On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Spectrophotometric analysis, thermal analysis and gravimetric determination of some metal ions with oxime and Schiff's base derivatives of N-furoylphenylhydroxylamine

The oxime and Schiff's base of N-furoylphenylhydroxylamine form complexes with Co²⁺, Cu²⁺, Zn²⁺ and Fe³⁺. These complexes were studied by means of the UV — Vis. spectra of nujol mulls, electron spin resonance (ESR) spectra and magnetic susceptibility to determine their stereochemistry. The complexes were characterized via elemental analyses, molar conductivities and thermogravimetric analyses. Organic reagents were used for the gravimetric determination of Co²⁺, Cu²⁺ and Fe³⁺ through the precipitation of their complexes. The compounds were also used for separation of a binary mixture of Cu²⁺ and Cu²⁺. Interferences were studied.     

Dominant modes of submerged thin cylindrical shells

The relationship between the dominant mode of the submerged thin cylindrical shell and the flexural wave velocity is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, it is difficult to estimate the dominant mode, especially if two or more vibration modes are involved. To estimate the dominant mode of a thin shell in vacuo, the concept of “modified bending stiffness” has been introduced. In this paper, the concept of modified bending stiffness is extended to estimate the dominant mode of a submerged thin cylindrical shell. The dominant mode of a submerged thin cylindrical shell is theoretically discriminated from the other mode based on the smallness of the modified bending stiffness of the submerged shell. The validity of our theory is confirmed by a good agreement between theoretical and experimental results on flexural wave velocity.     

EXISTENCE OF PERIODIC SOLUTIONS OF SYSTEM OF DIFFERENCE EQUATIONS

This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained.     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.     

Effect of the Parameters of Three-Mirror Resonators on the Spectral Characteristics of Single-Pulse Laser Generation with Self-Injection of Priming Radiation

Based on a semiclassical theory, investigations were made of the dynamics and spectral composition of pulsed generation with self-injection of priming radiation from the active part of a three-mirror linear resonator, the passive part of which contains an active loss modulator and serves as the output reflector of the laser. It is shown that there exists a range of resonator parameters at which pulsed lasing has virtually a single frequency irrespective of the detuning of the frequencies of the priming radiation and of the nearest eigenmode of the composite resonator. Considering graphically the phase conditions of generation, it is established that among pulsed lasers with self-injection of priming radiation which are constructed on the basis of three-mirror linear and branched resonators, the most efficient for creating single-frequency generation are those in which the length of the main resonator, where generation of the pulse occurs, is larger than the length of the additional one intended for forming the priming radiation. With an inverse ratio of the lengths of the resonators, the conditions of single-frequency pulsed generation becomes dependent on the priming radiation frequency.     

石油测井仪器可靠性指标探讨

在分析常用可靠性指标及其应用现状的基础上，根据可靠性理论及石油测井仪器的特点。提出了石油测井仪器的可靠性模型。在探讨常用可靠性指标对石油测井仪器适用性的同时，提出将平衡稳定工作时间NWTURE和免维修测井井次NOLWNM作为石油测井仪器可靠性指标的思想；探讨了获取可靠性指标的途径。给出了推荐使用的石油测井仪器可靠性指标。     

由光率体求导折射率及振动方向的新方法

从光率体出发，利用坐标轴旋转，导出了光在晶体中传播时折射率及振动方向的公式。     

一种有效的优化的多载波通信系统的功率分配算法

本文提出一种关于DMT系统传输纯数据流业务的最佳的功率分配算法，该算法使用了一种有效的表格查手工艺工和拉格朗日乘法器对分搜索办法，能够较快的收敛到最佳的功率点。同时，易于用硬件和软件实现。