Related papers: A note on limit shapes of minimal difference parti…
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…
We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a partial result towards the conjecture that not every…
Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X, in relation with the definability of types.
We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and…
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
We introduce the notion of a relative log scheme with boundary: a morphism of log schemes together with a (log schematically) dense open immersion of its source into a third log scheme. The sheaf of relative log differentials naturally…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
We present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions, extending previous constructions to the non-uniform case. We study in particular the dependence of quadratic…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
In this paper we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape dependent…
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.
In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well…