Related papers: Quantitative towers in finite difference calculus …
We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
In this work we reexamine the EPR paradox for composite systems with a finite number of levels. The analysis emphasizes the connection between measurements and conditional probabilities. This connection implies that when a measurement is…
This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…
A quantitative form of the Nullity Theorem is presented, which establishes a linear relation between the singular values of the two submatrices involved in the theorem up to the first order. The theorem is then extended to function spaces…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko…