Related papers: Energy integrals and small points for the Arakelov…
We investigate the logarithmic and power-type convexity of the length of the level curves for $a$-harmonic functions on smooth surfaces and related isoperimetric inequalities. In particular, our analysis covers the $p$-harmonic and the…
Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of…
The main result of this paper, Theorem 1.1, gives explicit formulae for the kernels of the ergodic decomposition measures for infinite Pickrell measures on spaces of infinite complex matrices. The kernels are obtained as the scaling limits…
In this paper, we develop an algorithm for computing Coleman--Gross (and hence Nekov\'a\v{r}) $p$-adic heights on hyperelliptic curves over number fields with arbitrary reduction type above $p$. This height is defined as a sum of local…
Critical measures in the complex plane are saddle points for the logarithmic energy with external field. Their local and global structure was described by Martinez-Finkelshtein and Rakhmanov. In this paper we start the development of a…
We conjecture a lower bound for the minimal canonical height of non-torsion rational points on a natural density 1 subset of the sextic twist family of Mordell curves. We then establish a lower bound that yields a partial result towards…
The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We…
We study the asymptotic growth of the number of rational points of bounded height on smooth projective split toric varieties with Picard rank 2 over number fields, with respect to Arakelov height functions associated with big metrized line…
In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal $p$-energy forms. Within this framework, we use the Poincar\'{e} inequality, the cutoff Sobolev inequality, and mild assumptions on…
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
We use linear programming techniques to find points of absolute minimum over the unit sphere $S^{d}$ in $\mathbb R^{d+1}$ of the total potential of a point configuration $\omega_N\subset S^{d}$ which is a spherical $(2m-1)$-design contained…
For some centrally symmetric convex bodies $K\subset \mathbb R^n$, we study the energy integral $$ \sup \int_{K} \int_{K} \|x - y\|_r^{p}\, d\mu(x) d\mu(y), $$ where the supremum runs over all finite signed Borel measures $\mu$ on $K$ of…
We propose a new approximation for the relaxed energy $E$ of the Dirichlet energy and prove that the minimizers of the approximating functionals converge to a minimizer $u$ of the relaxed energy, and that $u$ is partially regular without…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…
In this paper, for a geometrically integral projective scheme, we will give an upper bound of the product of the norms of its non-geometrically integral reductions over an arbitrary number field. For this aim, we take the adelic viewpoint…
Energy Correlators (EC) are the simplest IR finite observables, which connect theories and experiments. In this paper, we provide a systematic algorithm to calculate the canonical differential equations for energy correlators at generic…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
We have developed a new simple method to build the exact analytical expression of the eigenenergy as a function of the potential. The idea of our method is mainly based on the partitioning of the potential curve, solving the Schr\"odinger…
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…