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N. A. Baykara

Bio: N. A. Baykara is an academic researcher from Marmara University. The author has contributed to research in topics: Taylor series & Remainder. The author has an hindex of 6, co-authored 39 publications receiving 136 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the second part of the trilogy on the probabilistic evolution approach and related to the quantum dynamical systems as the first part is, the spectral investigation of the evolution matrix reveals important issues first and brings the importance of the zero eigenvalues to the surface.
Abstract: This is the second part of the trilogy on the probabilistic evolution approach and related to the quantum dynamical systems as the first part is. In this sense this work extends the content of the first part to the perhaps secondary but very important details. The spectral investigation of the evolution matrix reveals important issues first and brings the importance of the zero eigenvalues to the surface. The asymptotic convergence possibility and difficulties arising from there can be softened by redefining the state vector. Beside the redefinition, the dimensional extension by adding new elements to the state vector may facilitate the utilization of evolution matrix by bringing conicality or at least multinomiality. The space extension may also help us to deal with singular Hamiltonian systems. All these issues are focused on rather phenomenologically. Illustrative or not, no comprehensive implementation is given since the main purpose is just conceptuality.

16 citations

Journal ArticleDOI
TL;DR: In this article, a recently developed inversion method for pentadiagonal matrices is reconsidered in this work, and the mathematical structure of the previously suggested method is fully developed, and certain determinantial relations specific to pentadiagonian matrices are also established.
Abstract: A recently developed inversion method for pentadiagonal matrices is reconsidered in this work. The mathematical structure of the previously suggested method is fully developed. In the process of establishing the mathematical structure, certain determinantial relations specific to pentadiagonal matrices were also established. This led to a rather general necessary and sufficient condition for the method to work. All the so called forward and backward leading principal submatrices need to be non-singular. While this condition sounds restrictive it really is not so. These are in fact the conditions for forward and backward Gauss Eliminations without any pivoting requirement. Additionally, the method is more effective computational complexity wise then recently published competitive methods.

12 citations

Proceedings ArticleDOI
15 Sep 2008
TL;DR: In this paper, a new formulation is developed to approximate the remainder term of the Multivariate Taylor polynomial by means of the recently developed Fluctuation Theorem, which is tested on functions of two variables.
Abstract: Based on the Taylor’s Theorem for functions of several variables, a new formulation is developed here to approximate the remainder term of the Multivariate Taylor polynomial by means of the recently developed Fluctuation Theorem. This new formulation is tested on functions of two variables.

11 citations

Proceedings ArticleDOI
17 Sep 2010
TL;DR: This paper focuses on the weight function optimization in Enhanced Multivariance Product Representation (EMPR) via constancy maximization by tracing the same philosophy as HDMR weight function Optimization.
Abstract: This paper focuses on the weight function optimization in Enhanced Multivariance Product Representation (EMPR) via constancy maximization. This is done by tracing the same philosophy as HDMR weight function optimization.

10 citations

Proceedings ArticleDOI
15 Sep 2008
TL;DR: In this paper, the remainder term of the integral of the Taylor expansion is approximated by the fluctuation method, and a new numerical integration method is proposed to approximate the Taylor extension.
Abstract: A recently developed Fluctuation Method is used in approximating the remainder term of the integral of the Taylor expansion. This provides us with a new numerical integration method.

10 citations


Cited by
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Journal ArticleDOI
TL;DR: The Fuzzy Rule-based Adaptive Coronary Heart Disease Prediction Support Model, which gives content recommendation to coronary heart disease patients, is proposed, which uses a mining technique validated by medical experts to provide recommendations.
Abstract: This paper proposes the Fuzzy Rule-based Adaptive Coronary Heart Disease Prediction Support Model (FbACHD_PSM), which gives content recommendation to coronary heart disease patients. The proposed model uses a mining technique validated by medical experts to provide recommendations. FbACHD_PSM consists of three parts for heart disease risk prediction. First, a fuzzy membership function is constructed using medical guidelines and statistical methods. Then, a decision-tree rule induction technique creates mining-based rules that are subjected to validation by medical experts. As the rules may not be medically suitable, the experts add rules that have been verified and delete inappropriate rules. Thirdly, using fuzzy inference based on Mamdani's method, the model predicts the risk of heart disease. Based on this, final recommendations are provided to patients regarding normal living, nutrition control, exercise, and drugs. To implement our proposed model and evaluate its performance, we use a dataset from a single tertiary hospital.

