Schneider, Baruch

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Profile URL
https://hdl.handle.net/20.500.14365/7240
Name Variants
Schneider, B
Schneider, B.
Job Title
Email Address
baruch.schneider@ieu.edu.tr
Main Affiliation
02.02. Mathematics
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Former Staff
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ORCID ID
0000-0002-5122-3576
Scopus Author ID
7402401839
Turkish CoHE Profile ID
Google Scholar ID
CFfe5DYAAAAJ
WoS Researcher ID
FUM-4422-2022

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Scholarly Output

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WoS Citation Count

75

Scopus Citation Count

94

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JournalCount
Applıed Mathematıcs And Computatıon5
Medıterranean Journal of Mathematıcs2
Advances in Applıed Clıfford Algebras2
Complex Analysıs And Operator Theory1
Complex Varıables And Ellıptıc Equatıons1
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Now showing 1 - 10 of 20
  • Thumbnail Image
    Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Dirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis
    (Springer Basel Ag, 2016) Bory-Reyes, Juan; Abreu-Blaya, Ricardo; Hernandez-Simon, Luis M.; Schneider, Baruch
    This study aims to study a class of Dirichlet-type problems associated with the two-dimensional Helmholtz equation with complex potential. Orthogonal decompositions of the complex quaternionic-valued Sobolev space as well as the corresponding orthoprojections onto the subspaces of theses decompositions are obtained. Analytic representation formulas for the underlying solutions in terms of hypercomplex integral operators are established.
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    Article
    Citation - Scopus: 7
    Some Properties of a Cauchy-Type Integral for the Moisil-Theodoresco System of Partial Differential Equations
    (2006) Schneider B.
    Our main interest is an analog of a Cauchy-type integral for the theory of the Moisil-Theodoresco system of differential equations in the case of a piecewise-Lyapunov surface of integration. The topics of the paper concern theorems that cover basic properties of this Cauchy-type integral: the Sokhotskii-Plemelj theorem for it as well as a necessary and sufficient condition for the possibility of extending a given Hölder function from such a surface up to a solution of the Moisil-Theodoresco system of partial differential equations in a domain. A formula for the square of a singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between the theory of the Moisil-Theodoresco system of partial differential equations and some versions of quaternionic analysis. © 2006 Springer Science+Business Media, Inc.
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    Article
    Citation - WoS: 5
    Citation - Scopus: 4
    Poincare-Bertrand and Hilbert Formulas for the Cauchy-Cimmino Singular Integrals
    (Springer Basel Ag, 2017) Bory Reyes, Juan; Abreu Blaya, Ricardo; Antonio Perez-de la Rosa, Marco; Schneider, Baruch
    The Cimmino system offers a natural and elegant generalization to four-dimensional case of the Cauchy-Riemann system of first order complex partial differential equations. Recently, it has been proved that many facts from the holomorphic function theory have their extensions onto the Cimmino system theory. In the present work a Poincar,-Bertrand formula related to the Cauchy-Cimmino singular integrals over piecewise Lyapunov surfaces in is derived with recourse to arguments involving quaternionic analysis. Furthermore, this paper obtains some analogues of the Hilbert formulas on the unit 3-sphere and on the 3-dimensional space for the theory of Cimmino system.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Some Properties of the Clifford Cauchy Type Integrals Associated To Helmholtz Equation on a Piecewise Lyapunov Surfaces in R-M
    (Elsevier Science Inc, 2011) Schneider, Baruch
    Our main interest is an analog of a Cauchy type integral associated to Helmholtz equation in the case of a piecewise Lyapunov surfaces in higher dimensions. Here we study some basic properties of this integral. In realizing this study we follow the approach presented in [19-21] within the quaternionic Cauchy integrals theory. (C) 2011 Elsevier Inc. All rights reserved.
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    Article
    Citation - WoS: 2
    On the Asymptotic Solution for the Fourier-Bessel Multiple Scattering Coefficients of an Infinite Grating of Insulating Dielectric Circular Cylinders at Oblique Incidence
    (Elsevier Science Inc, 2008) Kavaklioglu, Oemer; Schneider, Baruch
    The 'asymptotic solution' for the classical electromagnetic problem of the diffraction of obliquely incident plane E-polarized waves by an infinite array of infinitely long insulating dielectric circular cylinders is investigated. Exploiting the elementary function representations of 'Schlomilch series', which was originally developed by Twersky [ V. Twersky, Elementary function representations of Schlomilch series. Arch. Ration. Mech. Anal. 8 ( 1961) 323 - 332.], we have obtained a 'new' set of equations describing the behavior of the 'Fourier-Bessel multiple scattering coefficients' of an infinite grating of circular dielectric cylinders for vertically polarized obliquely incident plane electromagnetic waves when the grating spacing 'd' is small compare to a wavelength. In addition, we have achieved to acquire the 'asymptotic solution for the multiple scattering coefficients of the infinite grating at oblique incidence' as a function of the ratio of the cylinder radius 'a' to grating spacing. (c) 2007 Elsevier Inc. All rights reserved.
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    Article
    Citation - WoS: 4
    Citation - Scopus: 1
    On the 2d Quaternionic Metaharmonic Layer Potentials
    (Springer Basel Ag, 2017) Bory Reyes, J.; Abreu Blaya, R.; Perez de la Rosa, M. A.; Schneider, B.
    This paper aims to study several boundary value properties, to derive a Poincare-Bertrand formula and to solve some Dirichlet-type problems for the 2D quaternionic metaharmonic layer potentials.
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    Conference Object
    Citation - WoS: 10
    Citation - Scopus: 10
    A Quaternionic Treatment of Inhomogeneous Cauchy-Riemann Type Systems in Some Traditional Theories
    (Springer Basel Ag, 2017) Bory Reyes, J.; Abreu Blaya, R.; Perez-de la Rosa, M. A.; Schneider, B.
    In this paper we provide a necessary and sufficient condition for the solvability of inhomogeneous Cauchy-Riemann type systems where the datum consists of continuous C-valued functions and we describe its general solution by embedding the system in an appropriate quaternionic setting.
  • Thumbnail Image
    Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Singular Integrals of the Time Harmonic Maxwell Equations Theory on a Piecewise Liapunov Surface
    (Tsing Hua Univ, Dept Mathematics, 2007) Schneider, Baruch
    We give a short proof of a formula of Poincare-Bertrand in the setting of theory of time-harmonic electromagnetic fields on a piece-wise Liapunov surface, as well as for some versions of quaternionic analysis.
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    Article
    Citation - Scopus: 25
    Is Cancer a Pure Growth Curve or Does It Follow a Kinetics of Dynamical Structural Transformation?
    (BioMed Central Ltd., 2017) González M.M.; Joa J.A.G.; Cabrales L.E.B.; Pupo A.E.B.; Schneider B.; Kondakçı, Süleyman; Ciria H.M.C.
    Background: Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. Methods: The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×105) are inoculated to 28 BALB/c male mice. Results: Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. Conclusions: The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK. © 2017 The Author(s).
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    Article
    Citation - Scopus: 2
    On the Hilbert Formulas on the Unit Circle for Alpha-Hyperholomorphic Function Theory
    (Taylor & Francis Ltd, 2018) Bory Reyes, J.; Abreu Blaya, R.; Perez-de la Rosa, M. A.; Schneider, B.
    We obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory in R-2 for a being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit discwith the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable.