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This book presents collective works published in the recent Special Issue (SI) entitled "Multivariate Approximation for Solving ODE and PDE". These papers describe the different approaches and related objectives in the field of multivariate approximation. The articles in fact present specific contents of numerical methods for the analysis of the approximation, as well as the study of ordinary differential equations (for example oscillating with delay) or that of partial differential equations of the fractional order, but all linked by the objective to present analytical or numerical techniques for the simplification of the study of problems involving relationships that are not immediately computable, thus allowing to establish a connection between different fields of mathematical analysis and numerical analysis through different points of view and investigation. The present contents, therefore, describe the multivariate approximation theory, which is today an increasingly active research area that deals with a multitude of problems in a wide field of research. This book brings together a collection of inter-/multi-disciplinary works applied to many areas of applied mathematics in a coherent manner.

nonlinear equations --- iteration methods --- one-point methods --- order of convergence --- oscillatory solutions --- nonoscillatory solutions --- second-order --- neutral differential equations --- multiple roots --- optimal convergence --- bivariate function --- divided difference --- inverse difference --- blending difference --- continued fraction --- Thiele–Newton’s expansion --- Viscovatov-like algorithm --- symmetric duality --- non-differentiable --- (G,αf)-invexity/(G,αf)-pseudoinvexity --- (G,αf)-bonvexity/(G,αf)-pseudobonvexity --- duality --- support function --- nondifferentiable --- strictly pseudo (V,α,ρ,d)-type-I --- unified dual --- efficient solutions --- Iyengar inequality --- right and left generalized fractional derivatives --- iterated generalized fractional derivatives --- generalized fractional Taylor’s formulae --- poisson equation --- domain decomposition --- asymmetric iterative schemes --- group explicit --- parallel computation --- even-order differential equations --- neutral delay --- oscillation --- Hilbert transform --- Hadamard transform --- hypersingular integral --- Bernstein polynomials --- Boolean sum --- simultaneous approximation --- equidistant nodes --- fourth-order --- delay differential equations --- riccati transformation --- parameter estimation --- physical modelling --- oblique decomposition --- least-squares

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This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.

Research & information: general --- Mathematics & science --- fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat's Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer --- fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat's Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer

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An engaging collection of intriguing problems that shows you how to think like a mathematical physicistPaul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar kind of glass called NASTYGLASS-and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin's goal, however, is always to guide readers-who will need only to have studied advanced high school math and physics-in expanding their mathematical thinking to make sense of the curiosities of the physical world.The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics-including algebra, trigonometry, geometry, and calculus-can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements.More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

Mathematics --- Almost surely. --- Ambiguity. --- Antiderivative. --- Approximation error. --- Arthur C. Clarke. --- Binomial coefficient. --- Binomial theorem. --- Birthday problem. --- Calculation. --- Cauchy–Schwarz inequality. --- Center of mass (relativistic). --- Centrifugal force. --- Closed-form expression. --- Coefficient. --- Combination. --- Computational problem. --- Conjecture. --- Continued fraction. --- Contradiction. --- Coprime integers. --- Counterexample. --- Crossover distortion. --- Cubic function. --- Derivative. --- Detonation. --- Diameter. --- Dimensional analysis. --- Dirac delta function. --- Disquisitiones Arithmeticae. --- Dissipation. --- Energy level. --- Enola Gay. --- Equation. --- Error. --- Expected value. --- Fermat's Last Theorem. --- Fictitious force. --- G. H. Hardy. --- Geometry. --- Googol. --- Gravitational constant. --- Gravity. --- Grayscale. --- Harmonic series (mathematics). --- Hypotenuse. --- Instant. --- Integer. --- Inverse-square law. --- Irrational number. --- MATLAB. --- Mass ratio. --- Mathematical joke. --- Mathematical physics. --- Mathematical problem. --- Mathematician. --- Mathematics. --- Mean value theorem. --- Metric system. --- Minicomputer. --- Monte Carlo method. --- Natural number. --- Oliver Heaviside. --- Paul J. Nahin. --- Pauli exclusion principle. --- Periodic function. --- Phase transition. --- Prime factor. --- Prime number. --- Probability theory. --- Probability. --- Projectile. --- Pure mathematics. --- Quadratic equation. --- Quadratic formula. --- Quantity. --- Quantum mechanics. --- Quintic function. --- Random number. --- Random search. --- Random walk. --- Remainder. --- Resistor. --- Richard Feynman. --- Right angle. --- Second derivative. --- Simulation. --- Slant range. --- Small number. --- Special case. --- Square root. --- Summation. --- The Drunkard's Walk. --- Theorem. --- Thermodynamic equilibrium. --- Thought experiment. --- Trepidation (astronomy). --- Uniform distribution (discrete). --- Upper and lower bounds. --- Weightlessness. --- Zero of a function.

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This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.

Research & information: general --- Mathematics & science --- fuzzy set --- n-Pythagorean --- n-PFS algebra --- triangular norms --- outer-independent Roman domination --- Roman domination --- vertex cover --- rooted product graph --- total domination --- domination --- secure domination --- secure Italian domination --- weak roman domination --- w-domination --- cryptanalysis --- group key establishment --- topology optimization --- optimization --- filtering --- method --- penalization --- weight factor --- FEM --- MATLAB --- SIMP --- estimated prime factor --- integer factorisation problem --- continued fraction --- Fermat’s Factoring Algorithm --- genetic algorithm --- AES(t) --- heuristics --- microaggregation --- statistical disclosure control --- graph theory --- traveling salesman problem --- data privacy --- location privacy --- differentials in graphs --- strong differential --- quasi-total strong differential --- quasi-total Italian domination number --- numerical semigroup --- forest --- ordinarization transform --- quasi-ordinarization transform --- load redistribution --- leveling power consumption per phase --- three-phase asymmetric distribution networks --- ideal power consumption --- mixed-integer convex optimization --- strongly total Roman domination --- total Roman domination --- lexicographic product graph --- improved crow search algorithm --- normal Gaussian distribution --- phase swapping problem --- power losses --- asymmetric distribution grids --- vortex search algorithm --- nonidentical parallel production lines --- axle housing machining --- mixed model production --- eligibility constraint --- fuzzy due date --- grey wolf optimizer --- n/a --- Fermat's Factoring Algorithm

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This volume is a collection of investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory, which are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. It contains invited and welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.

