arXiv subjects
Publications and source records attributed to Hassan Jolany.
In this paper we extend Hitchin-Kobayashi correspondence along holomorphic fibre space and we show that there exists a generalized Hermitian-Einstein metric which is twisted with Weil-Petersson current.In fact we generalise Song-Tian program for vector bundles
Existence of canonical metric on a Sasakian variety was a long standing conjecture and the major part of this conjecture is about varieties which do not have definite basic first Chern class . Most of the Sasakian varieties do not have definite basic first Chern class. We give a program by using Fujino's Minimal Model program to find canonical metric on the canonical model of Sasakian varieties.
In this short note, we give an identity for the $α$ function $$α(x,s)=\sum_{n=0}^\infty\frac{x^n}{(n!)^s}$$ where $s\in \mathbb{N}$, $x\in \mathbb{R}$, in the case $s=3$.
For projective varieties with definite first Chern class we have one type of canonical metric which is called Kähler-Einstein metric. But for varieties with an intermidiate Kodaira dimension we can have several different types of canonical metrics. In this paper we introduce a new notion of canonical metric for varieties with an intermidiate Kodaira dimension. We highlight that to get $C^\infty$-solution of CMA equation of relative Kähler Einstein metric we need Song-Tian-Tsuji measure (which has minimal singularities with respect to other relative volume forms) be $C^\infty$-smooth and special fiber has canonical singularities. Moreover, we conjecture that if we have relative Kähler-Einstein metric then our family is stable in the sense of Alexeev,and Kollar-Shepherd-Barron. By inspiring the work of Greene-Shapere-Vafa-Yau semi-Ricci flat metric, we introduce fiberwise Calabi-Yau foliation which relies in context of generalized notion of foliation. In final, we give Bogomolov-Miyaoka-Yau inequality for minimal varieties with intermediate Kodaira dimensions which admits relative Kähler-Einstein metric.
In this paper, we show that along $\mathbb Q$-Fano fibration, when general fibres, base and central fiber (with at worst Kawamata log terminal singularities)are K-poly stable then there exists a relative Kähler-Einstein metric. We introduce the fiberwise Kähler-Einstein foliation and we mention that the main difficulty to obtain higher estimates is to solve relative CMA equation along such foliation. We propose a program such that for finding a pair of canonical metric $(ω_X,ω_B)$, which satisfies in $$Ric(ω_X)=π^*ω_B+π^*(ω_{WP})+[\mathcal N]$$ on K-poly stable degeneration $π:X\to B$, where $Ric(ω_B)=ω_B$, we need to have Canonical bundle formula.
In this paper, by applying Greene-Shapere-Vafa-Yau semi-flat metric, we give a new proof of closed formula of Weil-Petersson metric on moduli space of Calabi-Yau varieties.
In this paper we extend the Dirichlet integral formula of Lobachevsky. Let $f(x)$ be a continuous function and satisfy in the $π$-periodic assumption $f(x+π)=f(x)$, and $f(π-x)=f(x)$, $0\leq x<\infty $. If the integral $\int_0^\infty \frac{\sin^4x}{x^4}f(x)dx$ defined in the sense of the improper Riemann integral, then we show the following equality $$\int_0^\infty \frac{\sin^4x}{x^4}f(x)dx=\int_0^{\fracπ{2} }f(t)dt-\frac{2}{3}\int_0^{\fracπ{2} }\sin^2tf(t)dt$$ hence if we take $f(x)=1$, then we have $$\int_0^\infty \frac{\sin^4x}{x^4}dx=\fracπ{3}$$ Moreover, we give a method for computing $\int_0^\infty \frac{\sin^{2n}x}{x^{2n}}f(x)dx$ for $n\in \mathbb N$
In this paper, we define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi poly-Bernoulli polynomials is established using the $r$-Whitney numbers of the second kind.
In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are defined using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. These are generalized further using the concept of Hurwitz-Lerch multiple zeta values.