59 citations

Journal ArticleDOI
TL;DR: Schatzman as discussed by the authors has a poetic turn of phrase, describing her subject as'more like a heavy matron than a gracious ballerina' but firmly grounds this comprehensive introduction in reality.
Abstract: Numerical analysis: a mathematical introduction, by Michelle Schatzman, translated by John Taylor. Pp. 496. £49.95 (hb), £24.95 (pb). 2002. ISBN 0 19 850279 6 (hb), 0 19 850852 2 (pb) (Oxford University Press). Schatzman has a poetic turn of phrase, describing her subject as 'more like a heavy matron than a gracious ballerina' but firmly grounds this comprehensive introduction in reality. In the opening chapter she is especially good at reorienting the reader to understand the effects of machine representations of numbers on calculations. She sets exercises in sections like 'Even the obvious problems are rotten' and 'Even the easy problems are hard' that bring out the fundamental issues. The second chapter continues the theme of re-education, with its 'self-guided visit in the garden of approximations of the continuous by the discrete' including approximation of natural logarithms, construction of the exponential and even matrix exponentials. Understanding that numerical analysis is hard for students, who lack the necessary maturity, Schatzman includes a third introductory chapter covering linear algebra.

56 citations

01 Jan 2014
TL;DR: In this article, the authors present a list of the top 10 most expensive products in the US for different categories: $1.00 [Mår82], $9.95 [Lun], $15.25 [Wol81], $28.25] and $88.00.
Abstract: (e, 2e) [AM83b, TMC84]. (n−) [MOT83]. (N − 1) [Mor89]. + [AM82, BNK86, Bow86, ES81, GT86, GT87a, GM86a, KU80, KS89b, KM89b, LB83, RBL84, SBE87, SS84b, SS87, YKZ89]. 1/Z [PS84]. $104.75 [Pic83b]. 12 [KU80]. 14 [SST84]. $15.00 [Mår80]. 1s [NMK84, Ten88b]. 1s2pJp ′ jJ [ST84]. 1s2s [DS80a]. 1s2s2pjJ [ST84]. 1s2s 2 [ST84]. 1s2s [DS81c]. 2 [BW85, MOT83, MK83, ddF86]. $26.25 [Wol81]. $28.50 [Pic83a]. 2′ [LMG85, SP82a]. 2: 1 [GP83a]. 3 [BW85, ddF86]. 3′ [KG80]. 3d [WS80b]. $49.00 [Sie83a]. 4L [FEKC84]. 4L+ 2 [FEKC84]. 4× 4 [Lin81a]. $59.00 [Gos80]. 5d [CPGP83]. $85.00 [LM81]. $88.00 [Mår82]. $9.95 [Lun82]. < pu|∂/∂v|s > [JL85]. < r−1 12 > [BB81a]. < r−1 1 > [BB81a]. = [Dat82, KU80, PXLC86, PFLB83, WBK86]. + [CEB86, CLM80, CD89a, CC82b, Con87, DF89, DLVÖ84, EY82, ESKG83, GLLOB88, GP82, JŻ85, Kog84, Kun86, LPS83b, NMK84, PC83b, Sch80a,

30 citations

Journal ArticleDOI
TL;DR: A probabilistic framework for describing dynamical systems inspired by quantum dynamical expectation dynamics is described, in which an abstract evolution operator corresponding to the Hamiltonian in quantum dynamics is constructed.
Abstract: In this paper we describe a probabilistic framework for describing dynamical systems. The approach is inspired by quantum dynamical expectation dynamics. Specifically, an abstract evolution operator corresponding to the Hamiltonian in quantum dynamics is constructed. The evolution of this operator defining PDE’s solution is isomorphic to the functional structure of the wave function as long as its initial form permits. This operator enables us to use one of the most important probabilistic concepts, namely expectations. The expectation dynamics are governed by equations which are constructed via commutator algebra. Based on inspiration from quantum dynamics, we have used both the independent variables and the symmetric forms of their derivatives. For construction of the expectation dynamics, the algebraic independent variable operators which multiply their operands by the corresponding independent variable suffice. In our descriptions, we remain at the conceptual level in a self-consistent manner. The phenomenological implications and the tremendous potential of this approach for scientific discovery and advancement is described in the companion to this paper.

23 citations