Download E-books An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's Inequality PDF

By Marek Kuczma

Marek Kuczma was once born in 1935 in Katowice, Poland, and died there in 1991.

After completing highschool in his domestic city, he studied on the Jagiellonian college in Kraków. He defended his doctoral dissertation lower than the supervision of Stanislaw Golab. within the yr of his habilitation, in 1963, he got a place on the Katowice department of the Jagiellonian collage (now collage of Silesia, Katowice), and labored there until eventually his death.

Besides his a number of administrative positions and his remarkable educating job, he entire first-class and wealthy clinical paintings publishing 3 monographs and a hundred and eighty clinical papers.

He is taken into account to be the founding father of the distinguished Polish university of sensible equations and inequalities.

"The moment 1/2 the identify of this e-book describes its contents appropriately. most likely even the main dedicated expert don't have suggestion that approximately three hundred pages might be written almost about the Cauchy equation (and on a few heavily similar equations and inequalities). And the ebook is not at all chatty, and doesn't even declare completeness. half I lists the necessary initial wisdom in set and degree concept, topology and algebra. half II supplies information on suggestions of the Cauchy equation and of the Jensen inequality [...], specifically on non-stop convex services, Hamel bases, on inequalities following from the Jensen inequality [...]. half III bargains with comparable equations and inequalities (in specific, Pexider, Hosszú, and conditional equations, derivations, convex features of upper order, subadditive capabilities and balance theorems). It concludes with an expedition into the sphere of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews)

"This e-book is a true vacation for the entire mathematicians independently in their strict speciality. you'll think what deliciousness represents this booklet for sensible equationists." (B. Crstici, Zentralblatt für Mathematik)


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Download E-books Anfangswertprobleme bei Partiellen Differentialgleichungen (Grundlehren der mathematischen Wissenschaften) (German Edition) PDF

Das vorliegende Buch handelt von partiellen Differentialgleichungen, d. h. von Differentialgleichungen mit zwei oder mehr als zwei unabhangi gen Veranderlichen. Urn eine bestimmte Losung einer partiellen Differen tialgleichung festzulegen, muB guy noch gewisse zusatzliche Daten vor schreiben. Je nach der artwork dieser zusatzlichen Daten spricht guy in gewissen Fallen von Anfangswertproblemen und in anderen Fallen von Randwertproblemen oder von Anfangs-Randwert-Problemen. Ein An fangswertproblem laBt sich z. B. fur die Wellengleichung I x x - I y y = zero stellen (vgl. 2); eine Losung I (x, y) dieser Gleichung liegt etwa in der oberen x, y-Halbebene eindeutig fest, wenn auf der x-Achse als Anfangskurve die Werte von lund der erst en partiellen Ableitung Iy (Anfangswerte) bekannt sind. Ein Randwertproblem kann z. B. fUr die Potentialgleichung Ixx + Ivy = zero gestellt werden (vgl. 1); hier liegt eine Losung I (x, y) etwa im Innern eines Kreises eindeutig fest, wenn guy die Werte von I auf dem Kreis (Randwerte) kennt. Als Bei spiel eines Anfangs-Randwert-Problems sei folgende Aufgabe genannt: Gesucht ist die Losung der Wellengleichung fUr einen in der oberen x, y-Halbebene gelegenen Halbstreifen, der von einer Strecke der x-Achse und zwei zur y-Achse parallelen Halbgeraden begrenzt wird; auf der Strecke der x-Achse sind die Werte von lund Iy (Anfangswerte) vorgegebi)ll, auf den beiden Halbgeraden die Werte von I allein (Rand werte). Anfangs-und Randwertprobleme konnen nicht nach Belieben gestellt werden, sondern fUr gewisse Differentialgleichungen sind nur Anfangswertprobleme, fUr andere nur Randwertprobleme "sachgemaB" .

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Download E-books Free and Moving Boundary Problems (Oxford Science Publications) PDF

By John Crank

Here's a wide-ranging, entire account of the mathematical formula of difficulties concerning loose limitations as they take place in such different parts as hydrology, metallurgy, chemical engineering, soil technology, molecular biology, fabrics technological know-how, and metal and glass construction. Many new equipment of resolution are mentioned, together with glossy desktop options which handle multidimensional, multiphase functional problems.

