2015, 1st ed. 2015, SpringerBriefs in Mathematics, ISBN 3319220985, 131

eBook

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 15

In this paper, we consider three types of functions given by sums of finite products of Bernoulli functions and derive their Fourier series expansions...

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | 42A16 | Fourier series | 11B68 | Partial Differential Equations | sums of finite products of Bernoulli functions | MATHEMATICS | MATHEMATICS, APPLIED | Fourier analysis | Theorems (Mathematics) | Usage | Sums

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | 42A16 | Fourier series | 11B68 | Partial Differential Equations | sums of finite products of Bernoulli functions | MATHEMATICS | MATHEMATICS, APPLIED | Fourier analysis | Theorems (Mathematics) | Usage | Sums

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 17

In a previous work, it was shown that Faber-Pandharipande-Zagier and Miki’s identities can be derived from a polynomial identity which in turn follows from a Fourier series expansion of sums of products of Bernoulli functions...

Genocchi polynomials | Mathematics | Fourier series | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | Genocchi functions | 42A16 | Partial Differential Equations | Bernoulli functions | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | FOURIER-SERIES | Q-EXTENSIONS | Binomial distribution | Fourier analysis | Theorems (Mathematics) | Usage | Tests, problems and exercises | Functions (mathematics) | Series expansion | Mathematical analysis | Sums

Genocchi polynomials | Mathematics | Fourier series | Ordinary Differential Equations | Functional Analysis | 11B83 | Analysis | Difference and Functional Equations | Mathematics, general | Genocchi functions | 42A16 | Partial Differential Equations | Bernoulli functions | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | FOURIER-SERIES | Q-EXTENSIONS | Binomial distribution | Fourier analysis | Theorems (Mathematics) | Usage | Tests, problems and exercises | Functions (mathematics) | Series expansion | Mathematical analysis | Sums

Journal Article

MATHEMATICS, ISSN 2227-7390, 09/2019, Volume 7, Issue 9, p. 833

In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series...

SUMMATION FORMULAS | MATHEMATICS | SERIES | closed form | ArcTan and ArcTanh functions | Catalan's constant | HARMONIC SUMS | Euler sums | Trigamma function | integral representation | partial fractions | FAMILY | Catalan’s constant

SUMMATION FORMULAS | MATHEMATICS | SERIES | closed form | ArcTan and ArcTanh functions | Catalan's constant | HARMONIC SUMS | Euler sums | Trigamma function | integral representation | partial fractions | FAMILY | Catalan’s constant

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 07/2016, Volume 636, pp. 66 - 76

.... Then the distance and rank aggregation problems can be solved efficiently in almost linear time. A chain sum order is complementary to a bucket order and consists of a set of disjoint total orders...

Ranking | Distance measures | [formula omitted]-hardness | Fixed-parameter complexity | Total and partial orders | NP-hardness | NP-HARD | TOURNAMENTS | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Online searching | Rankings | Internet/Web search services | Database searching | Analysis | Hardness | Equivalence | Searching | Chains | Polynomials | Agglomeration | Internet | Buckets

Ranking | Distance measures | [formula omitted]-hardness | Fixed-parameter complexity | Total and partial orders | NP-hardness | NP-HARD | TOURNAMENTS | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Online searching | Rankings | Internet/Web search services | Database searching | Analysis | Hardness | Equivalence | Searching | Chains | Polynomials | Agglomeration | Internet | Buckets

Journal Article

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 10/2011, Volume 37, Issue 1, pp. 421 - 442

It is well-known that the Fourier partial sums of a function exhibit the Gibbs phenomenon at a jump discontinuity...

