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View article: A study on control command synthesis algorithm for single-channel flying equipment with linear steering vane
A study on control command synthesis algorithm for single-channel flying equipment with linear steering vane Open
This paper presents the algorithm and mathematical foundation for control command synthesis applied to single-channel flying equipment equipped with a linear steering vane. The proposed algorithm is developed based on optimal control princ…
View article: A refined variant of Hartley convolution: Algebraic structures and related issues
A refined variant of Hartley convolution: Algebraic structures and related issues Open
In this work, we propose a novel convolution product associated with the $\mathscr{H}$-transform, denoted by $\underset{\mathscr{H}}{\ast}$, and explore its fundamental properties. Here, the $\mathscr{H}$-transform may be regarded as a ref…
View article: Composition structure of polyconvolution associated with index Kontorovich–Lebedev transform and Fourier integrals
Composition structure of polyconvolution associated with index Kontorovich–Lebedev transform and Fourier integrals Open
Using Kakichev's classical concept and extending Yakubovich-Britvina's approach (\textit{Results. Math.} 55(1-2):175-197, 2009) and (\textit{Integral Transforms Spec. Funct.} 21(4):259--276, 2010) for setting up Kontorovich-Lebedev convolu…
View article: $\mathcal{O}_α$-transformation and its uncertainty principles
$\mathcal{O}_α$-transformation and its uncertainty principles Open
In this paper, we introduce a family of $\mathcal{O}_α$-transformation based on kernels fusion of the fractional Fourier transform (abbreviated as FRFT) with angle $α\notin π\mathbb{Z}$. We point out this is a valid integral transform via …
View article: Chiến lược dài hạn cho chuyển đổi số: từ lý thuyết đến thực tiễn toàn cầu
Chiến lược dài hạn cho chuyển đổi số: từ lý thuyết đến thực tiễn toàn cầu Open
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View article: Analog version of Hausdorff--Young's theorem for quadratic Fourier transforms and boundedness of oscillatory integral operator
Analog version of Hausdorff--Young's theorem for quadratic Fourier transforms and boundedness of oscillatory integral operator Open
The purpose of this paper is twofold. The first aim is based on Riesz--Thorin's interpolation theorem, we prove new Hausdorff--Young type inequalities for the Quadratic Fourier transforms in (Ann. Funct. Anal. 2014;5(1):10--23) and linear …
View article: Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application
Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application Open
Derived from the results in [Giang et al.: \emph{Convolutions for the Fourier transforms with geometric variables and applications}, Math. Nachr. 283(12) (2010), 1758--1770], in this paper, we devoted to studying the boundedness properties…
View article: New polyconvolution product for Fourier‐cosine and Laplace integral operators and their applications
New polyconvolution product for Fourier‐cosine and Laplace integral operators and their applications Open
The goal of this paper is to introduce the notion of polyconvolution for Fourier‐cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated i…
View article: Trigonometric weighted generalized convolution operator associated with Fourier cosine-sine and Kontorovich-Lebedev transformations
Trigonometric weighted generalized convolution operator associated with Fourier cosine-sine and Kontorovich-Lebedev transformations Open
The main objective of this work is to introduce the generalized convolution with trigonometric weighted $γ=\sin y$ involving the Fourier cosine-sine and Kontorovich-Lebedev transforms, and to study its fundamental results. We establish bou…
View article: Boundedness in $L_p$ spaces for the Hartley-Fourier convolutions operator and their applications
Boundedness in $L_p$ spaces for the Hartley-Fourier convolutions operator and their applications Open
The paper deals with $L_p$-boundedness of the Hartley-Fourier convolutions operator and their applied aspects. We establish various new Young-type inequalities and obtain the structure of a normed ring in Banach space when equipping it wit…
View article: Boundedness in $$L_p$$ spaces for the Hartley-Fourier convolutions operator and their applications
Boundedness in $$L_p$$ spaces for the Hartley-Fourier convolutions operator and their applications Open
View article: New polyconvolution product for Fourier-cosine and Laplace integral operators and their applications
New polyconvolution product for Fourier-cosine and Laplace integral operators and their applications Open
The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms is investigated in…
View article: New Polyconvolution Product for Fourier-cosine and Laplace Integral Operators and Their Applications
New Polyconvolution Product for Fourier-cosine and Laplace Integral Operators and Their Applications Open
The goal of this paper is to introduce a new polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of polyconvolution operator and associated integral transforms is investigated in detail. The …
View article: On solvability of Barbashin's type equation and initial value problem via the structure of generalized convolutions
On solvability of Barbashin's type equation and initial value problem via the structure of generalized convolutions Open
The purpose of this article is to study the solvability of Barbashin-type integro-differential equation and initial value problem via the structure of well-known generalized convolutions. We give necessary and sufficient conditions for the…
View article: Some results of Watson, Plancherel type integral transforms related to the Hartley, Fourier convolutions and applications
Some results of Watson, Plancherel type integral transforms related to the Hartley, Fourier convolutions and applications Open
In this work, we study the Watson-type integral transforms for the convolutions related to the Hartley and Fourier transformations. We establish necessary and sufficient conditions for these operators to be unitary in the L 2 (R) space and…
View article: Reconstructing the wave speed and the source
Reconstructing the wave speed and the source Open
We are concerned with the inverse problem of recovering the unknown wave speed and also the source in a multidimensional wave equation. We show that the wave speed coefficient can be reconstructed from the observations of the solution take…
View article: A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms
A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms Open
In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovi…
View article: The reconstruction of a wave equation from one side measurement
The reconstruction of a wave equation from one side measurement Open
View article: The recovery of a parabolic equation from measurements at a single point
The recovery of a parabolic equation from measurements at a single point Open
By measuring the temperature at an arbitrary single point located inside an unknown object or on its boundary, we show how we can uniquely reconstruct all the coefficients appearing in a general parabolic equation which models its cooling.…
View article: Reconstruction of the coefficients of a star graph from observations of its vertices
Reconstruction of the coefficients of a star graph from observations of its vertices Open
Consider a three-edge star graph, made up of unknown Sturm-Liouville operators on each edge. By using the heat propagation through the graph and measuring the heat transfer occurring at its vertices, we show that we can extract enough spec…
View article: A Panorama of Mathematics: Pure and Applied
A Panorama of Mathematics: Pure and Applied Open
A totally positive matrix is a matrix having all its minors positive.The largest amount by which the single entries of such a matrix can be perturbed without losing the property of total positivity is given. Also some completion problems f…
View article: A panorama of mathematics : pure and applied : Conference Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait
A panorama of mathematics : pure and applied : Conference Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait Open
* An inverse problem in magnetohydrodynamics by A. Boumenir* Combinatorial properties of circulant Hadamard matrices by R. Euler, L. H. Gallardo, and O. Rahavandrainy* A new point of view on higher dimensional Kaluza-Klein theories by A. B…