister-in-law Francoise -- and to keep peace in the house, his wife Lise encourages her to give in. Buteau develops a love of his land that is positively erotic; Zola's descriptions of Buteau's intense emotions for the soil are impressive. Ultimately, it is money that drives Buteau, and his machinations to relieve his father of the old man's nest-egg are humorously chilling.

Fouan's elder son Jesus Christ (so-called because of his resemblance to a Certain Prophet) is a poacher and a drunk, living in a hovel with his daughter, whose attendance on her flock of geese allows her to spy on the entire community. His is a life completely devoted to pleasure -- he is not interested in property unless it can be turned to cold hard cash. Completely depraved, he is addicted to farting. When a book has a line reading "Jesus Christ was a very flatulent man and in his house many winds did blow," readers should know that this isn't going to be a tale about sallow governesses and dainty tea-parties.

A standout character is old man Fouan's even older sister La Grande, a formidably evil witch of a woman who carries a heavy stick to threaten anyone who crosses her path or disagrees with her. Zola risks caricature in creating this bitter old hag who holds sway over everyone (her driving motivation is to make everyone miserable), but she is neatly integrated with the rest of the large cast, though we never learn the source of her bitterness other than pure malice.

There are dozens of scenes to enjoy and characters to savor. I particularly liked: *The donkey getting drunk and vomiting all over the courtyard. *The death of Lise and Francoise's father, who has a stroke, and the family stands around bickering, debating whether to spring for a doctor, as he slowly dies -- followed by a hailstorm that destroys the crops as the neglected father goes into rigor mortis on the floor. *The juxtaposition of Lise going into labor at the same time as a favorite cow, which receives more attention from the neighbors -- Lise included. *The frustrations of the priest Godard, who refuses to hold any more services in the parish not so much because of the heathenness of the residents but because he must walk four miles. *The hypocrisy of M and Mme Charles, whose oh-so-respectable lives are built on the profits of running a brothel for decades -- a hypocrisy shared by the entire community. *The ongoing verbal battles between Flore Lengaigne the grocer's wife and Coelina Macqueron the tobacconist's wife, constantly fanned by the surface kindness of Mme Becu, the village gossip. *The snide fun made of Berthe Macqueron, the village beauty who is hairless below her neck and is called "Hasn't Got Any" behind her back. *Mme Frimat, who collects human excrement to use for fertilizer for her garden vegetables.

Book Description

This Elibron Classics book is a facsimile reprint of a 1771 edition published in Bouillon.

Design of the universe;: The heavens and the earth

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Design of the universe;: The heavens and the earth
Fritz Kahn
Manufacturer: Crown Publ
ProductGroup: Book
Binding: Unknown Binding

General | Science | Subjects | Books
ASIN: B0007DE182

Earth Apples (Pommes De Terre : the Poetry of Edward Abbey)

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Earth Apples (Pommes De Terre : the Poetry of Edward Abbey)
David Petersen , and Edward Abbey
Manufacturer: St Martins Pr
ProductGroup: Book
Binding: Hardcover

General | Poetry | Literature & Fiction | Subjects | Books

ASIN: 0312112653

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