Computational Mathematics and Numerical Analysis | Mathematics | Theory of Computation | Fourier partial sum | Asymptotics | de la Vallée-Poussin sum | Orthogonal expansion | Gibbs function | 42A24 | Generalized Gibbs phenomenon | Mathematics of Computing | 42A20 | 42A10 | Appl.Mathematics/Computational Methods of Engineering | 42A16 | Universities and colleges | Studies | Fourier analysis | Mathematical analysis | Asymptotic methods

Computational Mathematics and Numerical Analysis | Mathematics | Theory of Computation | Fourier partial sum | Asymptotics | de la Vallée-Poussin sum | Orthogonal expansion | Gibbs function | 42A24 | Generalized Gibbs phenomenon | Mathematics of Computing | 42A20 | 42A10 | Appl.Mathematics/Computational Methods of Engineering | 42A16 | Universities and colleges | Studies | Fourier analysis | Mathematical analysis | Asymptotic methods

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 14

..., we get the almost sure central limit theorem for the products of the some partial sums (∏i=1kSk,i(k−1)nμn)μβVk\(({\frac{\prod_{i=1}^{k}S_{k,i}}{(k-1)^{n}\mu ^{n}} )^{\frac{\mu}{\beta V_{k}}} }\), where β>0\(\beta>0...

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2019, Volume 25, Issue 6, pp. 3174 - 3183

In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the $$L_2...

Mathematics | Abstract Harmonic Analysis | Convergence almost-everywhere | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | Approximations and Expansions | Spherical partial sums | Generalized localization | Secondary 42B99 | Multiple Fourier series | Partial Differential Equations | Primary 42B05 | MATHEMATICS, APPLIED

Mathematics | Abstract Harmonic Analysis | Convergence almost-everywhere | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | Approximations and Expansions | Spherical partial sums | Generalized localization | Secondary 42B99 | Multiple Fourier series | Partial Differential Equations | Primary 42B05 | MATHEMATICS, APPLIED

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2014, Volume 264, pp. 236 - 260

...–Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell–Lerch sums...

Appell–Lerch sums | Mock theta functions | Hecke-type double sums | Partial theta functions | Indefinite theta series | Appell-Lerch sums | MATHEMATICS | ROGERS-RAMANUJAN IDENTITIES | HARD-HEXAGON MODEL | LOST NOTEBOOK | Mathematics - Number Theory

Appell–Lerch sums | Mock theta functions | Hecke-type double sums | Partial theta functions | Indefinite theta series | Appell-Lerch sums | MATHEMATICS | ROGERS-RAMANUJAN IDENTITIES | HARD-HEXAGON MODEL | LOST NOTEBOOK | Mathematics - Number Theory

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 08/2013, Volume 49, Issue 3, pp. 873 - 884

Let S-n((2)) denote the iterated partial sums. That is, S-n((2)) = S-1 + S-2 + ... + S-n, where S-i = X-1 + X-2 + ... + X-i. Assuming X-1, X-2...

Persistence | First passage time | One-sided probability | Iterated partial sums | Lower tail probability | Random walk | STATISTICS & PROBABILITY | Mathematics - Probability | 60F10 | 60G50

Persistence | First passage time | One-sided probability | Iterated partial sums | Lower tail probability | Random walk | STATISTICS & PROBABILITY | Mathematics - Probability | 60F10 | 60G50

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 06/2015, Volume 91, Issue 3, pp. 693 - 708

This paper proves non‐trivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess...

MATHEMATICS | PARTIAL GAUSSIAN SUMS | Theorems | Mathematical analysis | Estimates | Sums | Mathematics - Number Theory

MATHEMATICS | PARTIAL GAUSSIAN SUMS | Theorems | Mathematical analysis | Estimates | Sums | Mathematics - Number Theory

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2019, Volume 49, Issue 1, pp. 59 - 101

... $$(n_j)$$ ( n j ) be such that the almost everywhere relation $$\frac{1}{N}\sum _{j=1}^N S_{n_j}f \rightarrow f$$ 1 N ∑ j = 1 N S n j f → f is fulfilled for each integrable function f...

Cesàro means | a.e. convergence | 42A24 | Zalcwasser’s problem | Numerical Analysis | Analysis | Subsequences of partial sums | Mathematics | Trigonometric Fourier series | MATHEMATICS | Cesaro means | CONVERGENCE | Zalcwasser's problem | SUMMABILITY

Cesàro means | a.e. convergence | 42A24 | Zalcwasser’s problem | Numerical Analysis | Analysis | Subsequences of partial sums | Mathematics | Trigonometric Fourier series | MATHEMATICS | Cesaro means | CONVERGENCE | Zalcwasser's problem | SUMMABILITY

Journal Article

The Annals of probability, ISSN 0091-1798, 5/2014, Volume 42, Issue 3, pp. 1121 - 1160

...} is a suitably regular sequence of constants. Furthermore, let S(n)(t), 0≤t ≤1 be the corresponding linearly interpolated partial sum processes...

