Automorphisms and Derivations of Exceptional Simple Lie Algebras of Family <Emphasis Type="Italic">R</Emphasis>

In the paper we describe automorphisms and derivations of simple Lie algebras of family R. The Lie algebra of the automorphism group is found. Bibliography: 11 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 165–186.     

A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

A Mössbauer and Electrochemical Characterization of the Corrosion Products Formed from Marine and Marine-Antartic Environments

Hyperfine Interactions - Corrosion products formed on low alloy steel under two marine environments are characterised. Both environments are classified as C4 according to the ISO 9223 Standard. The...     

Poincaré-Hopf inequalities

In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.

     

Structuring Multi-attribute Value Hierarchies

The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated.     

Synthesis of alkylindoles (review)

Methods for obtaining alkylindoles, excluding the Fischer synthesis and direct alkylation, developed during the last 15 years are correlated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1155–1172, September, 1987.     

A note on the angular distribution of the characteristic surface loss intensity of electrons with non-normal incidence to the foils

By using a quantized theory of non-radiative surface plasmon in a semi-infinite electron gas, where retardation is taken into account, the differential surface loss intensity of electrons in a metal foil is calculated for the case of non-normal incidence of electron to the metal surface. The result shows that the differential surface loss intensity neither has a zero at θ = 0 for the case of normal incidence nor has a zero at a forward direction (θ ≠ 0, φ = 0) for the case of non-normal incidence, whose existences were predicted by electrostatic theories, but diverges as 1/θ at θ = 0 for both cases. It is also shown that, when the angle of incidence is greater than a certain critical value, there is a region of direction to which incident electrons can be scattered by exciting any one of surface plasmons with three different wave vectors.