Results 81 to 90 of about 953 (217)

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 (Cesàro-smoothed) spectral densities associated with the corresponding nonanalytic function of the spectral parameter, exhibit a certain nonlocal ...
S. A. Fulling, E. V. Gorbar, C. T. Romero   +2 more
doaj  

Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In 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
doaj   +1 more source

Autonomous Navigation of Pollen‐Inspired Magnetic Microrobots for Biomedical Applications

Advanced Robotics Research, EarlyView.
A sunflower pollen‐inspired magnetic microrobot enables controlled rolling navigation in vessel‐like environments. Its open geometry reduces hydrodynamic drag, while vision‐based closed‐loop control, shortest‐path planning, and reinforcement learning support target‐reaching and maze navigation with microrobot‐scale accuracy, highlighting a route toward
Ali Anil Demircali, Abdurrahim Yilmaz, Meysam Keshavarz, Jinshi Zhao, Ara Darzi, Eric Yeatman, Burak Temelkuran   +6 more
wiley   +1 more source

Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications

Mathematics
In 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
doaj   +1 more source

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
doaj   +1 more source

A Whole‐Head Finite Element Model for Electrical Neuromodulation via Visual Brain‐Machine Interfaces

Advanced Science, EarlyView.
A multimodal, personalized head model is presented that integrates the entire visual pathway with surrounding tissues to simulate electrical stimulation of the optic nerve. In vivo validation in humans and goats, plus systematic component‐elimination analysis, demonstrates the high accuracy of the comprehensive model.
Shengjian Lu, Tonghe Yang, Yuan Geng, Huan Wu, Yangrui Huang, Te Zheng, Haodi Chen, Shurui Huang, Yi Cao, Jian Yang, Wentao Yan, Yikui Zhang, Wencan Wu   +12 more
wiley   +1 more source

The heat kernel in Riemann normal coordinates and multiloop Feynman graphs in curved spacetime

Journal of High Energy Physics
We 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
doaj   +1 more source

Convergence of Approximate Solutions for Transport-diffusion Equation in the Half-space with Neumann Condition

Известия Иркутского государственного университета: Серия "Математика"
In this paper, we examine the question about the approximation of the solution to a transport-diffusion equation in a half-space with the homogenous Neumann condition.
R. Gherdaoui, S. Selvaduray, H. Fujita Yashima   +2 more
doaj   +1 more source

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.
openaire   +2 more sources

Generalized Heat Kernel Signatures. [PDF]

J. WSCG, 2011
In this work we propose a generalization of the Heat Kernel Signature (HKS). The HKS is a point signature derived from the heat kernel of the Laplace-Beltrami operator of a surface. In the theory of exterior calculus on a Riemannian manifold, the Laplace-Beltrami operator of a surface is a special case of the Hodge Laplacian which acts on r-forms, i. e.
Zobel, Valentin, Reininghaus, Jan, Hotz, Ingrid   +2 more
openaire   +1 more source