Related papers: On Shifting Semicircular Roots
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
We study explicit continued fraction expansions for certain series. Some of these expansions have symmetry that generalizes some remarkable examples discovered independently by Kmosek and Shallit. Furthermore, we prove the following…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
The phase behaviour of a single large semiflexible polymer immersed in a suspension of spherical particles is studied. All interactions are simple excluded volume interactions and the diameter of the spherical particles is an order of…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
The nonequilibrium structural and dynamical properties of semiflexible active polar polymers subject to linear flow are studied by numerical simulations. Filaments are confined in two dimensions and immersed in a fluid described by the…
It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities.…
Mass shifts induced by one-loop fluctuations of semi-local self-dual vortices are computed. The procedure is based on canonical quantization and heat kernel/ zeta function regularization methods. The issue of the survival of the classical…
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…
Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, including $spt$-crank, overpartition pairs, and $t$-core partitions. As corollaries, we obtain new proofs of…
Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H{\"o}lder…
We look at some extensions of the Stieltjes-Wigert weight functions. First we replace the variable x by x^2 in a family of weight functions given by Askey in 1989 and we show that the recurrence coefficients of the corresponding orthogonal…
On a compact Riemannian manifold, we study the various dynamical properties of the Schr\"odinger flow $(e^{it\Delta/2})$, through the notion of semiclassical measures and the quantum-classical correspondence between the Schr\"odinger…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every…
The author has previously constructed a class of admissible vector fields on the path space of an elliptic diffusion process $x$ taking values in a closed compact manifold. In this Note the existence of flows for this class of vector fields…