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This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
This two-part treatment of Hill's equation encompasses the subject's most pertinent information, explaining both basic theory and numerous details, including elementary formulas, oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention is given to stability problems and the question of coexistence of periodic solutions. 1966 edition.
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
FBI agent Max Carter lives his life by a strict set of rules—rules that don't allow for distraction, deviation...or a relationship. But tell that to his matchmaking mama. To avoid yet another set-up, he announces he has a girlfriend. And now has to produce said girlfriend at Christmas dinner. Maybe Santa has a suitable actress in that red bag of his... Gina Castillo is about to break her building’s iron-clad “no pets” policy to give her little brother the perfect Christmas gift—a dog. Too bad Max, the most inconveniently sexy tenant in the building, catches her red-handed. Gina expects to be evicted, but instead finds herself blackmailed into playing the role of his girlfriend. Two lies plus one dog should equal a hot mess of a holiday, but attraction and Christmas magic might just defy the rules...
In 1956, two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein's. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory—the basis of computers and the Internet—to the problem of making as much money as possible, as fast as possible. Shannon and MIT mathematician Edward O. Thorp took the "Kelly formula" to Las Vegas. It worked. They realized that there was even more money to be made in the stock market. Thorp used the Kelly system with his phenomenally successful hedge fund, Princeton-Newport Partners. Shannon became a successful investor, too, topping even Warren Buffett's rate of return. Fortune's Formula traces how the Kelly formula sparked controversy even as it made fortunes at racetracks, casinos, and trading desks. It reveals the dark side of this alluring scheme, which is founded on exploiting an insider's edge. Shannon believed it was possible for a smart investor to beat the market—and William Poundstone's Fortune's Formula will convince you that he was right.
Your formula to build a strong sense of self-worth so that you can better recognize opportunity, take action on your dreams, and enhance your resilience. A lack of self-confidence is one of the greatest maladies of today’s world, one that is responsible for the rampant helplessness, lack of self-control, aimlessness, procrastination, and despair that characterize modern society. But as the venerable steel magnate Andrew Carnegie emphasized to Hill, “Confidence is a state of mind, necessary to succeed, and the starting point of developing self-confidence is definiteness of purpose.” The time for self-doubt and self-criticism is over. Your faith in yourself and your abilities determines whether you fail or succeed. Napoleon Hill’s Self-Confidence Formula enables you to boost your self-confidence through the application of Hill’s strategies for controlling your thoughts. By implementing these principles, you will not only be able to operate at a higher plane of thought and action—attracting more opportunities, gaining influence, and strengthening relationships—but you will also be able to instill this critical quality in others. Napoleon Hill’s Self-Confidence Formula gives you the keys to success and fulfillment by equipping you to: unlearn fears, insecurities, and limitations acquired in childhood and adolescence condition your mind to believe in the certainty of your success take bold, confident action on your definite chief aim conquer your inferiority complex through the mastermind principle build the self-reliance and self-esteem of today’s youth You are now on the journey to confident, purposeful living. As you implement Hill’s principles, you will cultivate a state of mind primed to accept the abundance reserved for you.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
The New York Times bestselling author of The Unhoneymooners returns with a witty and effervescent novel about what happens when two people with everything on the line are thrown together by science—or is it fate? Perfect for fans of The Rosie Project and One Plus One. Single mom Jess Davis is a data and statistics wizard, but no amount of number crunching can convince her to step back into the dating world. Raised by her grandparents—who now help raise her seven-year-old daughter, Juno—Jess has been left behind too often to feel comfortable letting anyone in. After all, her father’s never been around, her hard-partying mother disappeared when she was six, and her ex decided he wasn’t “father material” before Juno was even born. Jess holds her loved ones close, but working constantly to stay afloat is hard...and lonely. But then Jess hears about GeneticAlly, a buzzy new DNA-based matchmaking company that’s predicted to change dating forever. Finding a soulmate through DNA? The reliability of numbers: This Jess understands. At least she thought she did, until her test shows an unheard-of 98% compatibility with another subject in the database: GeneticAlly’s founder, Dr. River Pena. This is one number she can’t wrap her head around, because she already knows Dr. Pena. The stuck-up, stubborn man is without a doubt not her soulmate. But GeneticAlly has a proposition: Get to know him and we’ll pay you. Jess—who is barely making ends meet—is in no position to turn it down, despite her skepticism about the project and her dislike for River. As the pair are dragged from one event to the next as the “Diamond” pairing that could make GeneticAlly a mint in stock prices, Jess begins to realize that there might be more to the scientist—and the science behind a soulmate—than she thought. Funny, warm, and full of heart, The Soulmate Equation proves that the delicate balance between fate and choice can never be calculated.
The approach by Hills is based upon two hypotheses: (1) inert gas transport is limited by diffusion in a single radial model of extra-vascular tissue, and (2) nucleation and phase equilibration between dissolved gas and gas in silent bubbles may preclude supersaturation in excess of 74 mmHg. Actually, two different models, not always clearly distinguished, are presented. One, expounded in theoretical analysis is concerned with gas concentration in a certain average sense over the extra-vascular space. The other, used for his proposed optimum decompression method presumes a restraint on point tensions to 74 mmHg over the diffusion field is necessary to preclude nucleation. (Author)