The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.     

Reactions of 1-alkynylphosphonates with group (IV) complexes

This article describes our recent methods for the synthesis of substituted vinylphosphonates by reacting 1-alkynylphosphnates with group (IV) complexes. cis-Vinylphosphonates, 1,3-butadienylphosphonates, 1-(hydroxymethyl)vinylphosphonates, 2-(hydroxymethyl)vinylphosphonates, (E) 3-oxo-1-alkenylphosphonates were produced as a result of the reactions between zirconium complexes and 1-alkynylphosphonates. On the other hand, titanium complexes afford 3-aminovinylphoshonates, 1,4-bis-phosphonates, and various other di- and tri-substituted vinylphosphonates. An evaluation of access of these recently synthesized vinylphosphonates as MMP-2 inhibitors has shown that certain compounds are very potent and promising.     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

一个Grüs型积分不等式的单参数推广

利用Cauchy中值定理给出Pachpatte B G建立的一个Grüss型积分不等式的单参数推广.     

Associated primes of graded components of local cohomology modules

The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal , is itself graded; all its graded components are finitely generated modules over , the component of of degree . It is known that the -th component of this local cohomology module is zero for all > 0$">. This paper is concerned with the asymptotic behaviour of as .

The smallest for which such study is interesting is the finiteness dimension of relative to , defined as the least integer for which is not finitely generated. Brodmann and Hellus have shown that is constant for all (that is, in their terminology, is asymptotically stable for ). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that is a homomorphic image of a regular ring): our answer is precisely the set of contractions to of certain relevant primes of whose existence is confirmed by Grothendieck's Finiteness Theorem for local cohomology.

Brodmann and Hellus raised various questions about such asymptotic behaviour when f$">. They noted that Singh's study of a particular example (in which ) shows that need not be asymptotically stable for . The second main aim of this paper is to determine, for Singh's example, quite precisely for every integer , and, thereby, answer one of the questions raised by Brodmann and Hellus.

     

Temperature‐dependent electroluminescence intensity in green and blue (In,Ga)N multiple‐quantum‐well diodes

The electroluminescence (EL) intensity has been investigated of green and blue (In,Ga)N multiple‐quantum‐well diodes grown on c ‐plane sapphire over a wide temperature range and as a function of current between 0.01 mA and 10 mA. The EL intensity of the green diode with p‐(Al,Ga)N electron blocking layer does not show low‐temperature quenching, especially at low injection levels, previously observed for the blue (In,Ga)N quantum‐well diodes. This finding rules out possi‐ bilities that the freeze‐out of holes at deep Mg acceptor levels and the failure of hole injections through the p‐(Al,Ga)N layer are directly responsible for the EL quenching at temperatures below 100 K. Variations of the EL efficiency with current level suggest that capture/escape efficiencies of injected carriers by the wells play an important role for the determination of EL external quantum efficiency. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System

In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division,Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package.     

Logarithmic derivatives of solutions to linear differential equations

Given an ordinary differential field of characteristic zero, it is known that if and satisfy linear differential equations with coefficients in , then is algebraic over . We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over that satisfies. Moreover, we provide explicit degree bounds and extend the result to fields with positive characteristic. Finally, we give an application of our method to a class of nonlinear differential equations.

     

Oxygen plasma and high pressure H<Subscript>2</Subscript>O vapor heat treatments used to fabricate polycrystalline silicon thin film transistors

Oxygen plasma and high pressure H₂O vapor heat treatment were applied to fabrication of n-channel polycrystalline silicon thin film transistors (poly-Si TFTs). 13.56 MHz-oxygen-plasma treatment at 250 °C, 100 W for 5 min effectively reduced defect states of 25-nm-thick silicon films crystallized by 30 ns-pulsed XeCl excimer laser irradiation. 1.3×10⁶-Pa-H₂O vapor heat treatment at 260 °C for 3 h was carried out in order to improve electrical properties of SiO_x gate insulators and SiO_x/Si interfaces. A carrier mobility of 470 cm²/V s and a low threshold voltage of 1.8 V were achieved for TFTs fabricated with crystallization at 285 mJ/cm². Received: 18 November 2002 / Accepted: 25 November 2002 / Published online: 11 April 2003 RID="*" ID="*"Corresponding author. Fax: +81-42/388-7109, E-mail: tsamesim@cc.tuat.ac.jp