Related papers: Heat content determines planar triangles
The X-ray spectra of late type stars can generally be well fitted by a two temperature component model of the corona. We fnd that the temperature of both components are strong functions of stellar age, although the temperature of the hotter…
It is shown that instantons in the O(3) model at finite temperature consist of fractional charge constituents and the (topological) properties of the latter are discussed.
We prove area bounds for planar convex bodies in terms of their number of interior integral points and their lattice width data. As an application, we obtain sharp area bounds for rational polygons with a fixed number of interior integral…
In this paper we study resolutions which arise as iterated mapping cones.
We show that the d-cube is determined by the spectrum of its distance matrix.
We derive three-body equations valid at finite densities and temperatures. These are based on the cluster mean field approach consistently including proper self energy corrections and the Pauli blocking. As an application we investigate the…
Governing equations for evolution of concentration and temperature in three-component systems were derived in the framework of classical irreversible thermodynamics using Onsager variational principle and were presented for…
This paper deals with the blow-up properties of positive solutions to a system of two heat equations.
We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues…
A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing…
We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the "boundary" (i.e., a given set of vertices). We prove a closed formula of combinatorial flavour, as it is expressed as a sum…
We obtain upper bounds on the heat content and on the torsional rigidity of a complete Riemannian manifold M, assuming a generalized Hardy inequality for the Dirichlet Laplacian on M.
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…
We introduce patterns on a triangular grid generated by paperfolding operations. We show that in case these patterns are defined using a periodic sequence of foldings, they can also be generated using substitution rules and compute…
We prove that triangulations with maximum degree at most 5 satisfy the List-Edge-Coloring Conjecture.
We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice,…
Tiling planar regions with dominoes is a classical problem in which the decision and counting problems are polynomial. We prove a variety of hardness results (both NP- and #P-completeness) for different generalizations of dominoes in three…
This paper gives a proof of the H\"older Inequality by using supersolutions of the Heat Equation. The proof is based on a monotonicity formula for the heat equation presented in Tobias Colding's lectures at MIT.
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…
The main result of this paper, is the complete parametric description of the family of triangles which have integer sidelengths and with one angle being sixty degrees.