We prove the conjectures of Graham–Kumar [GrKu08] and Griffeth– Ram [GrRa04] concerning the alternation of signs in the structure constants for torus-equivariant K-theory of generalized flag varieties G/P . These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a nat...

We show that integrals of the form ∫ 1 0 xLip(x)Liq(x)dx (m ≥ −2, p, q ≥ 1) and ∫ 1 0 log(x)Lip(x)Liq(x) x dx (p, q, r ≥ 1) satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, in the first case for all m, p, q and in the second case when p+ q+ r is even, these integrals are reducible to zeta values. In the case of odd p+q+r, we comb...

We consider a general spherically symmetric ansatz for [Formula: see text] connection depending on three arbitrary functions in gauge model with the triplet of scalar fields adjoint representation. A analytic solution Bogomol’nyi equations is derived. It depends two constants and one function radius. In particular gauge, coincides Protogenov’s solutions contains Bogomol’nyi–Prasad–Sommerfield s...

The purpose of this paper is to construct new q-Euler numbers and polynomials. Finally we will consider the Witt's type formula associated with these q-Euler numbers and polynomials, and construct q-partial zeta functions and p-adic q-l-functions which interpolate new q-Euler numbers and polynomials at negative integers.

To reduce the stress concentration and ensure structural safety for lattice structure designs, in this paper, a new optimization framework is developed optimal design of graded structures, innovatively integrating fillet designs as well yield buckling constraints. Both relative strut radii parameters are defined variables, BCC PC lattices. Numerical homogenization employed to characterize effec...

The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes’ type multiple FrobeniusEuler numbers and polynomials. By applying Mellin transformation to these functions, we define Barnes’ type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we define gene...

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and polynomials. Furthermore we construct multivariate Hurwitz type zeta function which interpolates the multivariate q-Euler numbers or polynomials at negative ...

In [1], the multiple Frobenius-Euler numbers and polynomials were constructed. In this paper we give some interesting formulae which are related to the multiple Frobenius-Euler polynomials. The main purpose of this paper is to give the Kummer type congruences for the multiple Frobenius-Euler numbers. §

in this research complexation of dioxovanadium(v) with nitrilotriacetic acid (nta) at differentionic strengths (0.1 to 1.0 mol dm-3) of sodium perchlorate as supporting electrolyte and ph rangeof 1.00-2.50 at 25 °c has been investigated by a combination of potentiometric and uvspectrophotometric measurements. stability constants of two species, v0211l- and vo2h2l havebeen calculated. ionic stre...