We consider a class of higher order corrections in the form of Euler densities of arbitrary rank n to the standard gravity action in D dimensions. We present a generating functional and an explicit form of the conserved energy-momentum tensors. We show that this class of corrections allows for domain-wall solutions despite the presence of higher powers of the curvature. The existence of such so...

and Applied Analysis 3 is called the auxiliary equation of the Euler differential equation 2.1 , and every solution of 2.1 is of the form yh x ⎧ ⎪⎨ ⎪⎩ c1x m1 c2x2 if m1 and m2 are distinct roots of 2.2 , c1 c2 lnx x 1−α /2 if 1 − α 2 is a double root of 2.2 , 2.3 where c1 and c2 are complex constants see 21, Section 2.7 . Theorem 2.1. Let α and β be complex constants such that no root of the au...

The main goal of this paper is to present the basis for a heterogeneous Euler/Venn diagram and First Order Logic (FOL) reasoning system. We will begin by defining a homogeneous reasoning system for Euler/Venn diagrams including named constants and show this system to be sound and complete. Then we will propose a heterogeneous rule of inference allowing the extraction of formulas of FOL from an ...

In the Laurent expansion ζ(s, a) = 1 s− 1 + ∞ ∑ k=0 (−1)γk(a) k! (s− 1) , 0 < a ≤ 1, of the Riemann-Hurwitz zeta function, the coefficients γk(a) are known as Stieltjes, or generalized Euler, constants. [When a = 1, ζ(s, 1) = ζ(s) (the Riemann zeta function), and γk(1) = γk.] We present a new approach to high-precision approximation of γk(a). Plots of our results reveal much structure in the gr...

Article history: Received 16 October 2008 Revised 11 June 2009 Communicated by David Goss MSC: primary 11J81 secondary 11J86, 11J91