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Polynomials --- Polynômes. --- Functions of complex variables --- Fonctions d'une variable complexe --- zeros des polynomes

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This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.

Zero coupon securities. --- Bonds, Zero coupon --- Liquid yield option notes --- Zero coupon bonds --- Zeros (Securities) --- Securities --- Finance. --- Mathematics. --- Econometrics. --- Quantitative Finance. --- Game Theory, Economics, Social and Behav. Sciences. --- Economics, Mathematical --- Statistics --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Mathematical economics --- Econometrics --- Methodology

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"The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry"--Provided by publisher.

Finance --- Interest rates --- Zero coupon securities --- 305.91 --- 333.605 --- 333.642 --- AA / International- internationaal --- Bonds, Zero coupon --- Liquid yield option notes --- Zero coupon bonds --- Zeros (Securities) --- Securities --- Money market rates --- Rate of interest --- Rates, Interest --- Interest --- Funding --- Funds --- Economics --- Currency question --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Nieuwe financiële instrumenten --- Termijn. Financial futures --- Interest rates. --- Zero coupon securities. --- Finance.

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Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

superposition --- SU(2) --- pseudo-remainder --- interval methods --- sparse polynomials --- element order --- Henneberg-type minimal surface --- timelike axis --- combinatorial decompositions --- sparse data structures --- mutually unbiased bases --- invariant surfaces --- projective special unitary group --- Minkowski 4-space --- free resolutions --- Dini-type helicoidal hypersurface --- linearity --- integrability --- Galois rings --- minimum point --- entanglement --- degree --- pseudo-division --- computational algebra --- polynomial arithmetic --- projective special linear group --- normal form --- Galois fields --- Gauss map --- implicit equation --- number of elements of the same order --- Weierstrass representation --- Lotka–Volterra system --- isolated zeros --- polynomial modules --- over-determined polynomial system --- simple Kn-group --- sum of squares --- four-dimensional space

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This volume was conceived as a Special Issue of the MDPI journal Mathematics to illustrate and show relevant applications of differential equations in different fields, coherently with the latest trends in applied mathematics research. All the articles that were submitted for publication are valuable, interesting, and original. The readers will certainly appreciate the heterogeneity of the 10 papers included in this book and will discover how helpful all the kinds of differential equations are in a wide range of disciplines. We are confident that this book will be inspirational for young scholars as well.

Research & information: general --- Mathematics & science --- q-Hermite polynomials --- zeros of q-Hermite polynomials --- differential equation --- splitted separation --- Lie symmetries --- gauss hypergeometric functions --- initial value problem --- Kepler-type orbits --- Runge-Kutta --- differential evolution --- dynamical systems --- stability --- economics --- relationships --- networks --- oscillatory problems --- SEIR ODE model --- COVID-19 transmission --- convalescent plasma transfusion (CPT) --- degeneracy --- elliptic PDE --- ladder operator --- commuting operator --- eigenvalues --- mixing process --- simultaneous differential equations --- variable production rate --- simulated annealing --- financial markets --- investment style --- border collision bifurcation --- fundamental analysis --- technical analysis --- market maker --- differential equations with discontinuous right-hand sides --- Hopfield artificial neural networks