Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Characterizations of power indices based on null player free winning coalitions

In this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Morphological and functional characterizations of Schwann cells stimulated with Mycobacterium leprae

Nerve damage, a characteristic of leprosy, is the cause of patient deformities and a consequence of Schwann cells (SC) infection by Mycobacterium leprae. Although function/dysfunction of SC in human diseases like leprosy is difficult to study, many in vitro models, including SC lines derived from rat and/or human Schwannomas, have been employed. ST88-14 is one of the cell lineages used by many researchers as a model for M. leprae/SC interaction. However, it is necessary to establish the values and limitations of the generated data on the effects of M. leprae in these SC. After evaluating the cell line phenotype in the present study, it is close to non-myelinating SC, making this lineage an ideal model for M. leprae/SC interaction. It was also observed that both M. leprae and PGL-1, a mycobacterial cell-wall component, induced low levels of apoptosis in ST88-14 by a mechanism independent of Bcl-2 family members.

Parallel characterizations of a generalized shapley value and a generalized banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.

Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.

Newborn screening for biotinidase deficiency in Brazil: biochemical and molecular characterizations

Biotinidase deficiency is an inherited metabolic disorder characterized by neurological and cutaneous symptoms. Fortunately, it can be treated and the symptoms prevented by oral administration of the vitamin biotin. Using dried blood-soaked filter paper cards, biotinidase activity was determined in the sera of 225,136 newborns in Brazil. Mutation analysis performed on DNA from 21 babies with low serum biotinidase activity confirmed that 3 had profound biotinidase deficiency (less than 10% of mean normal sera biotinidase activity), 10 had partial biotinidase deficiency (10 to 30% of mean normal serum activity), 1 was homozygous for partial biotinidase deficiency, 4 were heterozygous for either profound or partial deficiency, and 3 were normal. Variability in serum enzyme activities and discrepancies with mutation analyses were probably due to inappropriate handling and storage of samples sent to the laboratory. Obtaining an appropriate control serum at the same time as that of the suspected child will undoubtedly decrease the false-positive rate (0.09%). Mutation analysis can be used to confirm the genotype of these children. The estimated incidence of biotinidase deficiency in Brazil is about 1 in 9,000, higher than in most other countries. Screening and treatment of biotinidase deficiency are effective and warranted. These results strongly suggest that biotinidase deficiency should be included in the newborn mass screening program of Brazil.

Lithium Containing Complex Metal Oxides and Metal phosphates:Investigations on their synthesis and various characterizations for rechargeable lithium battery applications

The work presented in the thesis is centered around two important types of cathode materials, the spinel structured LixMn204 (x =0.8to1.2) and the phospho -oIivine structured LiMP04 (M=Fe and Ni). The spinel system LixMn204, especially LiMn204 corresponding to x= 1 has been extensively investigated to understand its structural electrical and electrochemical properties and to analyse its suitability as a cathode material in rechargeable lithium batteries. However there is no reported work on the thermal and optical properties of this important cathode material. Thermal diffusivity is an important parameter as far as the operation of a rechargeable battery is concerned. In LixMn204, the electronic structure and phenomenon of Jahn-Teller distortion have already been established theoretically and experimentally. Part of the present work is an attempt to use the non-destructive technique (NDT) of photoacoustic spectroscopy to investigate the nature of the various electronic transitions and to unravel the mechanisms leading to the phenomenon of J.T distortion in LixMn204.The phospho-olivines LiMP04 (M=Fe, Ni, Mn, Co etc) are the newly identified, prospective cathode materials offering extremely high stability, quite high theoretical specific capacity, very good cycIability and long life. Inspite of all these advantages, most of the phospho - olivines especially LiFeP04 and LiNiP04 show poor electronic conductivity compared to LixMn204, leading to low rate capacity and energy density. In the present work attempts have been made to improve the electronic conductivity of LiFeP04 and LiNiP04 by adding different weight percentage MWNT .It is expected that the addition of MWNT will enhance the electronic conductivity of LiFeP04 and LiNiP04 with out causing any significant structural distortions, which is important in the working of the lithium ion battery.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures

In this paper, the residual Kullback–Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specifiedmodels and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order