Related papers: A Nonlocal Functional Promoting Low-Discrepancy Po…

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let…

We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…

There is a well-known mapping between energy normal (super-) diffusion and normal (anomalous) heat conduction in one-dimensional (1D) nonlinear lattices. The momentum conserving nonlinear lattices exhibit energy super-diffusion behavior…

Let $\psi : \mathbb{R}_{>0}\rightarrow \mathbb{R}_{>0}$ be a non-increasing function. Denote by $W(\psi)$ the set of $\psi$-well-approximable points and by $E(\psi)$ the set of points $x\in[0,1]$ such that for any $0 < \epsilon < 1$ there…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

By exactly analyzing the spin-1/2 Luttinger liquid (LL) and numerically solving a model of a mobile impurity electron in the LL, we obtain the one-electron spectral function $A(p,\omega)$ in a one-dimensional (1D) metal in an entire range…

We study one-loop effective action of hypermultiplet theory coupled to external N=2 vector multiplet. We formulate this theory in N=1 superspace and develop a general approach to constructing derivative expansion of the effective action…

We study the periodic $L_2$-discrepancy of point sets in the $d$-dimensional torus. This discrepancy is intimately connected with the root-mean-square $L_2$-discrepancy of shifted point sets, with the notion of diaphony, and with the worst…

N-point energy correlators are powerful observables for studying strong interactions, with applications ranging from extractions of the strong coupling $\alpha_s$ to probes of jet modification in heavy-ion collisions and determination of…

We consider the asymptotics of sums of the form $$ \frac1{F_n^\sigma} \sum_{m = 1}^{F_n-1} \frac{f(m/F_n)}{\left|{\sin(\pi m/F_n)}\right|^\sigma} \frac{f(F_{n-1}m/F_n)}{\left|{\sin(\pi F_{n-1}m/F_n)}\right|^\sigma} $$ where $(F_n)_{n \in…

Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system.…

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities…

We prove that for any fixed d the generating function of the projection of the set of integer points in a rational d-dimensional polytope can be computed in polynomial time. As a corollary, we deduce that various interesting sets of lattice…

We consider a homogeneous space X=(X,d,m) of dimension $\nu \geq 1$ and a local regular Dirichlet form in L^{2}(X,m). We prove that if a Poincar\'{e} inequality holds on every pseudo-ball B(x,R) of X, with local characteristic constant…

We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…

The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the…

We compute rigorously the scaling limit of multi-point energy correlations in the critical Ising model on a torus. For the one-point function, averaged between horizontal and vertical edges of the square lattice, this result has been known…

For every $P \in \mathbb{Z}[x_1^{\pm 1}, \ldots, x_d^{\pm 1}] \setminus \{0\}$, and every $\varepsilon > 0$, we prove that there are a computable function $M = M(d,\varepsilon,\deg{P},h(P)) < \infty$ and a finite union $Z =…

Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…

Let $\mathsf{N}_{\rm d}\left[X\right]=\frac{1}{2\pi {\rm e}}{\rm e}^{2\mathsf{H}\left[X\right]}$ denote the entropy power of the discrete random variable $X$ where $\mathsf{H}\left[X\right]$ denotes the discrete entropy of $X$. In this…