相关论文: Consequences of the Continuity of the Monic Intege…

We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…

We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed density function $f(x) = |x|$. Under these conditions, we find that isoperimetric $3$-bubble and $4$-bubble results satisfy a regular structure. As our regions increase…

The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals $[-1,\alpha]\cup[\beta,1]$ has been given explicitly with the help of Jacobi's elliptic and theta functions already by Achieser in 1930.…

On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function $\phi$ such that $\phi^*=\phi_*$ on the closure of the domain. For $\phi$ satisfying certain additional criteria limiting its…

We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every…

We study the following question: Given an open set $\Omega$, symmetric about 0, and a continuous, integrable, positive definite function $f$, supported in $\Omega$ and with $f(0)=1$, how large can $\int f$ be? This problem has been studied…

It is well known that many random graphs with infinite variance degrees are ultrasmall. More precisely, for configuration models and preferential attachment models where the proportion of vertices of degree at least $k$ is approximately…

We revise and extend the algorithm provided in [1] to compute the finite Connes' distance between normal states. The original formula in [1] contains an error and actually only provides a lower bound. The correct expression, which we…

In this paper, we study the regularity of optimal mappings in Monge's mass transfer problem. Using the approximation to Monge's cost function given by the Euclidean distance c(x,y)=dist(x,y) through the costs…

On a metric space equipped with a doubling measure supporting a Poincar\'e inequality, we show that given a BV function, discarding a set of small $1$-capacity makes the function continuous outside its jump set and ``one-sidedly" continuous…

Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.

We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the…

Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a $\mathbb{Z}^k$-action on a compact metric space $X$, we study the following three problems…

In this note we give a presentation for the monoid $IO_n$ of all order-preserving transformations of a $n$-chain whose ranges are intervals. We also consider the submonoid $IO_n^-$ of $IO_n$ consisting of order-decreasing transformations,…

We investigate arithmetic properties of the sequence b(n) = B_MN(n) mod M obtained from the base-M to base-N shift map B_MN.We prove that b(n) is ultimately periodic exactly when every prime divisor of M also divides N; in that case we…

Khinchin proved that the arithmetic mean of continued fraction digits of Lebesgue almost every irrational number in $(0,1)$ diverges to infinity. Hence, none of the classical limit theorems such as the weak and strong laws of large numbers…

Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,...,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. For every monomial ideal $I\subset S$, We provide a recursive formula to determine a lower bound for the…

We study the regularity of minimizers to the functional \[ J(w)=\int_{\Omega} a^{ij}w_iw_j + Q\chi_{\{w>0\}}, \] over a bounded domain $\Omega$ and among the class of nonnegative functions in $W^{1,2}(\Omega)$ with prescribed boundary data.…

In [7], Kwapie\'{n} announced that every mean zero function $f\in L_\infty[0,1]$ can be written as a coboundary $f = g\circ T -g$ for some $g\in L_\infty[0,1]$ and some measure preserving transformation $T$ of $[0,1]$. Whereas the original…

We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Amp\`ere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we…