相关论文: Analysis on disconnected sets
We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter…
The analyzability of the universe into subsystems requires a concept of the "independence" of the subsystems, of which the relativistic quantum world supports many distinct notions which either coincide or are trivial in the classical…
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
We construct a combinatorially large measure zero subset of the Cantor set.
The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are…
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic…
In this paper, we study the observability of compactly perturbed infinite dimensional systems. Assuming that a given infinite-dimensional system with self-adjoint generator is exactly observable we derive sufficient conditions on a compact…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…
Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and…
Recent discoveries of manifestly exotic, narrow baryon resonances present a fundamental challenge for our theoretical understanding of low-energy QCD. This is a brief survey of their interpretation, emphasizing the possibility that diquark…
We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins'…
The discrete wave equation in a multidimensional uniform space with local defects and sources is considered. The characterization of all possible defect configurations corresponding to given amplitudes of waves at the receivers (detectors)…