相关论文: A Dirichlet-integral based dual-access collocation…

We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions…

We study the static black hole solutions of generalized two-dimensional dilaton-gravity theories generated by pointlike mass sources, in the hypothesis that the matter is conformally coupled. We also discuss the motion of test particles.…

We present an efficient algorithm for solving local linear systems with a boundary condition using the Green's function of a connected induced subgraph related to the system. We introduce the method of using the Dirichlet heat kernel…

Attention is given to the interface of mathematics and physics, specifically noting that fundamental principles limit the usefulness of otherwise perfectly good mathematical general integral solutions. A new set of multivector solutions to…

We use the recipe of arXiv:1003.2974 to find half-BPS near-horizon geometries in the t$^3$ model of $N=2$, $D=4$ gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but…

The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…

We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…

This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

In the presence of spacetime boundaries, diffeomorphisms in gravitational theories can become physical and acquire non-vanishing Noether charges. These charges obey an algebra which, within the extended phase-space formalism, faithfully…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence…

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

We provide a methodology for decoupling the bulk gravitational field equations of braneworld black holes to suppress the bulk singularities. Thus, we provide a regular braneworld black hole setup. To achieve this, we apply a Minimal…

Dirichlet walls -- timelike boundaries at finite distance from the bulk on which the induced metric is held fixed -- have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often…

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary…

We investigate the Jordan-Brans-Dicke action in the cosmological scenario of FLRW spacetime with zero spatially curvature and with an extra scalar field minimally coupled to gravity as matter source. The field equations are studied in two…

In the paper by means of Fourier transform method and similarity method we solve the Dirichlet problem for a multidimensional equation wich is a generalization of the Tricomi, Gellerstedt and Keldysh equations in the half-space, in which…

In this article we consider resummed expressions for the heat-kernel's trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space.…

We study the Dirichlet problem for functions whose graphs are spacelike hypersurfaces with prescribed curvature in the Minkowski space and we obtain some new interior second order estimates for admissible solutions to the corresponding…