Related papers: Regularity of an FI-module via the derivative func…
In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
The purpose of this paper is to give information on the FI-homology of the standard injective cogenerators of the category of FI-modules, where FI is the category of finite sets and injections. Working over a field k of characteristic zero,…
In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.
In this paper we study the properties of the finite topology on the dual of a module over an arbitrary ring. We aim to give conditions when certain properties of the field case are can be still found here. Investigating the correspondence…
We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
The ordinary differential equation $\dot{x}(t)=f(x(t)), \; t \geq 0 $, for $f$ measurable, is not sufficiently regular to guarantee existence of solutions. To remedy this we may relax the problem by replacing the function $f$ with its…
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can be characterized using quantitative, universal energy…
In this paper we study some properties of the Prabhakar integrals and derivatives and of some of their extensions such as the regularized Prabhakar derivative or the Hilfer--Prabhakar derivative. Some Opial- and Hardy-type inequalities are…
It is characterized when coarsening functors between categories of graded modules preserve injectivity of objects, and when they commute with graded covariant Hom functors.
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…
In this work we study a kind of coherence condition on FI_G-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its…
We numerically model fiber amplifier performance near and slightly above the mode instability threshold. These results are compared with recently published experimental work. Using weakly amplitude modulated pump light we obtain qualitative…
Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…