Related papers: Heat content determines planar triangles

A planar hypermap with a boundary is defined as a planar map with a boundary, endowed with a proper bicoloring of the inner faces. The boundary is said alternating if the colors of the incident inner faces alternate along its contour. In…

We provide conditions on the coefficients of a ternary cubic form that determine its Waring rank.

In this article, we study certain type of boundary behaviour of positive solutions of the heat equation on the upper half-space of $\R^{n+1}$. We prove that the existence of the parabolic limit of a positive solution of the heat equation at…

We exhibit infinite families of planar graphs with real chromatic roots arbitrarily close to 4, thus resolving a long-standing conjecture in the affirmative.

We consider a model of heat conduction networks consisting of oscillators in contact with heat baths at different temperatures. Our aim is to generalize the results concerning the existence and uniqueness of the stationnary state already…

We prove a result on the existence of linear forms of a given Diophantine type.

We show that the qualitative behavior of the nuclear caloric curve can be inferred from the energy dependence of the isoscaling parameters. Since there are strong indications that the latter are not distorted by the secondary decay of…

Understanding the intricate relation between illumination and temperature in metallic nano-particles is crucial for elucidating the role of illumination in various physical processes which rely on plasmonic enhancement but are also…

Due to the importance of collisions and impacts in early phases of the evolution of the planetary system, it is interesting to estimate the heating of a solid target due to an impact in it . A physically simple calculation of the…

We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a…

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…

The conditions determining that two triangles are congruent play a basic role in planimetry. By comparing not congruent triangles with respect to given sets of corresponding elements it is important to discover if they have any common…

Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ…

We prove that any triangulation of a surface different from the sphere and the projective plane admits an orientation without sinks such that every vertex has outdegree divisible by three. This confirms a conjecture of Bar\'at and Thomassen…

A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.

We revisit the classical problem of granular hopping conduction's temperature dependence, and offer a straightforward and simple explanation on a phenomenon that was widely observed over diverse material systems, but which has remained a…

It is shown every nonnegative solution of the heat equation in a bounded cylindrical domain has an integral representation in terms of a trace triple consisting of a bottom trace, a corner trace and a lateral trace on its parabolic…

We prove that a certain pair of isospectral planar sets are distinguished by torsional rigidity.

In this paper we present a new approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR geometry.

We construct a solution for a class of strongly perturbed semilinear heat equations which blows up in finite time with a prescribed blow-up profile. The construction relies on the reduction of the problem to a finite dimensional one and the…