Results 51 to 60 of about 26,365 (167)
Heat kernel for open manifolds
Differential Geometry and its Applications, 2010 In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of which was a relationship between the derivative of heat kernel of different degrees.
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IEEE AccessGraph neural networks have been widely applied in various domains, handling numerous entities with high-dimensional features. Their success largely stems from the powerful information propagation process. Among these networks, diffusion-based approaches,
Zhuo-Chen He
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Heat kernel methods for Lifshitz theories
Journal of High Energy Physics, 2017 We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time.
Andrei O. Barvinsky +5 more
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On the generalised heat kernel
Вычислительные технологии, 2004 The authors investigate the equation \(\frac{\partial}{\partial t}u(x,t)=-c^2(-\triangle)^ku(x,t)\) with the initial conditions \(u(x,0)=f(x)\), where \(x\in{\mathbb R}^n\). The operator \(\triangle^k\) is said to be the Laplace operator iterated \(k\) times and is defined as \(\triangle^k=(\frac{\partial^2}{\partial x_1^2}+ \frac{\partial^2}{\partial ...
Nonlaopon, К., Kananthai, A.
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Generalized heat kernel coefficients [PDF]
EPJ direct, 2001 Following Osipov and Hiller, a generalized heat kernel expansion is considered for the effective action of bosonic operators. In this generalization, the standard heat kernel expansion, which counts inverse powers of a c-number mass parameter, is extended by allowing the mass to be a matrix in flavor space.
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Spectral Riesz-Cesaro means: How the square root function helps us to see around the world
Electronic Journal of Differential Equations, 2000 The heat-kernel expansion for a nonanalytic function of a differential operator, and the integrated (Cesà ro-smoothed) spectral densities associated with the corresponding nonanalytic function of the spectral parameter, exhibit a certain nonlocal ...
S. A. Fulling +2 more
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Advances in Nonlinear AnalysisIn this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications
MathematicsIn this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition.
Xiangyun Xie, Haihui Wang, Yu Liu
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Heat Kernel Embeddings, Differential Geometry and Graph Structure
Axioms, 2015 In this paper, we investigate the heat kernel embedding as a route to graph representation. The heat kernel of the graph encapsulates information concerning the distribution of path lengths and, hence, node affinities on the graph; and is found by ...
Hewayda ElGhawalby, Edwin R. Hancock
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The heat kernel in Riemann normal coordinates and multiloop Feynman graphs in curved spacetime
Journal of High Energy PhysicsWe present a formalism for computing arbitrary scalar multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second order in
Igor Carneiro, Gero von Gersdorff
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