The Classification and Realization of Complete Lie Algebras with Commutative Nilpotent Radicals

in this paper, the classification and realization of complete Lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete Lie algebras are obtained.     

Modules over Operator Algebras and Its Module Maps

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Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

Improvement of the performance of facilitated transport membrane process through nonuniformity

Facilitated transport process has attracted much attention because high selectivity and high permeability may be achieved. However, most research on facilitated transport process is concerned only with uniform membranes. In this paper, a model predicting the gas separation performance of a hollow-fiber module with facilitated transport membrane is developed. The influence of feed rate, operation pressure, and permeant-feed flow pattern on the module performance are analyzed and the effect of the nonuniform distribution of reaction equilibrium constant is examined. The calculated results show that the nonuniform active distribution may cause an improved module performance. Because of the passive transport characteristics of the facilitated transport process, the mass transfer driving force across the membrane has a great influence on the improvement of the module performance through a facilitated transport effect.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Electronic structure of C60 films

A complete set of fundamental optical functions of fullerite (C₆₀) films in energy ranges of 2.5–5.0 and 4.0–9.0 eV is calculated using the known spectra of the imaginary and real parts of the dielectric constant. An integrated spectrum of the dielectric constant is decomposed into elementary components. Three basic parameters of each component (the maximum and halfwidth energies and oscillator strength) are determined. Based on the known theoretical calculations of fullerite zones, a scheme of the nature of these components of the dielectric constant is suggested. Udmurt State University, 71, Krasnogeroiskaya Str., Izhevsk, 426034, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 227–232, March–April, 1999.     

Conditions for the convergence in distribution of maxima of stationary normal processes

The asymptotic distribution of the maximum M_n=max_1?t?nξ_t in a stationary normal sequence ξ₁,ξ,… depends on the correlation r_t between ξ₀ and ξ_t. It is well known that if r_t log t → 0 as t → ∞ or if Σr²_t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.     

Decomposability index of tournaments

Given a tournament $T$, a module of $T$ is a subset $X$ of $V\left(T\right)$ such that for $x,y\in X$ and $v\in V\left(T\right)?X$, $(x,v)\in A\left(T\right)$ if and only if $(y,v)\in A\left(T\right)$. The trivial modules of $T$ are $?$, $\left\{u\right\}$ $(u\in V\left(T\right))$ and $V\left(T\right)$. The tournament $T$ is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of $T$, denoted by $\delta \left(T\right)$, is the smallest number of arcs of $T$ that must be reversed to make $T$ indecomposable. For $n\ge 5$, let $\delta \left(n\right)$ be the maximum of $\delta \left(T\right)$ over the tournaments $T$ with $n$ vertices. We prove that $?\frac{n+1}{4}?\le \delta \left(n\right)\le ?\frac{n?1}{3}?$ and that the lower bound is reached by the transitive tournaments.     

Characterizations of F-V-rings by Quasi-continuous Modules

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EXISTENCE OF OSCILLATORY SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH "MAXIMA

1IntroductionInthispaperweconsiderthefollowingneutraldifferentialequationwherep9T)aarepositive,gEC(R ,R)andA7g(t)=oo,andfeC(R xR',R).WeshallassumethatthereexistsafunctionF(t,u,v)6C(R;,R )suchthatFisnondecreasinginuandvandWeshallnotethatequationswithmaximaoccurintheproblemofautomaticregulationofvariousrealsystems[4],[6].Themaximaariseswhentheregu-lationlawcorrespondstothemaximaldeviationoftheregurablequantity.Ourmaingoalwillbetoestablishsufficientconditionsfortheexistenceofoscillatorysol…