The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Metin Demiralp - One of the best experts on this subject based on the ideXlab platform.
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weighted tridiagonal matrix enhanced multivariance products representation wtmempr for decomposition of multiway arrays applications on certain chemical system data sets
Journal of Mathematical Chemistry, 2017Co-Authors: Evrim Korkmaz Ozay, Metin DemiralpAbstract:This work focuses on the utilization of a very recently developed decomposition method, weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the Remainder Term of each step therein has been expanded into EMPR from step to step until no Remainder Term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a tridiagonal matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.
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separate node ascending derivatives expansion snade for univariate functions conceptuality and formulation
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014), 2015Co-Authors: Metin DemiralpAbstract:This work somehow focuses on the construction of a new Taylor expansion involving denumerable infinitely many nodes. It is a combined utilization of derivative integration formula for a univariate function with the expansions at different nodal points. This paper presents the conceptual sides of the expansion and gives the explicit formulation which involves multiparameter polynomials and again a multiparameter Remainder Term. Certain implicit and explicit recursions amongst the polynomials, a bound for the Remainder Term and the convergence of the scheme are presented in the second companion SNADE paper of this proceedings while the third companion SNADE paper focuses on the univariate integration. Node optimization via partial fluctuation suppression is given in the fourth SNADE paper.
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exponentially supported polynomial basis set using fluctuation free integration in the taylor expansion Remainder Term evaluation
INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009: (ICCMSE 2009), 2012Co-Authors: Meseret Tuba Gulpinar, Caner Gulpinar, Metin DemiralpAbstract:This work concerns with the Taylor expansion Remainder Term evaluation. The integral defining the Remainder is standardized in interval first, by using an appropriate affine transformation. Then it is approximated by the utilization of the fluctuation free integration which was developed quite recently. This method approximates the matrix representation of the function to be integrated in Terms of the matrix representation of the independent variable. The approximation quality depends on a lot of issues like curvature, smoothness, singularities, and the basis function used in the representation. This work investigates the basis functions containing a common factor of exponential function times an appropriate power of the independent variable. The purpose is to investigate the role of the decaying nature existing in the basis functions on the approximation quality.
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multivariable function approximation by using fluctuationlessness approximation applied on a weighted taylor expansion with Remainder Term
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory, 2011Co-Authors: Ercan Gurvit, N A Baykara, Metin DemiralpAbstract:Based on the Taylor's Theorem for functions of several variables, a newly developed formulation is applied to approximate the Remainder Term of the multivariate and weighted Taylor polynomial by means of the recently developed Fluctuation Theorem. This new formulation is meant to be used for highly oscillating and/or non-analytic functions of many variables which in fact depresses the use of the Fluctuationlessness approximation.
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taylor formula with Remainder Term evaluated under a weight factor at fluctuationlessness limit
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics, 2011Co-Authors: Ercan Gurvit, N A Baykara, Metin DemiralpAbstract:Taylor expansion of a weighted function is taken into consideration. Fluctuationlessness theorem is applied to the Remainder Term in integral form and finally an expression which provides an approximation method to a family of non‐analytic functions is obtained.
Allen L Roginsky - One of the best experts on this subject based on the ideXlab platform.
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a central limit theorem by Remainder Term for renewal processes
Advances in Applied Probability, 1992Co-Authors: Allen L RoginskyAbstract:Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a Remainder Term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).
N A Baykara - One of the best experts on this subject based on the ideXlab platform.
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Fluctuationlessness approximation and its applications on the Remainder Term of Taylor expansion: From scratch to present status
Journal | MESA, 2018Co-Authors: Ercan G¨urvit, N A BaykaraAbstract:The general expression of the Fluctuationlessness Theorem states that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independant variable's matrix representation over the same subspace via the same basis set, under that univariate function, when the fluctuation Terms are ignored. Just by using this basic idea, function approximation or numerical quadratures can be constructed. Furthermore this principle applied on the Remainder Term of a Taylor expansion a highly versatile approximation can be obtained. This review article is just about this approximation aspect of the Fluctuationlessness Theorem.
