We bound the nuclear dimension of crossed products associated to some partial actions finite groups or Z on dimensional locally compact Hausdorff second countable spaces. Our results apply globalizable actions, group minimal automorphisms, and automorphisms acting zero-dimensional spaces, a class one containing 1-dimensional CW complexes. This extends work global systems by Hirshberg Wu.

The concept of fractal index is introduced in connection with the idea of universal class h of particles or quasiparticles termed fractons which obey fractal statistics. We show the relation between fractons and conformal field theory(CFT)-quasiparticles taking into account the central charge c[ν] and the particle-hole duality ν ←→ 1 ν , for integer-value ν of the statistical parameter. The Hau...

We apply Lie algebraic methods of the type developed by Baker, Campbell, Hausdorff, and Zassenhaus to the initial value and eigenvalue problems for certain special classes of partial differential operators which have many important applications in the physical sciences. We obtain detailed information about these operators including explicit formulas for the solutions of the problems of interest...

We consider the minimization of an average-distance functional defined on a two-dimensional domain $\\Omega$ with Euler elastica penalization associated $\\partial\\Omega$, boundary $\\Omega$. The average distance is given by $$ \\int\_{\\Omega}\\operatorname{dist}^p(x,\\partial\\Omega)\\operatorname{d}x, where $p\\geq 1$ parameter and $\\operatorname{dist}(x,\\partial\\Omega)$ Hausdorff betwee...

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus...

We show that any infinite compact Hausdorff space S is the continuous image of a totally disconnected compact Hausdorff space S', having the same topological weight as S, by a map 95 which admits a regular linear operator of averaging, i.e., a projection of norm one of C(S') onto <p°C(S), where <p°: C(S) -*■ C(S') is the isometric embedding which takes fe C(S) into/« ¡p. A corollary of this the...

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg [1]. By means of a partial regularity theorem (proved elsewhere), it turns out that we are able to show the existence of a suitable weak solution to the Navier-Stokes equations with a singular set of positive one dimensional Hausdorff measure.

Assuming the axiom of constructibility, points in closed discrete subspaces of certain normal spaces can be simultaneously separated. This is a partial result towards the normal Moore space conjecture. The normal Moore space conjecture states that every normal Moore space is metrizable. This is known to be not provable from the usual axioms of set theory, since Silver [4] shows that Martin's ax...

The $(k,a)$-generalised Fourier transform is the unitary operator defined using $a$-deformed Dunkl harmonic oscillator.The main aim of this paper to prove $L^p$-$L^q$ boundedness $(k, a)$-generalised multipliers. To show we first establish Paley inequality and Hausdorff-Young-Paley for transform. We also demonstrate applications obtained results study well-posedness nonlinear partial differenti...