This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

We show that a well-known asymptotic series for the logarithm of central binomial coefficient is strictly enveloping in sense P\'olya and Szeg\"o, so error incurred truncating same sign as next term, bounded magnitude by term. consider closely related Binet's function, $\ln\Gamma(z+1/2)$, Riemann-Siegel theta make some historical remarks.

We construct a pointwise Boutet de Monvel-Sj\"ostrand parametrix for the Szeg\H{o} kernel of weakly pseudoconvex three dimensional CR manifold finite type assuming range its tangential operator to be closed; thereby extending earlier analysis Christ. This particularly extends Fefferman's boundary asymptotics Bergman domains in $\mathbb{C}^{2}$, agreement with D'Angelo's example. Finally our res...

A bstract We develop a new technique for computing class of four-point correlation functions heavy half-BPS operators in planar $$ \mathcal{N} N = 4 SYM theory which admit factorization into product two octagon form factors with an arbitrary bridge length. show that the can be expressed as Fredholm determinan...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...

In the present work, by making use of Gegenbauer polynomials, we introduce and study a certain family λ -pseudo bistarlike id="M2"> biconvex functions with respect to symmetrical points defined in open unit disk. We obtain estimates for initial coefficients solve Fekete–Szeg id="M3"> o ...