by using euler-maclaurin's summation formula and the way of real analysis, a more accurate multiplehilbert-type inequality and the equivalent form are given. we also prove that the same constantfactor in the equivalent inequalities is the best possible.

The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical de nite integral due to Euler and other de nite integrals are also considered together with closed-form evaluations of some series involving the Riemann and Hurwitz Zeta functions.

We prove in this paper an effective recursion formula for all intersection numbers of mixed ψ and κ classes on moduli spaces of curves. Several related general recursive formulas are also proved. Some of these formulas contain certain tautological constants, which are given by the secant Euler numbers and series expansion of Bessel functions of the first kind.

The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. These techniques will be il...

We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl typ...

the protonation of different species of glycylisoleucine were studied in the ph range of 1.5 - 10 at25 °c using potentiometric technique. investigations were performed in sodium perchlorate andtetraethylammonium iodide as background electrolytes at i (0.1, 0.2, 0.3, 0.4, 0.5, and 0.6) moldm-3. the parameters based on the protonation constants were calculated, and their dependenceson ionic stren...