Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

CaractErisation Par DSC Des Sequences De Transformation Au Cours D'un Chauffage Lent Des Alliages Amf A Base De Cu–Al–Ni

Quenching of the eutectoidal composition of the shape memory alloys (SMA’s) allowed us to display the gradual transition of the martensitic structure as a function of the composition. Indeed, we have verified that for low Al and Ni percentages, the martensite structure obtained is β′, while, for high Al and Ni (Al<13.3 mass%) contents, the martensite structure is essentially of β₁′ type. Elsewhere, we have observed that a nickel addition (<4.3 mass%) operates simultaneously on the composition of the eutectoidal pointand the domain of the different martensitic structures types. During reheating of the quenched structure, the transformation sequences of the martensite to the parent phase (β1), then the decomposition of the later phase into the equilibrium phases, and finally, the redissolution of all phases to form the β phase at high temperature, are rather similar. This revised version was published online in August 2006 with corrections to the Cover Date.     

有限时滞微分系统依照双测度的实际稳定性

本文对具有有限时滞的泛函微分方程建立了关于依照两种测度的实际稳定性的Razumikhin型判定定理，其中未采用通常的辅助函数，且可运用多个含有状态变量x的部分变元的Lyapunov函数，得出部分变远实际稳定性的判定定理，从而改进了已有的结果。     

On a result of Ozawa concerning uniqueness of meromorphic functions

In this paper we prove a uniqueness theorem for meromorphic functions sharing three values with some weight which improves some known results.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Active long pulse shaping technique of pulsed CO2 laser using multi-pulse discharge control

We describe the pulse forming of pulsed CO₂ laser using multi-pulse superposition technique. Various pulse shapes, high duty cycle pulse forming network (PFN) are constructed by time sequence. This study shows a technology that makes it possible to make various long pulse shapes by activating SCRs of three PFN modules consecutively at a desirable delay time with the aid of a PIC one-chip microprocessor. The power supply for this experiment consists of three PFN modules. Each PFN module uses a capacitor, a pulse forming inductor, a SCR, a high voltage pulse transformer, and a bridge rectifier on each transformer secondary. The PFN modules operate at low voltage by driving the primary of HV pulse transformer. The secondary of the transformer has a full-wave rectifier, which passes the pulse energy to the load in a continuous sequence.We investigated various long pulse shapes as different trigger time intervals of SCRs among three PFN modules. As a result, we could obtain laser beam with various pulse shapes and durations from about 250 to 1000 μs.     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Analysis of a 2D “liquid”plasma lattice

Adustyplasmacanbedefinedasacomplicatedplasmacontainingsmallsolidmattercalleddustgrainsordustparticles,whichareusuallychargednegatively,duetoelectronshighermobilitythanion,bycollectingelectronsandionsfromthebackgroundplasma.Theuniverseisfilledwithdustyplasmassuchasplanetaryrings,comettails,andnebulae.Also,inindustrialplasmaprocessing,particulatessuspendedinplasmaarethemajorcontaminationinsemiconductormanufacture.Studiesondustyplasmahavebeenextendedtofar-flungtopicssuchaswaves,instabilities,stro…     

A note on strong β-I-sets and strongly β-I-continuous functions

Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.     

Equilibrium Shapes of Pressure Vessel Domes in Asymmetric Winding

Errors in the programs of winding pressure vessels can lead to an asymmetric reinforcement structure, which affects the equilibrium shape of their domes and the tension in the left and right families of filaments. In this paper, equations determining the equilibrium shape of the domes, the tension in filaments, and the shear stresses between layers are obtained. Examples with winding trajectories in the form of geodesics and constant-deviation lines are considered. It is found that, for pressure vessels, in the absence of external torque, the tension levels in filaments of the left and right families differ considerably. It is also revealed that, for actual friction coefficients in winding, the shear stresses taken up by the binder are insignificant. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 743–752, November–December, 2005.