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Numerical Analysis or Numerical Method in Symmetry

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ISBN: 9783039283729 9783039283736 Year: Pages: 194 DOI: 10.3390/books978-3-03928-373-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:08
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Abstract

This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Keywords

risk assessment --- numerical analysis --- ignition hazard --- effective field strength --- offshore plant --- Hamiltonian system --- complex Lagrangian --- Noether symmetries --- first integrals --- symplectic Runge–Kutta methods --- effective order --- partitioned runge-kutta methods --- symplecticity --- hamiltonian systems --- Runge-Kutta type methods --- fourth-order ODEs --- order conditions --- B-series --- quad-colored trees --- k-hypergeometric differential equations --- non-homogeneous --- k-hypergeometric series --- special function --- general solution --- Frobenius method --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- recurrence relations --- differential equations --- composition properties --- orthogonality properties --- numerical analysis --- heat generation --- chemical reaction --- thin needle --- nanofluid --- fourth-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- particle accelerator --- coupling impedance --- dual integral equations --- Clenshaw-Curtis quadrature --- steepest descent method --- logarithmic singularities --- Cauchy singularity --- highly oscillatory integrals --- second-order --- nonoscillatory solutions --- oscillatory solutions --- delay differential equations --- Fredholm integral equations --- multiresolution analysis --- unitary extension principle --- oblique extension principle --- B-splines --- wavelets --- tight framelets --- Swift–Hohenberg type of equation --- surfaces --- narrow band domain --- closest point method --- operator splitting method

Current Trends in Symmetric Polynomials with their Applications

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ISBN: 9783039216208 9783039216215 Year: Pages: 238 DOI: 10.3390/books978-3-03921-621-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Fubini polynomials --- w-torsion Fubini polynomials --- fermionic p-adic integrals --- symmetric identities --- Chebyshev polynomials --- sums of finite products --- hypergeometric function --- Fubini polynomials --- Euler numbers --- symmetric identities --- elementary method --- computational formula --- two variable q-Berstein polynomial --- two variable q-Berstein operator --- q-Euler number --- q-Euler polynomial --- Fubini polynomials --- Euler numbers --- congruence --- elementary method --- q-Bernoulli numbers --- q-Bernoulli polynomials --- two variable q-Bernstein polynomials --- two variable q-Bernstein operators --- p-adic integral on ?p --- the degenerate gamma function --- the modified degenerate gamma function --- the degenerate Laplace transform --- the modified degenerate Laplace transform --- Fibonacci --- Lucas --- linear form in logarithms --- continued fraction --- reduction method --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Hermite --- generalized Laguerre --- Legendre --- Gegenbauer --- Jacobi --- third-order character --- classical Gauss sums --- rational polynomials --- analytic method --- recursive formula --- fermionic p-adic q-integral on ?p --- q-Euler polynomials --- q-Changhee polynomials --- symmetry group --- Apostol-type Frobenius–Euler polynomials --- three-variable Hermite polynomials --- symmetric identities --- explicit relations --- operational connection --- q-Volkenborn integral on ?p --- Bernoulli numbers and polynomials --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- Changhee polynomials --- Changhee polynomials of type two --- fermionic p-adic integral on ?p --- Chebyshev polynomials of the first, second, third, and fourth kinds --- sums of finite products --- representation --- catalan numbers --- elementary and combinatorial methods --- recursive sequence --- convolution sums --- well-posedness --- stability --- acoustic wave equation --- perfectly matched layer --- Fibonacci polynomials --- Lucas polynomials --- trivariate Fibonacci polynomials --- trivariate Lucas polynomials --- generating functions --- central incomplete Bell polynomials --- central complete Bell polynomials --- central complete Bell numbers --- Legendre polynomials --- Laguerre polynomials --- generalized Laguerre polynomials --- Gegenbauer polynomials --- hypergeometric functions 1F1 and 2F1 --- Euler polynomials --- Bernoulli polynomials --- elementary method --- identity --- congruence --- new sequence --- Catalan numbers --- elementary and combinatorial methods --- congruence --- conjecture --- fluctuation theorem --- thermodynamics of information --- stochastic thermodynamics --- mutual information --- non-equilibrium free energy --- entropy production

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

Discrete Mathematics and Symmetry

Author:
ISBN: 9783039281909 9783039281916 Year: Pages: 458 DOI: 10.3390/books978-3-03928-191-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:08
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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Keywords

strongly regular graph --- automorphism group --- orbit matrix --- binary polyhedral group --- icosahedron --- dodecahedron --- 600-cell --- Electric multiple unit trains --- high-level maintenance planning --- time window --- 0–1 programming model --- particle swarm algorithm --- fixed point --- split-quaternion --- quadratic polynomial --- split-octonion --- neutrosophic set --- neutrosophic rough set --- pessimistic (optimistic) multigranulation neutrosophic approximation operators --- complete lattice --- rough set --- matroid --- operator --- attribute reduction --- graded rough sets --- rough intuitionistic fuzzy sets --- dominance relation --- logical conjunction operation --- logical disjunction operation --- multi-granulation --- planar point set --- convex polygon --- disjoint holes --- fuzzy logic --- pseudo-BCI algebra --- quasi-maximal element --- KG-union --- quasi-alternating BCK-algebra --- quality function deployment --- engineering characteristics --- group decision making --- 2-tuple --- metro station --- emergency routes --- graph partitioning --- graph clustering --- invariant measures --- partition comparison --- finite automorphism groups --- graph automorphisms --- Fuzzy sets --- ring --- normed space --- fuzzy normed ring --- fuzzy normed ideal --- fuzzy implication --- quantum B-algebra --- q-filter --- quotient algebra --- basic implication algebra --- Detour–Harary index --- maximum --- unicyclic --- bicyclic --- cacti --- three-way decisions --- intuitionistic fuzzy sets --- multi-granulation rough intuitionistic fuzzy sets --- granularity importance degree --- complexity --- Chebyshev polynomials --- gear graph --- pyramid graphs --- edge detection --- Laplacian operation --- regularization --- parameter selection --- performance evaluation --- aggregation operator --- triangular norm --- ?-convex set --- atom-bond connectivity index --- geometric arithmetic index --- line graph --- generalized bridge molecular graph --- graceful labeling --- edge graceful labeling --- edge even graceful labeling --- polar grid graph --- graph --- good drawing --- crossing number --- join product --- cyclic permutation --- nonlinear --- synchronized --- linear discrete --- chaotic system --- algorithm --- generalized permanental polynomial --- coefficient --- co-permanental --- isoperimetric number --- random graph --- intersection graph --- social network --- Abel–Grassmann’s groupoid (AG-groupoid) --- Abel–Grassmann’s group (AG-group) --- involution AG-group --- commutative group --- filter --- graceful labeling --- edge even graceful labeling --- cylinder grid graph --- selective maintenance --- multi-state system --- human reliability --- optimization --- genetic algorithm --- hypernear-ring --- multitransformation --- embedding --- distance matrix (spectrum) --- distance signlees Laplacian matrix (spectrum) --- (generalized) distance matrix --- spectral radius --- transmission regular graph --- graph --- good drawing --- crossing number --- join product --- cyclic permutation --- cyclic associative groupoid (CA-groupoid) --- cancellative --- variant CA-groupoids --- decomposition theorem --- construction methods

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