A simple new closed form of the Green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. The result is verified by applying several examples.

We propose a new ring resonator side-coupled M-Z interferometer all-optical switch throughthe pumped nonlinear directional coupler. By controlling pump power P to lead the coupler reflectivityr approaching to 1, the resonator finesse will be enhanced dramatically, and then the minimumswitching power in silica-based practice devices can be obtained. As a sample, we use a nonlinearcoupler made by two erbium-doped fibers, and launch a 514.5nm-pump light into one of the cores tomake the reflective- index difference between two cores. Based on the asymmetric-coupler theory, wesimulate the relationship between r and P , and show that the required pump power is only 0.8mWfor r →1 .

In this paper, strong laws of large numbers (SLLN) are obtained for the sums ƒ°=nii X1, undercertain conditions, where {X ,n . 1} n is a sequence of pairwise negatively dependent random variables.

A chaos control method suggested by Erjaee has been reviewed. It has been shown that thistechnique can be applied in various evolutionary systems of 2-dimensional types. The method has beenapplied for cases of the Henon map, as well as Burger’s map. The limitations of the control techniquehave also been discussed by considering the Standard Map and the Gumowski-Mira map. The resultsobtained through numerical calculations are very interesting and significant. This technique has someadvantages over many other techniques of chaos control in discrete systems.

In this experimental work, by using the method of plasma-chemical etching, we have dealtwith the causes of the creation of a distorted layer on the surface of silicon wafers during mechanicalmachining processes, in addition, the elucidation of connections between the structure of this layer andcharacteristic parameters of the mechanical strength of these wafers have been studied. Experimentalresults obtained at room temperature show that after cutting and grinding processes, the mean value ofmechanical strength σ, which is apparently independent of the types of conductivity, is significantlylower than its theoretical value. Analysis of the dependence of mechanical parameters on the time ofplasma-chemical etching indicates that the lower values obtained for the mechanical strength of siliconwafers is basically due to the existence of a distorted layer and corresponding internal stresses created onthe surface of these wafers after mechanical machining. Plasma-chemical etching leads to an increase inσ value. Dependency of σ on the etching time is qualitatively described by the microstructure of thedistorted layer and parameters of the micro relief surface of the wafers. Correlation between parametersσ, H, K and the microstructure of the distorted layer allows us to suggest the method of plasma chemicaletching as a method of investigating the microstructure of the distorted layer after the mechanicalmachining processes.

Several tables have been given due to a − minimal sets. Our main aim in this paper is tocomplete these tables by employing several examples.

An improved MIT bag model with hyper central interactions is used to calculate the staticproperties of hadrons containing u, d, s and c quarks. We present a theoretical approach to the internalstructure of three-body hyper central interacting quarks in a hadron, in which we take hadron as a bag.We discuss a few of the results obtained using a six-dimension harmonic oscilator (h.o) potential, havinga two-body character, which turns out to be a hyper central confinement part. The other potential is sixdimensional,which is attractive for small separation, originating from the color charge of hyper colorterm. However the potential can easily be generalized in order to allow a systematic analysis. Wecalculate the relativistic wave function for quarks in a scalar-vector hyper central potential, analytically.Finally, vanishing the normal component of vector current at the surface of the baryon bag as a boundarycondition equivalent to confinement, results in the static properties and the strength of hyper Coulomblike potential parameter. This depends on the mass parameters contrary to almost all previous versions.The calculated static properties for baryon are better than in the uncorrected versions of the model.PACS index 12.39 .Ba, 12.39. Ki, 12.39. Pn

The largest class of algebraic hyper structures satisfying the module like axioms is the v H -module. In this paper, we consider the category of v H -modules and prove that the direct limit alwaysexists in this category. Direct limits are defined by a universal property, and so are unique. The mostpowerful tool in order to obtain a module from a given v H - module is the quotient out procedure. To usethis method we consider the fundamental equivalence relationε * , and then prove some of the resultsabout the connection between the fundamental modules, direct systems and direct limits.

In the analysis of spatial point patterns, complete spatial randomness (CSR) hypothesis,which is a restriction of a homogenous Poisson process to study region A, operates as a dividinghypothesis between “regular” and “aggregated” patterns. Meanwhile, many alternatives to CSR inaggregated patterns are extensions of homogenous Poisson processes themselves. Therefore, when theCSR hypothesis is rejected, results related to Poisson processes may be used to formulate plausiblealternatives to CSR. In this paper, we propose a new statistic for testing CSR and then by applying it inconjunction with a notion of kernels of a point pattern, we determine the “parents” of a Poisson clusterprocess when the CSR hypothesis is rejected and a Neyman-Scott process is assumed for the pointpattern under alternative hypothesis. We have made power studies for our test statistic by simulation, andhave also surveyed the performance of our method on a certain point pattern. Finally, the whole methodis carried on certain real life data.

In this paper we initiate the study of real group algebras and investigate some of its aspects.Let L1 (G) be a group algebra of a locally compact group G,τ :G →G be a group homeomorphismsuch that τ 2 =τοτ = 1, the identity map, and Lp (G,τ ) = { f ∈ Lp (G) : fοτ = f } ( p ≥ 1) . In thispaper, among other results, we clarify the structure of Lp (G,τ ) and characterize amenability ofL1 (G,τ ) and identify its multipliers.

Analysis of time series data can involve the inversion of large covariance matrices. For theclass of ARMA (p, q) processes there are no exact explicit expressions for these inverses, except for theMA (1) process. In practice, the sample covariance matrix can be very large and inversion can becomputationally time consuming and so approximate explicit expressions for the inverse are desirable.This paper offers some of these approximations.