Related papers: A sufficient condition for a Rational Differential…

Let $A$ be a rational function. For any decomposition of $A$ into a composition of rational functions $A=U\circ V$ the rational function $\widetilde A=V\circ U$ is called an elementary transformation of $A$, and rational functions $A$ and…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

Let $D(s)$ be a fractional derivation of order $s$. For a real $p\ne 0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p) D(s) A(p)^{-1}=D(p s)$ for all $s$. The kernel of the operator $A(p)$ is…

We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface…

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a…

Let $F$ be a rational function of one complex variable of degree $m\geq 2$. The function $F$ is called simple if for every $z\in \mathbb C\mathbb P^1$ the preimage $F^{-1}\{z\}$ contains at least $m-1$ points. We show that if $F$ is a…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

Let F be a continuous injective map from an open subset of R^n to R^n. Assume that, for infinitely many k>1, F induces a bijection between the rational points of denominator k in the domain and those in the image (the denominator of…

For any countable group $\Gamma$ satisfying the ``weak Rohlin property'', and for any dynamical property, the set of $\Gamma$-actions with that property is either residual or meager. The class of groups with the weak Rohlin property…

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators.…

In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…

A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…

Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…

A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…

We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f…

The paper investigates the reachability in finite time of pseudo-rational systems of order zero. A bound on the minimal time of reachability is obtained and the reachability property for integrable functions is characterized in terms of a…

In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear operators associated with the system satisfy the Fredholm…

The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…

There is a commutative algebra of differential-difference operators, acting on polynomials on R_2, associated with the reflection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free…