Related papers: Simple derivations in two variables

We prove the following: there is a primitive recursive function f_-^*(-,-), in the three variables, such that: for every natural numbers t,n>0, and c, for any natural number k>=f^*_t(n,c) the following holds. Assume L is an alphabet with…

In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) -->…

Let $X$ be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) $f$. Integral expressions for the c.f.\ of the r.v.'s $\max(0,X)$ in terms of $f$ are given, as well as other related results. Applications…

We defined (n+1)-ary derivations of $n$-ary algebras. We described (n+1)-derivations of simple and semisimple finite-dimensional Filippov algebras over algebraically closed field zero characteristic. We constructed new examples of…

Given an algebraic difference equation of the form \[\sigma^n(y)=f\big(y, \sigma(y),\dots,\sigma^{n-1}(y)\big)\] where $f$ is a rational function over a field $k$ of characteristic zero on which $\sigma$ acts trivially, it is shown that if…

Let W be a finite dimensional representation of a linearly reductive group G over a field k. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under G of the symmetric…

We study $h$-vectors of simplicial complexes which satisfy Serre's condition ($S_r$). We say that a simplicial complex $\Delta$ satisfies Serre's condition ($S_r$) if $\tilde H_i(\lk_\Delta(F);K)=0$ for all faces $F \in \Delta$ and for all…

Motivated by the Shapiro Shapiro conjecture, we consider the following: given a field $k$, under what conditions must a rational function with only $k$-rational ramification points be equivalent (after post-composition with a fractional…

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic…

A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.

Let $N_m = x^m + y^m$ be the $m$-th Newton polynomial in two variables, for $m \geq 1$. Dvornicich and Zannier proved that in characteristic zero three Newton polynomials $N_a, N_b, N_c$ are always sufficient to generate the symmetric field…

A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…

For a given testing problem, let $U_1,...,U_n$ be individually valid and conditionally on the data i.i.d.\ P-variables (often called P-values). For example, the data could come in groups, and each $U_i$ could be based on subsampling just…

We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…

This paper is a basis of a part of my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a discussion of…

Consider a field $k$ of characteristic $0$, not necessarily algebraically closed, and a fixed algebraic curve $f=0$ defined by a tame polynomial $f\in k[x,y]$ with only quasi-homogeneous singularities. We prove that the space of holomorphic…

We examine three probabilistic formulations of the sentence a and b are totally unrelated with respect to a given set of variables U. First, two variables a and b are totally independent if they are independent given any value of any subset…