On the irrationality measure for certain series

Let K be either the rational number field or an imaginary quadratic field. We give irrationality results for the number , where q (∣q∣ > 1) is an integer in K, r∈ K ^× (∣r∣ < ∣q∣), and with q ⁿ ≠ r ^l (n ≥ 1). Authors’ addresses: Kenji Amano, NS solutions Corporation, 2-27-1 Shinkawa, Chuo-ku, Tokyo 104-0033, Japan; Yohei Tachiya, Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan     

Weighted-Hardy functions with Hadamard gaps on the unit ball

We prove that an analytic function f on the unit ball B with Hadamard gaps, that is, (the homogeneous polynomial expansion of f) satisfying n_k+1/n_k?λ>1 for all k∈N, belongs to the space if and only if . Moreover, we show that the following asymptotic relation holds . Also we prove that lim_r→1(1-r²)^α‖Rf_r‖_p=0 if and only if . These results confirm two conjectures from the following recent paper [S. Stevi?, On Bloch-type functions with Hadamard gaps, Abstr. Appl. Anal. 2007 (2007) 8 pages (Article ID 39176)].     

Two-phase flow boiling heat transfer of FC-72 in parallel micro-channels

Experimental research is performed on two-phase flow boiling heat transfer in micro-channels. FC-72 is used as the working fluid. In order to analyze the heat transfer mechanism during two-phase flow boiling, the dimensionless parameters, e.g., boiling number and convection number, are used, and the effect of these parameters on the heat transfer can be confirmed during flow boiling in the micro-channel. In addition, the transition criterion from bubbly/slug flow to annular flow is proposed from the modified Weber number. Based on the boiling heat transfer mechanism obtained from the experiments, a new correlation is proposed to predict the heat transfer coefficient. The new correlation predicts well the experimental results within a mean absolute error of 5.2%.     

The density functional study of the stabilities,bond characters,static linear polarisabilities,and aromaticities of the ’in-out’ isomerism Hn-60@CnH60（n=70,72,74）

This paper uses the density functional theory to analyse the stabilities,bond characters,static linear polarisabilities,and aromaticities of the ’in-out’ isomerism H n-60 @C n H 60 (n=70,72,74).The binding energies,C-H bond energies,and energy gaps explore that the ’in-out’ isometric perhydrogenation of C n (n=70,72,74) can remarkably improve the stabilities.The static linear polarisabilies of H n-60 @C n H 60 (n=70,72,74) are indeed relative to their shapes,while they show almost nonaromatic character.This study can suggest that the ’in-out’ isometric perhydrogenation of fullerenes could lead to the invention of entirely novel potential hydrogen storage nanomaterials.     

Transient analysis of boiling heat transfer in periodic drying out miniature pools

The evolution of the two-phase thermal control technique is moving in the direction of the use of devices which operate in stable periodic or chaotic unsteady regimes. In these devices the heat transfer coefficient relative to the evaporator walls therefore changes over time and it is hardly predictable, especially in the case of boiling regime. This paper deals with the analysis of the boiling coefficient evolutions over time during the operations of a thermal control devices which periodically operates, the Periodic Two-Phase Thermosyphon (PTPT). An experimental technique for measuring the transient boiling heat transfer coefficient in a thick flat evaporator is shown.     

FC-72在竖直壁面上及微小三角型通道内的沸腾传热

本文对浸在FC-72液池中的竖直壁面及两个微小三角形通道进行了沸腾实验研究,考虑了管道尺寸对沸腾传热特性的影响。两个微小三角形通道的边长分别为1.5和2.5 mm,水力直径分别为0.87和1.44 mm,长度50 mm,采用铜块上开V型沟槽,再覆盖上透明的玻璃片构成。热流密度由贴在铜块背后的膜状加热器提供。实验得到了沸腾曲线和传热系数,并用DV摄影机拍摄到了沸腾状况。实验结果显示,管道尺寸对沸腾传热特性有显著的影响,CHF值随通道尺寸的减小而减小,小通道在低热流密度时传热系数较大。     

Criteria of unitary equivalence of Hermitian operators with a degenerate spectrum

Nonimprovable, in general, estimates of the number of necessary and sufficient conditions for two Hermitian operators to be unitarily equaivalent in a unitary space are obtained when the multiplicities of eigenvalues of operators can be more than 1. The explicit form of these conditions is given. In the Appendix the concept of conditionally functionally independent functions is given and the corresponding necessary and sufficient conditions are presented.     

Trace polynomials and invariant theory

LetA be a finite-dimensional simple (non-associative) algebra over an algebraically closed fieldF of characteristic 0. LetG be the group of its automorphisms which acts onkA, the direct sum ofk copies ofA. SupposeA is generated byk elements. In this paper, generators of the field of rational invariantF(kA) ^G are described in terms of operations of the algebraA.     

Complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines

Recently E. Sanchez has given a necessary and sufficient condition for the existence of a solution of a fuzzy $\text{A 1 X = C}$, with 1 the extension of a given binary operation in the universe of discourse.Using many valued logic we generalize this result and get a characterization also of the cases if $\text{A 1 X = C}$ has only nearly a solution.Additionally, we consider fuzzy relation equations and get similar results.     

Stability of axial motions of nonlinearly elastic loops

We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish orbitai stability (modulo this collection of relative equilibria). For a well-defined class of soft materials, there is an upper bound on the axial speed sufficient for stability; stiff materials are shown to be orbitally stable at any axial speed.