By using the fermionic p-adic q-Volkenborn integral, we construct generating functions of higher-order (h, q)-extension of Euler polynomials and numbers. By using these numbers and polynomials, we give new approach to the complete sums of products of (h, q)-extension of Euler polynomials and numbers one of which is given by the following form: are the multinomial coefficients and E (h) m,q (y) ...

We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler flows. The Euler system is reduced to a single elliptic equation for the stream function. The existence, uniqueness and asymptotic behaviors of the solutions fo...

We introduce Euler/X, a toolkit for logic-based taxonomy integration. Given two taxonomies and a set of alignment constraints between them, Euler/X provides tools for detecting, explaining, and reconciling inconsistencies; finding all possible merges between (consistent) taxonomies; and visualizing merge results. Euler/X employs a number of different underlying reasoning systems, including firs...

are known as the first kind Euler numbers cf. 1 . From the generating function of the first kind Euler numbers, we note that E0 1 and En − ∑n k 0 n k Ek for n ∈ N. The first few are 1,−1/2, 0, 1/4,−1/2, . . . and E2k 0 for k ∈ N. Those numbers play an important role in number theory. For example, the Euler zeta-function essentially equals an Euler numbers at nonpositive integer: ζE −m Em for m ...

It is well-known that the Euler product for the Riemann zeta function ζ(s) is still valid for !(s) = 1 and s "= 1. In this paper, we extend this result to zeta functions of number fields. In particular, the Dedekind zeta function ζk(s) for any algebraic number field k and the Hecke zeta function ζ(s,χ) for the rational number field are shown to have the Euler product on the line !(s) = 1 except...

In this paper, we describe a new simple linear algorithm for motion and structure from three weak perspective projections using Euler angles. We first determine the epipolar equation between each pair of images, which determines the first and third Euler angles for the rotation between that pair of images, leaving only the second Euler angle undetermined. In the next step, combining the three r...

Euler diagrams are an effective and intuitive way of representing relationships between sets. As the number of sets represented grows, Euler diagrams can become ‘cluttered’ and lose some of their intuitive appeal. In this paper we consider various measures of ‘clutter’ for abstract Euler diagrams and show that they compare well with results obtained from an empirical study. We also show that al...