In this paper we investigate special generalized Bernoulli polynomials with a,b,c parameters that generalize classical Bernoulli numbers and polynomials. The present paper deals with some recurrence formulae for the generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters. Poly-Bernoulli numbers satisfy certain recurrence relationships which are used in many computations involving poly-Bernoulli numbers. Obtaining a closed formula for generalization of poly-Bernoulli numbers with a,b,c paramerers therefore seems to be a natural and important problem. By using the generalization of poly-Bernoulli polynomials with a,b,c parameters of negative index we define symmetrized generalization of poly-Bernoulli polynomials with a,b parameters of two variables and we prove duality property for them. Also by stirling numbers of the second kind we will find a closed formula for them. Furthermore we generalize the Arakawa-Kaneko Zeta functions and by using the Laplace-Mellin integral, we define generalization of Arakawa-Kaneko Zeta functions with a,b parameters and we obtain an interpolation formula for the generalization of poly-Bernoulli numbers and polynomials with a,b parameters. Furthermore we present a link between this type of Zeta functions and Dirichlet series. By our interpolation formula, we will interpolate the generalization of Arakawa-Kaneko Zeta functions with a,b parameters.
In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly- Euler polynomials. Moreover, we introduce a more general form of multi poly-Euler polynomials and obtain some identities parallel to those of the generalized poly-Euler polynomials.
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling numbers and generalized Bernoulli polynomials are derived. Moreover, the generating function, interpolation function of these polynomials of several variables and also the derivatives of these polynomials and their generating function are given. Finally, we get new interesting identities of modified $q$-Bernoulli numbers and $q$-Euler numbers applying $p$-adic $q$-integral representation on $\mathbb {Z}_p$ and $p$-adic fermionic $q$-invariant integral on $\mathbb {Z}_p$, respectively, to the inverse of $q$-Bernstein polynomials.
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore seems to be a natural and important problem.
The aim of this paper is the computing one of topological indices of One-pentagonal carbon Nanocone. One-pentagonal carbon nanocone consists of one pentagone as its core surrounded by layers of hexagons .if there are n layers,then the graph of this molecules is denoted by G_n .In This paper our aim is to calculate the hyper-Wiener index of G_n explicitly .
This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for Poincare conjecture. In the second one which is the main propose of our memoire, we exhibit a complete proof of Calabi-Yau conjecture.
The Concepts of poly-Bernoulli numbers $B_n^{(k)}$, poly-Bernoulli polynomials $B_n^{k}{(t)}$ and the generalized poly-bernoulli numbers $B_{n}^{(k)}(a,b)$ are generalized to $B_{n}^{(k)}(t,a,b,c)$ which is called the generalized poly-Bernoulli polynomials depending on real parameters \textit{a,b,c}. Some properties of these polynomials and some relationships between $B_n^{k}$, $B_n^{(k)}(t)$, $B_{n}^{(k)}(a,b)$ and $B_{n}^{(k)}(t,a,b,c)$ are established
In this paper, we focus on the q-Genocchi numbers and polynomials. We shall introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integral on Zp which are very important in the study of Frobenius-Genocchi numbers and polynomials. Also, we give Cauchy-integral formula for the q-Genocchi polynomials and moreover by using measure theory on p-adic integral we derive the distribution formula q-Genocchi polynomials. Finally, we present a new definition of q-Zeta-type function by using Mellin transformation which is the interpolation function of the q-Genocchi polynomials at negative integers.
In the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method of generating function and p-adic q-integral representation on Zp. We summarize our results as follows. In section 2, by using combinatorial techniques we present two formulas for q-Euler numbers with weight alpha. In section 3, we derive distribution formula (Multiplication Theorem) for Dirichlet type of q-Euler numbers and polynomials with weight . Moreover we define partial Dirichlet type zeta function and Dirichlet q-L-function, and obtain some interesting combinatorial identities for interpolating our new definitions. In addition, we derive behavior of the Dirichlet type of q-Euler L-function with weight alpha, Lq (s; x j) at s = 0. Furthermore by using second kind stirling numbers, we obtain an explicit formula for Dirichlet type q-Euler numbers with weight alpha. Moreover a novel formula for q-Euler-Zeta function with weight in terms of nested series of E;q (n j) is derived . In section 4, by introducing p-adic Dirichlet type of q-Euler measure with weight, and we obtain some combinatorial relations, which interpolate our previous results. In section 5, which is the main section of our paper. As an application, we introduce a novel concept of dynamics of the zeros of analytically continued q-Euler polynomials with weight alpha.