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Download E-books An Introduction to Phase-Integral Methods (Dover Books on Mathematics) PDF

By John Heading

The phase-integral procedure in arithmetic, often referred to as the Wentzel-Kramers-Brillouin (WKB) process, is the point of interest of this introductory therapy. writer John Heading effectively steers a path among simplistic and rigorous ways to supply a concise review for complex undergraduates and graduate scholars in arithmetic and physics.
Since the variety of purposes is massive, the textual content considers just a short collection of issues and emphasizes the strategy itself instead of distinctive purposes. the method, as soon as derived, is proven to be considered one of crucial simplicity that contains purely the appliance of sure well-defined ideas. beginning with a historic survey of the matter and its recommendations, matters comprise the Stokes phenomenon, one and transition issues, and purposes to actual difficulties. An appendix and bibliography finish the text.

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Download E-books Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations (Synthesis Lectures on Mathematics and Statistics) PDF

By Yu Huang

This ebook includes lecture notes for a semester-long introductory graduate direction on dynamical platforms and chaos taught by way of the authors at Texas A&M collage and Zhongshan collage, China. There are ten chapters typically physique of the booklet, masking an hassle-free thought of chaotic maps in finite-dimensional areas. the subjects contain one-dimensional dynamical structures (interval maps), bifurcations, basic topological, symbolic dynamical platforms, fractals and a category of infinite-dimensional dynamical platforms that are brought about via period maps, plus speedy fluctuations of chaotic maps as a brand new standpoint built by means of the authors lately. appendices also are supplied so as to ease the transitions for the readership from discrete-time dynamical platforms to continuous-time dynamical structures, ruled through usual and partial differential equations.

desk of Contents: basic period Maps and Their Iterations / overall adaptations of Iterates of Maps / Ordering between sessions: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant units / The Smale Horseshoe / Fractals / speedy Fluctuations of Chaotic Maps on RN / Infinite-dimensional structures precipitated by way of Continuous-Time distinction Equations

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Download E-books Physics of Fractal Operators (Institute for Nonlinear Science) PDF

By Bruce West, Mauro Bologna, Paolo Grigolini

This article describes the statistcal habit of complicated platforms and indicates how the fractional calculus can be utilized to version the habit. The dialogue emphasizes actual phenomena whose evolution is better defined utilizing the fractional calculus, equivalent to structures with long-range spatial interactions or long-time reminiscence. The booklet offers normal thoughts for figuring out wave propagation via random media, the nonlinear reaction of advanced fabrics, and the fluctuations of warmth shipping in heterogeneous fabrics.

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Download E-books Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students (Software, Environments, Tools) (Software, Environments and Tools) PDF

By Bard Ermentrout

Simulating, reading, and Animating Dynamical structures: A consultant to XPPAUT for Researchers and scholars offers subtle numerical equipment for the quick and exact resolution of a number of equations, together with usual differential equations, hold up equations, fundamental equations, useful equations, and a few partial differential equations, in addition to boundary price difficulties. It introduces many modeling suggestions and techniques for interpreting the ensuing equations. teachers, scholars, and researchers will all reap the benefits of this booklet, which demonstrates the right way to use software program instruments to simulate and research units of equations that come up in a number of functions. teachers will how one can use software program of their differential equations and modeling sessions, whereas scholars will how one can create animations in their equations that may be displayed at the world-wide-web. Researchers might be brought to worthy tips that would let them take complete benefit of XPPAUT's features.

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Download E-books Chaotic Numerics: An International Workshop on the Approximation and Computation of Complicated Dynamical Behavior July 12-16, 1993 Deakin Universit (Contemporary Mathematics) PDF

A lot of what's identified approximately particular dynamical structures is received from numerical experiments. even if the discretization procedure often has no major impression at the effects for easy, well-behaved dynamics, acute sensitivity to alterations in preliminary stipulations is a trademark of chaotic habit. How convinced can one be that the numerical dynamics displays that of the unique procedure? Do numerically calculated trajectories continually shadow a real one? What position does numerical research play within the examine of dynamical platforms? And conversely, can advances in dynamical structures offer new insights into numerical algorithms? those and comparable matters have been the focal point of the workshop on Chaotic Numerics, held at Deakin college in Geelong, Australia, in July 1993. The contributions to this ebook are in response to lectures provided in the course of the workshop and supply a huge assessment of this zone of study.

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Download E-books Regularity Problem for Quasilinear Elliptic and Parabolic Systems (Lecture Notes in Mathematics) PDF

The smoothness of options for quasilinear structures is without doubt one of the most crucial difficulties in smooth mathematical physics. This ebook bargains with normal or powerful recommendations for normal quasilinear second-order elliptic and parabolic structures. purposes in sturdy mechanics, hydrodynamics, elasticity and plasticity are described.
The effects awarded are in line with major principles: the common iterative technique, and particular, occasionally sharp, coercivity estimates in weighted areas. Readers are assumed to have a customary heritage in research and PDEs.

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