Brownian motion | Determinism | Zero | Eigenvalues | Partial sums | Coordinate systems | Mathematical vectors | Random variables | Banach space | Covariance matrices | Cluster sets | Functional LIL-type results | Partial sum processes | GENERALIZED LAW | functional LIL-type results | partial sum processes | BANACH-SPACES | LIL BEHAVIOR | STATISTICS & PROBABILITY | ITERATED LOGARITHM | Mathematics - Probability | 60F17 | 60F15

Brownian motion | Determinism | Zero | Eigenvalues | Partial sums | Coordinate systems | Mathematical vectors | Random variables | Banach space | Covariance matrices | Cluster sets | Functional LIL-type results | Partial sum processes | GENERALIZED LAW | functional LIL-type results | partial sum processes | BANACH-SPACES | LIL BEHAVIOR | STATISTICS & PROBABILITY | ITERATED LOGARITHM | Mathematics - Probability | 60F17 | 60F15

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 07/2017, Volume 260, Issue 2, pp. 665 - 679

•A partial preference model based on the weighted sum is presented and studied.•A generic method based on cones computes the preferred points...

Partial preference information | Multiple objective programming | Weighted sum | CRITERIA | POTENTIAL OPTIMALITY | RANKING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DOMINANCE | DECISION-MAKING | LINEAR PARTIAL INFORMATION | COEFFICIENTS | VALUES | PROBABILITIES | Problem solving | Mathematical optimization | Analysis | Algorithms | Computer Science

Partial preference information | Multiple objective programming | Weighted sum | CRITERIA | POTENTIAL OPTIMALITY | RANKING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DOMINANCE | DECISION-MAKING | LINEAR PARTIAL INFORMATION | COEFFICIENTS | VALUES | PROBABILITIES | Problem solving | Mathematical optimization | Analysis | Algorithms | Computer Science

Journal Article

Journal of Integer Sequences, 10/2013, Volume 16, Issue 9

Journal Article

Econometric theory, ISSN 0266-4666, 02/2014, Volume 30, Issue 1, pp. 252 - 284

We establish asymptotic normality of weighted sums of linear processes with general triangular array weights and when the innovations in the linear process are martingale differences...

ARTICLES | Ergodic theory | Brownian motion | Density estimation | Economic models | Covariance | Stationary processes | Partial sums | Regression analysis | Martingales | Estimators | REGRESSION | FRACTIONAL BROWNIAN-MOTION | STATISTICS & PROBABILITY | STOCHASTIC VOLATILITY | AUTOREGRESSIVE TIME-SERIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATIONARY-PROCESSES | MODELS | CONDITIONAL HETEROSKEDASTICITY | UNIT-ROOT | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | INVARIANCE-PRINCIPLE | CENTRAL-LIMIT-THEOREM | Studies | Economic theory | Mathematics

ARTICLES | Ergodic theory | Brownian motion | Density estimation | Economic models | Covariance | Stationary processes | Partial sums | Regression analysis | Martingales | Estimators | REGRESSION | FRACTIONAL BROWNIAN-MOTION | STATISTICS & PROBABILITY | STOCHASTIC VOLATILITY | AUTOREGRESSIVE TIME-SERIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATIONARY-PROCESSES | MODELS | CONDITIONAL HETEROSKEDASTICITY | UNIT-ROOT | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | INVARIANCE-PRINCIPLE | CENTRAL-LIMIT-THEOREM | Studies | Economic theory | Mathematics

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 07/2017, Volume 25, Issue 2, pp. 123 - 133

This article deals with the ratio of normalized Mittag-Leffler function E (z) and its sequence of partial sums (E (z...

33E12 | Analytic functions | partial sums | Mittag-Leffler function | 30A10 | univalent function | Partial sums | Univalent function | MATHEMATICS | FUNCTION E-ALPHA(X) | MATHEMATICS, APPLIED | CONVEX-FUNCTIONS | ANALYTIC-FUNCTIONS

33E12 | Analytic functions | partial sums | Mittag-Leffler function | 30A10 | univalent function | Partial sums | Univalent function | MATHEMATICS | FUNCTION E-ALPHA(X) | MATHEMATICS, APPLIED | CONVEX-FUNCTIONS | ANALYTIC-FUNCTIONS

Journal Article

Mathematical programming, ISSN 1436-4646, 2013, Volume 145, Issue 1-2, pp. 133 - 161

We propose a version of the bundle scheme for convex nondifferentiable optimization suitable for the case of a sum-function where some of the components are “easy...

