Related papers: Heat content determines planar triangles
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We study a thermodynamically consistent model describing phenomena in a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for…
We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the…
We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on $n-1$ curves divides the determinant based on $n$ curves.…
Coronal heating refers to the physical processes that shape and structure the corona of the Sun and are responsible for its multi-million Kelvin temperatures. These processes are revealed in a number of different observational…
We study the asymptotic behaviour of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions. Assuming the existence of a complete asymptotic series we…
A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic…
We show that the number of unit-area triangles determined by a set $S$ of $n$ points in the plane is $O(n^{20/9})$, improving the earlier bound $O(n^{9/4})$ of Apfelbaum and Sharir [Discrete Comput. Geom., 2010]. We also consider two…
We prove that if G is a triangulation of the torus and \chi(G) \neq 5, then there is a 3-coloring of the edges of G so that the edges bounding every face are assigned three different colors.
We establish a connection between a sharp double-sided Harnack bound for positive solutions of a fractional heat equation and the circular geometry in higher dimensions. The present work extends and generalizes the results obtained in the…
We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time $T$ only at one blow-up point. We also give a sharp description of its blow-up profile. The…
We present a quantitative criterion for the thermal stability of thermonuclear shell sources. We find the thermal stability of shell sources to depend on exactly three factors: they are more stable when they are geometrically thicker, less…
Thomassen conjectured that triangle-free planar graphs have an exponential number of $3$-colorings. We show this conjecture to be equivalent to the following statement: there exists a positive real $\alpha$ such that whenever $G$ is a…
An exact treatment of the Anderson - Hasegawa two - site model, incorporating the presence of superexchange and polarons, is used to compute the heat capacity. The calculated results point to the dominance of the lattice contribution,…
On objects of a triangulated category with a stability condition, we construct a topology.
We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension $D\geq 3.$ Thus, every finite energy solution resolves, continuously in time, into a finite superposition of asymptotically…
Light carries momentum and, upon interaction with material structures, can exert forces on them. Here, we show that a planar structure with asymmetric optical response is spontaneously accelerated when placed in an environment at a…
We illustrate, with a simple example of domain perturbation problem, how Linear Algebra can be applied to determine the behavior of a family of partial differential equations posed in a thin rectangular domain. (In portuguese)
We construct entire solutions of bistable reaction-diffusion equations by mixing finite planar fronts, which form a finite-dimensional manifold. These entire solutions are generalized traveling fronts, that is, transition fronts. We also…
We show that the isomorphism of 3-connected planar graphs can be decided in deterministic log-space. This improves the previously known bound UL$\cap$coUL of Thierauf and Wagner.