Sphericity and roundness have been employed in sedimentological and geomorphological studies to represent the gross shape of a gravel particle. The original complex definitions of gravel sphericity and roundness led to the use of visual charts or simplified parameters. Although the accurate derivation of sphericity requires the surface area of a gravel particle, manual measurement of the area i...

Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.

Let L be a lattice in R. We upper bound the number of points of L contained in a small sphere, centered anywhere in R. One way to do this is based on the observation that if the radius of the sphere is sufficiently small then the lattice points contained in that sphere give rise to a spherical code with a certain minimum angle. Another method involves Gaussian measures on L in the sense of [2]....

This article is divided into two parts. In the first part, we prove some useful theorems on finite topological spaces. In the second part, in order to consider a family of neighborhoods to a point in a space, we extend the notion of finite topological space and define a new topological space, which we call formal topological space. We show the relation between formal topological space struct (F...

Post-focus compression (PFC), the lowering of fundamental frequency and intensity after focus, is previously found in English but not in Cantonese. This study examines the possible transfer of PFC between these two languages through bilingualism. It is found that out of ten bilingual EnglishCantonese speakers, eight have PFC in their English, but none has PFC in their Cantonese. This finding su...

For a nonsymm etri c threshold network equippe d with an asynchronous dynamics, we show that if the product of weights in any cycle of units is nonnegative, then each tr ajectory converges to a stable state with probability one. We also show that such networks have a natural feed-forward layer struc ture and stabilit y is achieved in a hierarchical order due to this struct ure. It follows then ...

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. use classification to show that, when $G$ is connected reductive group with derived subgroup, two conjugacy classes $\mathcal{O}_1$, $\mathcal{O}_2$ of lie same sheet, up shift by central element $G$, if and only coordinate rings $\mathcal{O}_1$ are isomorphic as $G$-modules. As consequence, we pro...

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X–ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the dynamical state of the cluster. We introduce a new concept of allocation of the fundamental plane of clusters derived from their intrinsic morphological properti...

In this paper, three SIAM-Review problems selected from Vol. 34 (1992) are reconsidered and treated using methods according to my own vision on them. 1 Consider the functions S(v) and C(v) defined as the sums of two infinite double series : S(v) = +∞ m=0 +∞ n=1 (−1) m+n sin(2v √ m 2 + n 2) √ m 2 + n 2 , (1.1) C(v) = +∞ m=0 +∞ n=1 (−1) m+n cos(2v √ m 2 + n 2) √ m 2 + n 2 , (1.2) whereby it is in...

By use of Green 's functions f o r the diffusional motion a very concise formulation and computation of correlation functions is possible. For an axially symmetric overall diffusion with internal rotation about one and two axes correlation functions of a second rank spherical tensor are calculated. The results comprise all the solutions of the pertinent problem as given so far and allow the ext...