In this paper we study the Casimir force for a piston configuration in R 3 with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is " free to move " along a transverse dimension to the curved one and in the other case the piston " moves " along the curved one. We find that the Casimir force has opposite sig...

Hyperbolic space groups are isometry groups, acting discontinuously on the hyperbolic 3-space with compact fundamental domain. One possibility to classify them is to look for fundamental domains of these groups. Here are considered supergroups for four series of groups with simplicial fundamental domains. Considered simplices, denoted in [9] by T19, T46, T59, belong to family F12, while T31 bel...

Hecke proved analytically that when h > 2 or when h = 2 CDS (m/q), q E Z, q > 3, then B(h) = (7: Im I > 0, / Re 7 1 < h/2, [ 7 j > 1) is a fundamental region for the group G(h) = (SA , T), where S,+ : 7 --f 7 + X and T: 7 ---t -l/~. He also showed that B(A) fails to be a fundamental region for all other A > 0 by proving that G(X) is not discontinuous. We give an elementary proof of these facts ...

The most secure type of grasp of a frictionless woorkpiece is the form-closure grasp. However, task constraints may make achieving form-closure impossible or undesirable. In this case, one needs to employ a force-closure 1 grasp. In this paper, we study the subclass of force-closure grasps known as second-order stable grasps, which typically have a small number of contacts. We derive conditions...

In this paper, we study a fundamental domain for Sp(g,Z) ⋉ H (g,h) Z \Hg × C .

We consider the Buffon’s problem for the lattice Rα,a which has the fundamental cell composed by the union of octagon, with all sides of lengths a and the angles (π − α) and ( 2 + α) with α ∈ ] 0, π 2 [ , and of the square with side of length a (see Fig. 1). We determine the probability of intersection of a body test needle of length l, l < a. For α = π 4 we also give the estimate of this proba...

A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra.

Let S be the unit sphere in R and let 〈 · , · 〉 denote the usual inner product in R. We characterize those functions K in L([−1, 1]), p ≥ 1, for which the associated set of zonal functions {x ∈ S → K(〈x, y〉) : y ∈ S } is fundamental in L(S). We then study fundamentality of sets generated by either spherical convolution or spherical shifting, thus providing methods of construction of fundamental...

In this paper, we describe a new approach, allowing as much as possible, an automatic extraction of the micromelodic information of the speech signal using the original curved of the fundamental frequency and its macromelodic curve obtained by MOMEL, the algorithm of MOdelisation MELodic. The results reinforce the idea that microprosodic effect exists and seems to be possible to be included in ...