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Univariate approximate integration via nested Taylor multivariate function decomposition
2014Co-Authors: Ercan Gurvit, N A BaykaraAbstract:This work is based on the idea of nesting one or more Taylor decompositions in the Remainder Term of a Taylor decomposition of a function. This provides us with a better approximation quality to the original function. In addition to this basic idea each side of the Taylor decomposition is integrated and the limits of integrations are arranged in such a way to obtain a universal [0;1] interval without losing from the generality. Thus a univariate approximate integration technique is formed at the cost of getting multivariance in the Remainder Term. Moreover the Remainder Term expressed as an integral permits us to apply Fluctuationlessness theorem to it and obtain better results.
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multivariable function approximation by using fluctuationlessness approximation applied on a weighted taylor expansion with Remainder Term
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory, 2011Co-Authors: Ercan Gurvit, N A Baykara, Metin DemiralpAbstract:Based on the Taylor's Theorem for functions of several variables, a newly developed formulation is applied to approximate the Remainder Term of the multivariate and weighted Taylor polynomial by means of the recently developed Fluctuation Theorem. This new formulation is meant to be used for highly oscillating and/or non-analytic functions of many variables which in fact depresses the use of the Fluctuationlessness approximation.
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taylor formula with Remainder Term evaluated under a weight factor at fluctuationlessness limit
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics, 2011Co-Authors: Ercan Gurvit, N A Baykara, Metin DemiralpAbstract:Taylor expansion of a weighted function is taken into consideration. Fluctuationlessness theorem is applied to the Remainder Term in integral form and finally an expression which provides an approximation method to a family of non‐analytic functions is obtained.
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the fluctuationlessness approach to the numerical integration of functions with a single variable by integrating taylor expansion with explicit Remainder Term
Journal of Mathematical Chemistry, 2011Co-Authors: N A Baykara, Ercan Gurvit, Metin DemiralpAbstract:In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit Remainder Term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration method. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the Remainder Term and errors are analyzed.
Futoshi Takahashi - One of the best experts on this subject based on the ideXlab platform.
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sharp hardy leray inequality for curl free fields with a Remainder Term
Journal of Functional Analysis, 2021Co-Authors: Naoki Hamamoto, Futoshi TakahashiAbstract:Abstract In this paper, we give a new and a simpler approach to the result in [8] concerning the best constant of Hardy-Leray inequality for curl-free fields. As a by-product, we obtain an improved inequality with a Remainder Term. The non-attainability of the best constant is an easy consequence of the new inequality. The proof is based on a decomposition of curl-free fields into radial and spherical parts.
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AN ISOPERIMETRIC INEQUALITY WITH Remainder Term
Communications in Contemporary Mathematics, 2006Co-Authors: Futoshi TakahashiAbstract:We prove a version of the isoperimetric inequality for mappings with Remainder Term. Let S = (32π)1/3 and Q(u) = ∫R2 u · ux1 ∧ ux2dx for a mapping u : R2 → R3 in a function space $\mathcal{W}$ defined below. Let $\mathcal{M}$ be a set of functions in $\mathcal{W}$ for which we have equality in the classical isoperimetric inequality S|Q(u)|2/3 ≤ ∫R2 |∇u|2dx. We show that for some positive constant C > 0, \[ \int_{{\bf R}^{\bf 2}} |\nabla u|^2 dx - S |Q(u)|^{2/3} \ge C d(u, \mathcal{M})^2 \] holds for any $u \in \mathcal{W}$. Here, $d(u, \mathcal{M})$ denotes the distance of u from $\mathcal{M}$ in $\mathcal{W}$.
Vladimir Shevelev - One of the best experts on this subject based on the ideXlab platform.
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exact exponent in the Remainder Term of gelfond s digit theorem in the binary case
Acta Arithmetica, 2009Co-Authors: Vladimir ShevelevAbstract:We give a simple formula for the exact exponent in the Remainder Term of Gelfond's digit theorem in the binary case.
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exact exponent of Remainder Term of gelfond s digit theorem in binary case
arXiv: Number Theory, 2008Co-Authors: Vladimir ShevelevAbstract:We give a simple formula for the exact exponent in the Remainder Term of Gelfond's digit theorem in the binary case.