Bundle methods | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Nondifferentiable optimization | Multicommodity network design | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Lagrangian relaxation | 90C25 | Numerical Analysis | Stabilized partial Dantzig–Wolfe decomposition | Combinatorics | Stabilized partial Dantzig-Wolfe decomposition | COLUMN GENERATION | UNIT COMMITMENT | MATHEMATICS, APPLIED | COST FLOW PROBLEMS | ALGORITHM | DECOMPOSITION | CONVEX-OPTIMIZATION | CUTTING PLANE METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBGRADIENT METHODS | LAGRANGIAN-RELAXATION | CYCLE-BASED NEIGHBORHOODS | Methods | Algorithms | Studies | Lagrange multiplier | Analysis | Mathematical programming | Bundling | Computation | Mathematical analysis | Solvers | Mathematical models | Tuning | Convergence

Bundle methods | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Nondifferentiable optimization | Multicommodity network design | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Lagrangian relaxation | 90C25 | Numerical Analysis | Stabilized partial Dantzig–Wolfe decomposition | Combinatorics | Stabilized partial Dantzig-Wolfe decomposition | COLUMN GENERATION | UNIT COMMITMENT | MATHEMATICS, APPLIED | COST FLOW PROBLEMS | ALGORITHM | DECOMPOSITION | CONVEX-OPTIMIZATION | CUTTING PLANE METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBGRADIENT METHODS | LAGRANGIAN-RELAXATION | CYCLE-BASED NEIGHBORHOODS | Methods | Algorithms | Studies | Lagrange multiplier | Analysis | Mathematical programming | Bundling | Computation | Mathematical analysis | Solvers | Mathematical models | Tuning | Convergence

Journal Article

Stochastics, ISSN 1744-2508, 08/2016, Volume 88, Issue 6, pp. 803 - 812

.... Under some suitable conditions, the author shows that a universal version of almost sure central limit theorem for products of sums of partial sums holds under the assumptions that the mixing...

mixing sequence | logarithmic averages | Almost sure central limit theorem | products of sums of partial sums | Ø-mixing sequence | MATHEMATICS, APPLIED | phi-mixing sequence | STATISTICS & PROBABILITY | EXTENSION | Theorems | Probability theory | Images | Randomness | Random variables | Coefficients | Coefficient of variation | Sums

mixing sequence | logarithmic averages | Almost sure central limit theorem | products of sums of partial sums | Ø-mixing sequence | MATHEMATICS, APPLIED | phi-mixing sequence | STATISTICS & PROBABILITY | EXTENSION | Theorems | Probability theory | Images | Randomness | Random variables | Coefficients | Coefficient of variation | Sums

Journal Article

The Annals of probability, ISSN 0091-1798, 9/2013, Volume 41, Issue 5, pp. 3606 - 3616

Let X₁, X₂,... be a centred sequence of weakly stationary random variables with spectral measure F and partial sums Sn = X₁ + ··· + Xn. We show that var(Sn...

Integers | Sufficient conditions | Statistical variance | Mathematical sequences | Mathematical theorems | Infinity | Spectral energy distribution | Partial sums | Spectral index | Gin | Stationary sequences | Fourier analysis | Tempered distributions | Long-range dependence | STATISTICS & PROBABILITY | tempered distributions | long-range dependence | LIMIT-THEOREMS | Mathematics - Probability | 42A24 | 60G10

Integers | Sufficient conditions | Statistical variance | Mathematical sequences | Mathematical theorems | Infinity | Spectral energy distribution | Partial sums | Spectral index | Gin | Stationary sequences | Fourier analysis | Tempered distributions | Long-range dependence | STATISTICS & PROBABILITY | tempered distributions | long-range dependence | LIMIT-THEOREMS | Mathematics - Probability | 42A24 | 60G10

Journal Article

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