Symmetric and Asymmetric Gaps in Some Fields of Formal Power Series

2000 Mathematics Subject Classification: 03E04, 12J15, 12J25.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

Cardiovascular effects of short term exposure to electric and magnetic fields of electricity power transmission

In the electrical industry the 50 Hz electric and magnetic fields are often higher than in the average working environment. The electric and magnetic fields can be studied by measuring or by calculatingthe fields in the environment. For example, the electric field under a 400 kV power line is 1 to 10 kV/m, and the magnetic flux density is 1 to 15 µT. Electricand magnetic fields of a power line induce a weak electric field and electric currents in the exposed body. The average current density in a human being standing under a 400 kV line is 1 to 2 mA/m2. The aim of this study is to find out thepossible effects of short term exposure to electric and magnetic fields of electricity power transmission on workers' health, in particular the cardiovascular effects. The study consists of two parts; Experiment I: influence on extrasystoles, and Experiment II: influence on heart rate. In Experiment I two groups, 26 voluntary men (Group 1) and 27 transmission-line workers (Group 2), were measured. Their electrocardiogram (ECG) was recorded with an ambulatory recorder both in and outside the field. In Group 1 the fields were 1.7 to 4.9 kV/m and 1.1 to 7.1 pT; in Group 2 they were 0.1 to 10.2 kV/m and 1.0 to 15.4 pT. In the ECG analysis the only significant observation was a decrease in the heart rate after field exposure (Group 1). The drop cannot be explained with the first measuring method. Therefore Experiment II was carried out. In Experiment II two groups were used; Group 1 (26 male volunteers) were measured in real field exposure, Group 2 (15 male volunteers) in "sham" fields. The subjects of Group 1 spent 1 h outside the field, then 1 h in the field under a 400 kV transmission line, and then again 1 h outside the field. Under the 400 kV linethe field strength varied from 3.5 to 4.3 kV/m, and from 1.4 to 6.6 pT. Group 2spent the entire test period (3 h) in a 33 kV outdoor testing station in a "sham" field. ECG, blood pressure, and electroencephalogram (EEG) were measured by ambulatory methods. Before and after the field exposure, the subjects performed some cardiovascular autonomic function tests. The analysis of the results (Experiments I and II) showed that extrasystoles or arrythmias were as frequent in the field (below 4 kV/m and 4 pT) as outside it. In Experiment II there was no decrease detected in the heart rate, and the systolic and diastolic blood pressure stayed nearly the same. No health effects were found in this study.

Algorithmic Computation of Formal Fourier Series

KAAD (Katholischer Akademischer Ausländer-Dienst)

Fields of two power conductor

The goal of this work is find a description for fields of two power conductor. By the Kronecker-Weber theorem, these amounts to find the subfields of cyclotomic field $\mathbb{Q}(\xi_{2^r})$, where $\xi_{2^r}$ is a $2^r$-th primitive root of unit and $r$ a positive integer. In this case, the cyclotomic extension isn't cyclic, however its Galois group is generated by two elements and the subfield can be expressed by $\mathbb{Q}(\theta)$ for a $\theta\in\mathbb{Q}(\xi_{2^r})$ convenient.

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determinization of timed Petri nets behaviors

International audience

The sound-field characterisation of a power transformer

In order to effectively suppress the noise radiation from large electrical power transformers, both the structure-borne and air-borne sound fields need to be characterised. The characterisation can be made either from theoretical predictions or by in-situ measurements. This paper presents the study of the sound radiation from a large power transformer in a substation. The radiation pattern can be predicted from the measured acceleration distribution and the predicted value is not affected by other noise sources. Alternatively, the farfield sound pressure level can be predicted from the sound pressure level measured at NEMA locations. Both the near- and far-field power radiation can be in-situ measured using the sound intensity technique. It is shown that both the vibration of a transformer tank wall and the radiated noise consist of a series of tonal components mainly at the first few harmonic frequencies of 100 Hz. Also, the neglect of the noise radiation from the transformer (top and bottom) lids does not affects the accuracy of the transformer radiation characterisation. (C) 1998 Elsevier Science Ltd. All rights reserved.

Formal Power Analysis of Systems-on-Chip

The design methods and languages targeted to modern System-on-Chip designs are facing tremendous pressure of the ever-increasing complexity, power, and speed requirements. To estimate any of these three metrics, there is a trade-off between accuracy and abstraction level of detail in which a system under design is analyzed. The more detailed the description, the more accurate the simulation will be, but, on the other hand, the more time consuming it will be. Moreover, a designer wants to make decisions as early as possible in the design flow to avoid costly design backtracking. To answer the challenges posed upon System-on-chip designs, this thesis introduces a formal, power aware framework, its development methods, and methods to constraint and analyze power consumption of the system under design. This thesis discusses on power analysis of synchronous and asynchronous systems not forgetting the communication aspects of these systems. The presented framework is built upon the Timed Action System formalism, which offer an environment to analyze and constraint the functional and temporal behavior of the system at high abstraction level. Furthermore, due to the complexity of System-on-Chip designs, the possibility to abstract unnecessary implementation details at higher abstraction levels is an essential part of the introduced design framework. With the encapsulation and abstraction techniques incorporated with the procedure based communication allows a designer to use the presented power aware framework in modeling these large scale systems. The introduced techniques also enable one to subdivide the development of communication and computation into own tasks. This property is taken into account in the power analysis part as well. Furthermore, the presented framework is developed in a way that it can be used throughout the design project. In other words, a designer is able to model and analyze systems from an abstract specification down to an implementable specification.

Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved