Related papers: Energy estimates in sum-product and convexity prob…

When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…

For any $\alpha $ small, we construct infinitely many $C^{1,\alpha}$ very weak solutions to the 2-Hessian equation with prescribed boundary value. The proof relies on the convex integration method and cut-off technique.

In this work, we investigated the existence of compacton-like configuration in the O(3)-sigma model. We consider a minimally coupled O(3)-sigma model with a gauge field governed by a generalized Chern-Simons term. Contrary to that…

Suppose $K/\mathbb{Q}_p$ is finite and $\overline{r}\colon G_K\to \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ is a reducible Galois representation. In this paper we prove that we can use the results by the author in [Ste22] to obtain a…

A celebrated result of Bousquet-M\'elou and Jehanne states that the bivariate power series solutions of so-called combinatorial polynomial equations with one catalytic variable, also known as catalytic equations, are algebraic series. We…

The computation of the ground states of special multi-component Bose-Einstein condensates (BECs) can be formulated as an energy functional minimization problem with spherical constraints. It leads to a nonconvex quartic-quadratic…

New estimates of the potentials of solutions to the compressible Navier-Stokes equations are derived. The result obtained are applied to boundary value problems for the compressible Navier-Stokes equations with the critical adiabatic…

We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and…

We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.

Let $N_d(G,X)$ denote the number of degree $d$ extensions of $\mathbb{Q}$ with Galois closure $G$ and $|\Delta_K|\leq X$. Malle's conjecture predicts an asymptotic of the form $N_d(G,X)\sim CX^{\alpha}(\log X)^\beta$. Previously, Kl\"uners…

Let $V$ be an $n$-dimension real vector space with a direct sum decomposition $V = V_1 \oplus \cdots \oplus V_r$. Let $\mathcal{P} = \{(A_i, B_i) : i \in [m]\}$ be a skew Bollob\'as system of subspaces of $V$ such that each $i\in [m]$, $…

We show how to efficiently solve problems involving a quantitative measure, here called energy, as well as a qualitative acceptance condition, expressed as a B\"uchi or Parity objective, in finite weighted automata and in one-clock weighted…

We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then extend many of these results to incorporate group actions. Our…

Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…

Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one…

We analyze sumsets A+B = {a+b : a in A, b in B} where A,B are sets of integers, A is infinite, and B has positive upper Banach density. For each k, we show that A+B contains at least the expected density of k-term arithmetic progressions…

A family of disjoint pairs of finite sets $\mathcal{P}=\{(A_i,B_i)\mid i\in[m]\}$ is called a Bollob\'as system if $A_i\cap B_j\neq\emptyset$ for every $i\neq j$, and a skew Bollob\'as system if $A_i\cap B_j\neq\emptyset$ for every $i<j$.…

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…

The exact forms of the degenerate Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation (Niven, Physics Letters A, 342(4) (2005) 286), are…

In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…