Certain Bounds of Regularity of Elimination Ideals on Operations of Graphs

Elimination ideals are regarded as a special type of Borel type ideals, obtained from degree sequence of a graph, introduced by Anwar and Khalid. In this paper, we compute graphical degree stabilities of K n ∨ C m and K n ∗ C m by using the DVE method. We further compute sharp upper bound for Castelnuovo–Mumford regularity of elimination ideals associated to these families of graphs.

Fuzzy Differential Subordinations Based Upon the Mittag-Leffler Type Borel Distribution

In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series Bλ,α,β(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function Eα,β(z). Using the above-mentioned operator Bλ,α,β, we also introduce and study a class Mλ,α,βFη of holomorphic and univalent functions in the open unit disk Δ. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function pΨq(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.

Partial regularities and a*-invariants of Borel type ideals

We express the partial regularities and a*-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition, we consider the behaviors of those invariants under intersections and sums.

ASYMPTOTIC APPROXIMATIONS AND A BOREL-TYPE RESULT FOR CR FUNCTIONS

We show that for any smooth CR manifold which has a peak function (in a weak sense) at some point p, formal power series at p can be approximated asymptotically by continuous CR functions. Furthermore, if the peak function satisfies a certain growth property, the asymptotic approximation is actually smooth. This in fact allows to invert, in a Borel-type theorem, the natural map taking a smooth CR function to its formal Taylor series.

Asymptotic Power Series of Field Correlators

We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of theWatson lemma recently proved elsewhere, we discuss a large class of functions determined by the same asymptotic power expansion and represented by various forms of integrals of the Laplace-Borel type along a general contour in the Borel complex plane. Some remarks on possible applications in QCD are made.

Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket

We prove there exist exponentially decaying generalized eigenfunctions on a blow-up of the Sierpinski gasket with boundary. These are used to show a Borel-type theorem, specifically that for a prescribed jet at the boundary point there is a smooth function having that jet.