Related papers: Cube spaces and the multiple term return times the…
In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete…
In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…
The Furstenberg recurrence theorem (or equivalently, Szemer\'edi's theorem) can be formulated in the language of von Neumann algebras as follows: given an integer $k \geq 2$, an abelian finite von Neumann algebra $(\M,\tau)$ with an…
We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the…
We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. We show that all finite-dimensional alternative algebras, as well as all algebras obtained from the real numbers via the…
By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the $N$-dimensional superintegrable Kepler-Coulomb model with non-central terms and the…
We investigate the multiplicity of solutions for a Hamiltonian system coupling two systems associated with mixed boundary conditions. Corresponding to the first system, we impose periodic boundary conditions and assume the twist assumption…
In this paper, we study the three-term nested recurrence relation $B(n)=B(n-B(n-1))+B(n-B(n-2))+B(n-B(n-3))$ subject to initial conditions where the first $N$ terms are the integers $1$ through $N$. This recurrence is the three-term analog…
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…
We define and study the functorial spectrum for every triangulated tensor category. A reconstruction result for topologically noetherian schemes similar to (and based on) a theorem by Balmer is proved. An alternative proof of the…
Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow…
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove…
We present short proofs of Toru\'nczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.
Using as a main tool our recent result on the strict minimax inequality proved in [5], in this note we establish a multiplicity theorem for a problem of the type $$\cases{-K\left(\int_{\Omega}|\nabla u(x)|^2dx\right)\Delta u = h(x,u) & in…
Consider a system $(X, \mathcal{F}, \mu, T)$, bounded functions $f_1, f_2 \in L^\infty(\mu)$ and $a,b \in \ZZ.$ We show that there exists a set of full measure $X_{f_1, f_2}$ in $X$ such that for all $x \in X_{f_1, f_2}$ and for every…
The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. We describe a relation of between the cohomology of this loop…
Clemens' conjecture states that the the number of rational curve in a generic quintic threefold is finite. If it is false we prove that certain periods of rational curves in such a quintic threefold must vanish. Our method is based on a…
We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we…