Related papers: A Tangential Markov Inequality on Exponential Curv…

Let $A$ be a pseudo-differential operator with symbol $q(x,\xi)$. In this paper we derive sufficient conditions which ensure the existence of a solution to the $(A,C_c^{\infty}(\mathbb{R}^d))$-martingale problem. If the symbol $q$ depends…

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with $\theta$^Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration $C_t \to D_0+jL$. We show…

We prove that there is an absolute constant $c > 0$ such that every polynomial $P$ of the form $$P(z) = \sum_{j=0}^{n}{a_jz^j}\,, \quad |a_0| = 1\,, \quad |a_j| \leq M\,, \quad a_j \in \Bbb{C}\,, \quad M \geq 1\,,$$ has at most…

We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa…

Consider the trilinear form for twisted convolution on $\mathbb{R}^{2d}$: \begin{equation*} \mathcal{T}_t(\mathbf{f}):=\iint f_1(x)f_2(y)f_3(x+y)e^{it\sigma(x,y)}dxdy,\end{equation*} where $\sigma$ is a symplectic form and $t$ is a…

Let K be a p-adic field, R the valuation ring of K, and P the maximal ideal of R. Let $Y subseteq R^{2}$ be a non-singular closed curve, and Y_{m} its image in R/P^{m} times R/P^{m}, i.e. the reduction modulo P^{m} of Y. We denote by Psi an…

Let $w_{\alpha}(t)=t^{\alpha}\,e^{-t}$, $\alpha>-1$, be the Laguerre weight function, and $|\cdot|_{w_\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\alpha}:=\Big(\int_{0}^{\infty}w_{\alpha}(t)| f(t)|^2\,dt\Big)^{1/2}. $$…

Let $X:=(X_t)_{t\geq 0}$ be an ergodic Markov process on $\real^d$, and $p>0$. We derive upper bounds of the $p$-Wasserstein distance between the invariant measure and the empirical measures of the Markov process $X$. For this we assume,…

We show that every continuous simple curve with $\sigma$-finite length has a tangent at positively many points. We also apply this result to functions with finite lower scaled oscillation; and study the validity of the results in higher…

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…

If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of secant planes of a two-variable smooth function is a plane…

Consider a Markov chain $(X_i)_{i\ge0}$ with invariant measure $\mu$ that admits the representation $X_{i+1}=\Phi(X_i,U_i)$, where $(U_i)_{i\ge0}$ are i.i.d. random variables and $\Phi$ is a measurable map. We introduce a tangent-decoupled…

Below the roughening temperature, the equilibrium crystal shape (ECS) is composed of both facets and a smoothly curved surface. As for the ``normal'' profile (perpendicular to the facet contour), the ECS has the exponent 3/2 which is…

The well known Jensen inequality, holds true for every convex functions. However, we found that it is possible to apply it to some problems related to nonconvex functions for which Jensen's inequality holds true locally. Having considered a…

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…

I investigate on the number t of real eigenvectors of a real symmetric tensor. In particular, given a homogeneous polynomial f of degree d in 3 variables, i prove that t is greater or equal than 2c+1, if d is odd and t is greater or equal…

According to a conjecture of Pach, there are $O(n)$ tangent pairs among any family of $n$ Jordan arcs in which every pair of arcs has precisely one common point and no three arcs share a common point. This conjecture was proved for two…

We consider a large class of piecewise expanding maps T of [0,1] with a neutral fixed point, and their associated Markov chain Y_i whose transition kernel is the Perron-Frobenius operator of T with respect to the absolutely continuous…

For a transitive countably piecewise monotone Markov interval map we consider the question whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous,…

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…