Research & information: general --- Mathematics & science --- subordination --- functions with positive real part --- reciprocals --- univalent functions --- starlikeness --- convexity --- close-to-convexity --- hyper-Bessel functions --- Hardy space --- distribution --- fractional Laplacian --- Riesz fractional derivative --- delta sequence --- convolution --- subordinations --- starlike functions --- convex functions --- close-to-convex functions --- cardioid domain --- Hankel determinant --- m-fold symmetric functions --- harmonic univalent functions --- with symmetric conjecture point --- integral expressions --- coefficient estimates --- distortion --- umbral methods --- harmonic numbers --- special functions --- integral representations --- laplace and other integral transforms --- analytic functions --- quasi-Hadamard --- differential operator --- closure property --- riemann zeta function --- asymptotics --- exponential sums --- multivalent functions --- q-Ruschweyh differential operator --- q-starlike functions --- circular domain --- q-Bernardi integral operator --- Bessel functions --- Appell–Bessel functions --- generating functions --- Chebyshev polynomials --- Euler sums --- Catalan’s constant --- Trigamma function --- integral representation --- closed form --- ArcTan and ArcTanh functions --- partial fractions --- Lambert series --- cotangent sum --- modular transformation --- Dedekind sum --- lemniscate of Bernoulli Hankel determinant --- determinant --- inverse --- Mersenne number --- periodic tridiagonal Toeplitz matrix --- Sherman-Morrison-Woodbury formula --- Fibonacci number --- Lucas number --- Toeplitz matrix --- Hankel matrix --- univalent function --- second Hankel determinant --- bi-close-to-convex functions --- gamma function and its extension --- Pochhammer symbol and its extensions --- hypergeometric function and its extensions --- τ-Gauss hypergeometric function and its extensions --- τ-Kummer hypergeometric function --- Fox-Wright function --- p-valent analytic function --- Hadamard product --- q-integral operator --- generalized Lupaş operators --- q analogue --- Korovkin’s type theorem --- convergence theorems --- Voronovskaya type theorem --- starlike function --- subordinate --- Janowski functions --- conic domain --- q-convex functions --- q-close-to-convex functions --- theta-function identities --- multivariable R-functions --- Jacobi’s triple-product identity --- Ramanujan’s theta functions --- q-product identities --- Euler’s pentagonal number theorem --- Rogers-Ramanujan continued fraction --- Rogers-Ramanujan identities --- combinatorial partition-theoretic identities --- Schur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identities --- Schur’s second partition theorem --- subordination --- functions with positive real part --- reciprocals --- univalent functions --- starlikeness --- convexity --- close-to-convexity --- hyper-Bessel functions --- Hardy space --- distribution --- fractional Laplacian --- Riesz fractional derivative --- delta sequence --- convolution --- subordinations --- starlike functions --- convex functions --- close-to-convex functions --- cardioid domain --- Hankel determinant --- m-fold symmetric functions --- harmonic univalent functions --- with symmetric conjecture point --- integral expressions --- coefficient estimates --- distortion --- umbral methods --- harmonic numbers --- special functions --- integral representations --- laplace and other integral transforms --- analytic functions --- quasi-Hadamard --- differential operator --- closure property --- riemann zeta function --- asymptotics --- exponential sums --- multivalent functions --- q-Ruschweyh differential operator --- q-starlike functions --- circular domain --- q-Bernardi integral operator --- Bessel functions --- Appell–Bessel functions --- generating functions --- Chebyshev polynomials --- Euler sums --- Catalan’s constant --- Trigamma function --- integral representation --- closed form --- ArcTan and ArcTanh functions --- partial fractions --- Lambert series --- cotangent sum --- modular transformation --- Dedekind sum --- lemniscate of Bernoulli Hankel determinant --- determinant --- inverse --- Mersenne number --- periodic tridiagonal Toeplitz matrix --- Sherman-Morrison-Woodbury formula --- Fibonacci number --- Lucas number --- Toeplitz matrix --- Hankel matrix --- univalent function --- second Hankel determinant --- bi-close-to-convex functions --- gamma function and its extension --- Pochhammer symbol and its extensions --- hypergeometric function and its extensions --- τ-Gauss hypergeometric function and its extensions --- τ-Kummer hypergeometric function --- Fox-Wright function --- p-valent analytic function --- Hadamard product --- q-integral operator --- generalized Lupaş operators --- q analogue --- Korovkin’s type theorem --- convergence theorems --- Voronovskaya type theorem --- starlike function --- subordinate --- Janowski functions --- conic domain --- q-convex functions --- q-close-to-convex functions --- theta-function identities --- multivariable R-functions --- Jacobi’s triple-product identity --- Ramanujan’s theta functions --- q-product identities --- Euler’s pentagonal number theorem --- Rogers-Ramanujan continued fraction --- Rogers-Ramanujan identities --- combinatorial partition-theoretic identities --- Schur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identities --- Schur’s second partition theorem