Results 1 to 10 of about 707 (119)
An information geometrical evaluation of Shannon information metrics on a discrete n-dimensional digital manifold [PDF]
Heliyon, 2023 The definition and nature of information have perplexed scientists due to its dual nature in measurements. The information is discrete and continuous when evaluated on a metric scale, and the Laplace-Beltrami operator and Gauss-Bonnet Theorem can map one
Ahmet Koltuksuz +2 more
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Bootstrap bounds on closed hyperbolic manifolds
Journal of High Energy Physics, 2022 The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds.
James Bonifacio
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Generalized Helical Hypersurface with Space-like Axis in Minkowski 5-Space
Universe, 2023 We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. We compute the first and second fundamental form matrices, Gauss map, and shape operator matrix of the hypersurface.
Erhan Güler
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the $m(x)$-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain.
Mikhail Borsuk, Damian Wiśniewski
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LORETA With Cortical Constraint: Choosing an Adequate Surface Laplacian Operator
Frontiers in Neuroscience, 2018 Low resolution electromagnetic tomography (LORETA) is a well-known method for the solution of the l2-based minimization problem for EEG/MEG source reconstruction. LORETA with a volume-based source space is widely used and much effort has been invested in
Todor Iordanov +7 more
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SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG. [PDF]
PLoS ONE, 2015 Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction.
Uwe Graichen +5 more
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The best approximation of closed operators by bounded operators in Hilbert spaces
Karpatsʹkì Matematičnì Publìkacìï, 2022 We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system.
V.F. Babenko +2 more
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Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2016 We consider the eigenvalue problem for the p(x)-Laplace - Beltrami operator on the unit sphere. We prove an integro - differential inequality related to the smallest positive eigenvalue of this problem.
Damian Wiśniewski, Mariusz Bodzioch
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A formula for complex zonal polynomials of second order
Revista de Matemática: Teoría y Aplicaciones, 2009 A formula for complex zonal polynomials of second order is derived by solving a particular partial differential equation. Keywords: Laplace-Beltrami operator, zonal polynomials, Hermitian matrix, Legendre’s differential equation.
Francisco J. Caro Lopera +2 more
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Nonlinear Choquard equations on hyperbolic space [PDF]
Opuscula Mathematica, 2022 In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the ...
Haiyang He
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