Volume 14 (2022), Number 2
Mathematical Considerations on Randomized Orthogonal Decomposition Method for Developing Twin Data Models
Author(s): DIANA A. BISTRIAN
Abstract: This paper introduces the approach of Randomized Orthogonal Decomposition (ROD) for producing twin data models in order to overcome the drawbacks of existing reduced order modelling techniques. When compared to Fourier empirical decomposition, ROD provides orthonormal shape modes that maximize their projection on the data space, which is a significant benefit. A shock wave event described by the viscous Burgers equation model is used to illustrate and evaluate the novel method. The new twin data model is thoroughly evaluated using certain criteria of numerical accuracy and computational performance.
DownloadBounds for the Normalized Determinant of Hadamard Product of Two Positive Operators in Hilbert Spaces
Author(s): SILVESTRU SEVER DRAGOMIR
Abstract: For positive invertible operators on a Hilbert space and a fixed unit vector , define the normalized determinant by . In this paper we obtain upper and lower bounds for the determinant of the Hadamard product of two operators under some natural assumptions such as and , where , () are constants.
Download- Convex Functions
Author(s): SERCAN GÜLSU, MAHIR KADAKAL and İMDAT İŞCAN
Abstract: In this paper, the concept of -convex function is given the first time in the literature. Some inequalities of Hadamard’s type for -convex functions are given. Some algebraic properties of -convex functions and special cases are discussed. In addition, we establish some new integral inequalities for -convex functions by using an integral identity.
DownloadOn Physical and Mathematical Wave Fronts in Temperature Waves
Author(s): NASSAR H.S. HAIDAR
Abstract: A rather ”tenuous” existence of mathematical wavefronts in parabolic temperature waves is revealed to accompany a certain hyperbolicity dormant in these waves. The revelation is based on a proof that temperature waves do satisfying a certain new telegrapher’s equation, equivalent to Fourier’s heat conduction equation. This parabolic-equivalent hyperbolic heat equation happens to be similar to the famous Cattaneo-Vernotte non-Fourier heat conduction equation. A basic result of this work is that temperature waves can mathematically support proper wavefronts of infinite span. Physically, however they can support wavefronts only in ”shortened” form. The paper reports also on an associated shrinkage of a triangle for detectable wavefronts of such waves, and on an unknown frequency dependence of the inclination of wavefronts in classical (parabolic) temperature waves. This, added to the strong spatial damping and significant dispersion of these waves, has been forming a pathological obstacle in the experimental verification of their support to conventional wavefronts.
DownloadImpulsive Fractional Differential Equations Involving the Caputo-Hadamard Fractional Derivative in a Banach Space
Author(s): AMOURIA HAMMOU and SAMIRA HAMANI
Abstract: In this paper we establish existence results for a class of initial value problems for impulsive fractional differential equations involving the Caputo-Hadamard fractional derivative of order .
DownloadConvergence Results for Sequential Henstock Stieltjes Integral in Real Valued Space
Author(s): ILUEBE V.O. and MOGBADEMU A.A.
Abstract: In this paper, we prove the convergence theorems for the Sequential Henstock Stieltjes integral of the real valued functions and give an example to show its applicability.
DownloadNew 3D Thermoelastic Influence Functions, Caused by a Unitary Point Heat Source, Applied in a Quarter of Layer
Author(s): VICTOR ȘEREMET and ION CREȚU
Abstract: The aim of this paper consist in the constructing of the main thermoelastic displacements Green’s functions (MTDGFs) for a generalized 3D BVP of uncoupled thermoelasticity for a quarter of layer. To reach this aim are derived structural formulas for MTDGFs, expressed via respective Green’s functions for Poisson’s equation (GFPE) by using harmonic integral representations method (HIRM). These structural formulas are validated by the checking the equations of thermoelasticity with respect to point of response in which the thermoelastic displacements appeared and with respect to point of application the heat source and the nonhomogeneous Poisson’s equation. In addition, they satisfy the homogeneous mechanical boundary conditions for MTDGFs with respect to point application the displacements and to mechanical boundary conditions and temperature Green’s function with respect to point of application the heat source. The thermoelastic volume dilatation (TVD) derived separately from respective integral representations has been equal to the TVD derived by using structural formulas for MTDGFs. The final analytical expressions for MTDGFs obtained on the base of mentioned above structural formulas for sixteen new 3D BVPs of thermoelasticity within quarter of layer contain Bessel functions of the zero-order of the second type. These results are presented graphically.
DownloadSome Sum Formulas and New Identities of Bi-Periodic Jacobsthal and Bi-Periodic Jacobsthal Lucas Sequence
Author(s): SUKRAN UYGUN
Abstract: In this article, it is considered that the new generalizations of the Jacobsthal sequence and Jacobsthal-Lucas sequence. These sequences can arise in the study of continued fractions of quadratic irrationals. Some well-known sequences are special cases of this generalization. Jacobsthal and Jacobsthal-Lucas sequence is a special case with . Some new identities and properties of these generalized sequences are investigated with the aid of its Binet formula, recurrence relation etc. We study specially some different sum formulas for these sequences. Then, by these formulas we get properties for Jacobsthal sequence, Jacobsthal-Lucas sequence.
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