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Stable Sequential Pontryagin Maximum Principle in Optimal Control Problems with Phase Restrictions
In this paper, we obtain optimality conditions in an optimal control problem with pointwise phase constraints of the equality and inequality types...
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Upper bounds for eigenvalues of Cauchy-Hankel tensors
We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors. It is proved that an m -order infinite dimensional...
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Identification of a Time Dependent Source Function in a Parabolic Inverse Problem Via Finite Element Approach
In the present paper, we study one-dimensional inverse source problem of identifying a time-dependent source function from the over-specification...
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The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation
In this article, we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation. This problem...
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Two Regularization Methods for Identifying the Source Term Problem on the Time-Fractional Diffusion Equation with a Hyper-Bessel Operator
In this paper, we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator. First,...
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On Fractional Asymptotical Regularization of Linear Ill-Posed Problems in Hilbert Spaces
In this paper, we study a fractional-order variant of the asymptotical regularization method, called Fractional Asymptotical Regularization (FAR) ,...
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The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain
In this paper, we consider an inverse problem for determining the initial value of heat equation with inhomogeneous source on a columnar symmetric...
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Truncated spectral regularization for an ill-posed non-linear parabolic problem
It is known that the nonlinear nonhomogeneous backward Cauchy problem u t ( t ) + Au ( t ) = f ( t, u ( t )), 0 ⩽ t < τ with u ( τ ) = φ , where A is a densely...
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Fourier Multipliers and Dirac Operators
We use Fourier multipliers of the Dirac operator and Cauchy transform to obtain composition theorems and integral representations. In particular we...
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The Simplified Tikhonov Regularization Method for Solving a Riesz–Feller Space-Fractional Backward Diffusion Problem
In this paper, we consider a backward diffusion problem for a space-fractional diffusion equation. Such a problem is obtained from the classical...
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An a posteriori Fourier regularization method for identifying the unknown source of the space-fractional diffusion equation
In this paper, we identify the unknown source which depends only on spatial variable for a fractional diffusion equation using the Fourier method....
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On spectral distribution of kernel matrices related to radial basis functions
This paper focuses on spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional...
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A quasi-boundary value regularization method for identifying an unknown source in the Poisson equation
In this paper, we consider the problem for identifying the unknown source in the Poisson equation in a half unbounded domain. A conditional stability...
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Solving deconvolution type problems by wavelet decomposition methods
The paper considers an inverse problem associated with equations of the form Kf = g , where K is a convolution-type operator. The aim is to find a...
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A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
In this work, we develop a derivative free iterative method for the implementation of Lavrentiev regularization for approximately solving the...
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Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper...
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Expanding the applicability of Lavrentiev regularization methods for ill-posed problems
In this paper, we are concerned with the problem of approximating a solution of an ill-posed problem in a Hilbert space setting using the Lavrentiev...
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Positive eigenvalue-eigenvector of nonlinear positive map**s
We show that an (eventually) strongly increasing and positively homogeneous map** T defined on a Banach space can be turned into an Edelstein...
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Extension problem and fractional operators: semigroups and wave equations
We extend results of Caffarelli–Silvestre and Stinga–Torrea regarding a characterization of fractional powers of differential operators via an...
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Finite Dimensional Realization of a Guass-Newton Method for Ill-Posed Hammerstein Type Operator Equations
Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator...