Related papers: Pseudojump inversion in special r. b. $\Pi^0_1$ cl…

We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and…

Reverse Mathematics is a program in the foundations of mathematics. It provides an elegant classification in which the majority of theorems of ordinary mathematics fall into only five categories, based on the 'Big Five' logical systems.…

Assuming that $0^#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\mathcal A$ such that \[ Sp({\mathcal A}) = \{{\bf x}':{\bf x}\in Sp ({\mathcal A})\}, \] where…

The most common difference that occurs among the consecutive primes less than or equal to $x$ is called a jumping champion. Occasionally there are ties. Therefore there can be more than one jumping champion for a given $x$. In 1999 A.…

For each subchain $X'$ of a chain $X$, let $T_{RE}(X, X')$ denote the semigroup under composition of all full regressive transformations, $\alpha:X\rightarrow X'$ satisfying $x\alpha\leq x$ for all $x\in X$. Necessary and sufficient…

We prove that the Cohesiveness Principle (COH) is $\Pi^1_1$ conservative over $RCA_0 + I\Sigma^0_n$ and over $RCA_0 + B\Sigma^0_n$ for all $n \geq 2$ by recursion-theoretic means. We first characterize COH over $RCA_0 + B\Sigma^0_2$ as a…

The $3k-4$ Theorem is a classical result which asserts that if $A,\,B\subseteq \mathbb Z$ are finite, nonempty subsets with \begin{equation}\label{hyp}|A+B|=|A|+|B|+r\leq |A|+|B|+\min\{|A|,\,|B|\}-3-\delta,\end{equation} where $\delta=1$ if…

We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding…

A cohomological vanishing property is proved for finitely supported ideals in an arbitrary d-dimensional regular local ring. (Such vanishing implies some refined Briancon-Skoda-type results, not otherwise known in mixed characteristic.) It…

When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…

Let $\pi$ be a set of primes such that $|\pi|\geqslant 2$ and $\pi$ differs from the set of all primes. Denote by $r$ the smallest prime which does not belong to $\pi$ and set $m=r$ if $r=2,3$ and $m=r-1$ if $r\geqslant 5$. We study the…

Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the normal bundle of Z in X is convex with a minor assumption, we prove that genus-zero GW-invariants of Y with cohomology insertions from X, are identical to…

Let $M$ be a positive homogeneously presented cancellative monoid ${< L \mid R >}_{mo}$ equipped with the degree map $\deg:M \to \Z_{\ge0}$ defined by assigning to each equivalence class of words the length of the words, and let $P_{M,…

The program Reverse Mathematics in the foundations of mathematics seeks to identify the minimal axioms required to prove theorems of ordinary mathematics. One always assumes the base theory, a logical system embodying computable…

For an oriented graph $D$, the inversion of $X\subseteq V(D)$ in $D$ is the graph obtained by reversing the orientation of all arcs with both ends in $X$. The inversion number $\mathrm{inv}(D)$ is the minimum number of inversions needed to…

We provide a support theorem for the law of the solution to an SDE with jump noise. This theorem applies to general SDEs with jumps and is illustrated by examples of SDEs with quite degenerate jump noises where the theorem leads to an…

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem…

This paper studies the set of $n\times n$ matrices for which all row and column sums equal zero. By representing these matrices in a lower dimensional space, it is shown that this set is closed under addition and multiplication, and…

We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…

Assuming the well-known conjecture that [x,x+x^t] contains a prime for t > 0 and x sufficiently large, we prove: For 0 < r < 1, there exists 0 < s < r < 1, 0 < d < 1, and infinitely many primes q such that if S is a subset of Z/qZ having…