The constraint satisfaction problem (CSP) of a first-order theory T is the computational deciding whether given conjunction atomic formulas satisfiable in some model T. We study complexity CSP$(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. prove that if temporal structures, i.e., structures all relations have definition $(Q;<)$, then P or NP-compl...

in proposition 2.6 in (g‎. ‎gruenhage‎, ‎a‎. ‎lutzer‎, ‎baire and volterra spaces‎, ‎textit{proc‎. ‎amer‎. ‎math‎. ‎soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $d$ is $g_delta$ in $x$ was overlooked‎. ‎so we‎ ‎proved some conditions by which a baire space is equivalent to a‎ ‎volterra space‎. ‎in this note we show that if $x$ is a‎ ‎monotonically normal $t_1$...

We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set $$s_1, \ldots , s_n \in {\mathbb {R}}^p$$ with corresponding responses $$t_1,\ldots ,t_n {R}}^q$$ fitting k-layer network $$\nu _\theta : {R}}^p \rightarrow involves estimation of weights $$\theta {R}}^m$$ via an ERM: $$\begin{aligned} \inf _{\theta {R}}^m} \ \sum _{i=...

We prove that given a measure preserving system \begin{document}$ (X,\mathcal{B},\mu,T_1,\dots, T_d) $\end{document} with commuting, ergodic transformations id="M2">\begin{document}$ T_i such id="M3">\begin{document}$ T_iT_j^{-1} are for all id="M4">\begin{document}$ i \neq j $\end{document}</i...

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments displacement, with exponents that do not depend linearly on order moment. The concerning small-order are dominated random motion, while higher-order grow faster trajectories, such as ballistic excursions or "light fronts". Often a situation two linear dependencies their order. Here, we introduce simple exa...

Let \(Cb_n\) be the group of basis conjugating automorphisms a free \(\mathbb {F}_n\), and \(C_n\) {F}_n\). Valerij G. Bardakov has constructed representations \(Cb_n\), in groups \(GL_n(\mathbb {Z}[{t_1}^{\pm 1}, \ldots ,{t_n}^{\pm 1}])\) {Z}[{t}^{\pm respectively, where \(t_1, , t_n, t\) are indeterminate variables. We show that these reducible we determine irreducible components {C})\), whic...

Introduction. Let r be a bounded linear operator on a Banach space B and let t_1 exist. Consider a closed subspace C of B which is invariant under t, i.e. rCQC. The restriction of r to C is an operator T on the Banach space C. Suppose now that t^CÇ^C, so that T has no inverse. The class of operators T arising in this way has rather special properties, which are in general quite different from t...

Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C [—1,1], we construct a new sequence {p„(x;fi)} of orthogonal polynomials on£ = T~1(Eq) (T is a polynomial of degree TV) with an orthogonality measure [i that is related to noIf Eo = [—1,1], then E = T_1([-l,l]) will in general consist of TV intervals. We give explicit formulas rel...

Let $C$ be a smooth curve over an algebraically closed field $\mathbf{k}$, and let $E$ locally free sheaf of rank $r$. We compute, for every $d>0$, the generating function motives $[\mathrm{Quot}_C(E,\boldsymbol{n} )] \in K_0(\mathrm{Var}_{\mathbf{k}})$, varying $\boldsymbol{n} = (0\leq n_1\leq\cdots\leq n_d)$, where $\mathrm{Quot}_C(E,\boldsymbol{n} )$ is nested Quot scheme points, parametrisi...