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Uncertainty quantification (UQ) is a mainstream research topic in applied mathematics and statistics. To identify UQ problems, diverse modern techniques for large and complex data analyses have been developed in applied mathematics, computer science, and statistics. This Special Issue of Mathematics (ISSN 2227-7390) includes diverse modern data analysis methods such as skew-reflected-Gompertz information quantifiers with application to sea surface temperature records, the performance of variable selection and classification via a rank-based classifier, two-stage classification with SIS using a new filter ranking method in high throughput data, an estimation of sensitive attribute applying geometric distribution under probability proportional to size sampling, combination of ensembles of regularized regression models with resampling-based lasso feature selection in high dimensional data, robust linear trend test for low-coverage next-generation sequence data controlling for covariates, and comparing groups of decision-making units in efficiency based on semiparametric regression.

Kullback–Leibler divergence --- geometric distribution --- accuracy --- AUROC --- allele read counts --- mixture model --- low-coverage --- entropy --- gene-expression data --- SCAD --- data envelopment analysis --- LASSO --- high-throughput --- sandwich variance estimator --- adaptive lasso --- semiparametric regression --- ?1 lasso --- Laplacian matrix --- elastic net --- feature selection --- sea surface temperature --- gene expression data --- Skew-Reflected-Gompertz distribution --- lasso --- next-generation sequencing --- BH-FDR --- stochastic frontier model --- ?2 ridge --- geometric mean --- resampling --- Gompertz distribution --- adapative lasso --- group efficiency comparison --- sensitive attribute --- MCP --- probability proportional to size (PPS) sampling --- randomization device --- SIS --- Yennum et al.’s model --- ensembles

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The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler’s proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.

Mathematics --- Mathematical recreations. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Arbitrarily large. --- Arithmetic. --- Big O notation. --- Binomial theorem. --- Bonse's inequality. --- Circumference. --- Coefficient. --- Combination. --- Complete theory. --- Computation. --- Coprime integers. --- Diameter. --- Divisor. --- Equilateral triangle. --- Euler's formula. --- Euler's theorem. --- Exterior (topology). --- Factorial. --- Factorization. --- Fermat's Last Theorem. --- Fermat's theorem. --- Fourth power. --- Fractional part. --- Geometric mean. --- Geometric series. --- Geometry. --- Hypotenuse. --- Integer factorization. --- Intersection (set theory). --- Irrational number. --- Line segment. --- Logarithm. --- Long division. --- Mathematical induction. --- Mathematics. --- Metric space. --- Natural number. --- Non-Euclidean geometry. --- Number theory. --- Parallelogram. --- Parity (mathematics). --- Pedal triangle. --- Perfect number. --- Polyhedron. --- Power of 10. --- Prime factor. --- Prime number theorem. --- Prime number. --- Prime power. --- Pure mathematics. --- Pythagorean theorem. --- Rational number. --- Rectangle. --- Regular polygon. --- Regular polyhedron. --- Remainder. --- Reuleaux triangle. --- Rhomboid. --- Rhombus. --- Right angle. --- Right triangle. --- Scientific notation. --- Sign (mathematics). --- Special case. --- Straightedge. --- Summation. --- Theorem. --- Transfinite number. --- Variable (mathematics). --- Waring's problem.

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This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.

Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Matrices --- 512.64 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory --- Addition. --- Analytic continuation. --- Arithmetic mean. --- Banach space. --- Binomial theorem. --- Block matrix. --- Bochner's theorem. --- Calculation. --- Cauchy matrix. --- Cauchy–Schwarz inequality. --- Characteristic polynomial. --- Coefficient. --- Commutative property. --- Compact space. --- Completely positive map. --- Complex number. --- Computation. --- Continuous function. --- Convex combination. --- Convex function. --- Convex set. --- Corollary. --- Density matrix. --- Diagonal matrix. --- Differential geometry. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence relation. --- Existential quantification. --- Extreme point. --- Fourier transform. --- Functional analysis. --- Fundamental theorem. --- G. H. Hardy. --- Gamma function. --- Geometric mean. --- Geometry. --- Hadamard product (matrices). --- Hahn–Banach theorem. --- Harmonic analysis. --- Hermitian matrix. --- Hilbert space. --- Hyperbolic function. --- Infimum and supremum. --- Infinite divisibility (probability). --- Invertible matrix. --- Lecture. --- Linear algebra. --- Linear map. --- Logarithm. --- Logarithmic mean. --- Mathematics. --- Matrix (mathematics). --- Matrix analysis. --- Matrix unit. --- Metric space. --- Monotonic function. --- Natural number. --- Open set. --- Operator algebra. --- Operator system. --- Orthonormal basis. --- Partial trace. --- Positive definiteness. --- Positive element. --- Positive map. --- Positive semidefinite. --- Positive-definite function. --- Positive-definite matrix. --- Probability measure. --- Probability. --- Projection (linear algebra). --- Quantity. --- Quantum computing. --- Quantum information. --- Quantum statistical mechanics. --- Real number. --- Riccati equation. --- Riemannian geometry. --- Riemannian manifold. --- Riesz representation theorem. --- Right half-plane. --- Schur complement. --- Schur's theorem. --- Scientific notation. --- Self-adjoint operator. --- Sign (mathematics). --- Special case. --- Spectral theorem. --- Square root. --- Standard basis. --- Summation. --- Tensor product. --- Theorem. --- Toeplitz matrix. --- Unit vector. --- Unitary matrix. --- Unitary operator. --- Upper half-plane. --- Variable (mathematics).

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This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu.

Ostrowski inequality --- Hölder’s inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler–Maclaurin summation formula --- Abel’s partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite–Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi–Dirac entropy --- Bose–Einstein entropy --- arithmetic mean --- geometric mean --- Young’s inequality --- Simpson’s inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson’s inequality --- harmonically convex functions --- Simpson inequality --- (n,m)–generalized convexity --- n/a --- Hölder's inequality --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- Hermite-Hadamard inequality --- Phragmén-Lindelöf alternative --- Fermi-Dirac entropy --- Bose-Einstein entropy --- Young's inequality --- Simpson's inequalities --- Simpson's inequality --- (n,m)-generalized convexity