A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.

     

Effects of various washing procedures on the chromium content of human scalp hair

The effects of four wash procedures on the concentration of chromium in a pooled sample of human scalp hair are compared. The wash solutions examined are Triton X-100, sodium lauryl sulphate, acetone, and a mixture (1 + 1) of hexane and ethanol. The plateaux reached for hair chromium concentration are functions of the number of washings, and are characteristic for each wash solution. The wash procedure recommended involves two 20-min washes with aqueous 1% sodium lauryl sulphate solution after a hexane rinse.     

On a classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

After introducing briefly the principles of theerror linearization method, which is able to determine the coefficients of the first order error approximation, a collection of examples is presented to demonstrate its efficiency as a test bench for analyzing numerical algorithms. These examples illustrate the propagation of initial errors, the effect of cancellation, the easy location of the most unstable parts of an algorithm, calculation of condition numbers, approximating the statistical behavior of accumulated errors and the convergence of iterative methods.     

On the viscous dissipation in the boundary layer of a high Prandtl number fluid in laminar flow over a flat plate

Summary An asymptotic expansion for large Prandtl number fluids has been obtained for the recovery factor in a laminar flow over flat plate. The expression underestimates the recovery factor by no more than 1% as long as the Prandtl number is greater than seven.

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Zusammenfassung Die adiabatische Oberflächentemperatur (recovery factor) für ein Fluid mit hoher Prandtl-Zahl wurde für laminare Strömung über eine ebene Platte mit Hilfe einer asymptotischen Entwicklung bestimmt. Der Ausdruck unterschätzt das genaue Resultat um weniger als 1 % für Prandtl-Zahlen höher als 7.

     

Boundary relations and their Weyl families

The concepts of boundary relations and the corresponding Weyl families are introduced. Let be a closed symmetric linear operator or, more generally, a closed symmetric relation in a Hilbert space , let be an auxiliary Hilbert space, let

and let be defined analogously. A unitary relation from the Krein space to the Krein space is called a boundary relation for the adjoint if . The corresponding Weyl family is defined as the family of images of the defect subspaces , , under . Here need not be surjective and is even allowed to be multi-valued. While this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex Hilbert space and the class of unitary relations , it also generalizes the notion of so-called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems. Moreover, these new notions yield, for instance, the following realization theorem: every -valued maximal dissipative (for ) holomorphic family of linear relations is the Weyl family of a boundary relation, which is unique up to unitary equivalence if certain minimality conditions are satisfied. Further connections between analytic and spectral theoretical properties of Weyl families and geometric properties of boundary relations are investigated, and some applications are given.

     

Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let −Dω(·,z)D+q be a differential operator in L²(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form

     

A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

This paper presents a novel method of multi-objective optimization by learning automata (MOLA) to solve complex multi-objective optimization problems. MOLA consists of multiple automata which perform sequential search in the solution domain. Each automaton undertakes dimensional search in the selected dimension of the solution domain, and each dimension is divided into a certain number of cells. Each automaton performs a continuous search action, instead of discrete actions, within cells. The merits of MOLA have been demonstrated, in comparison with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and non-dominated sorting genetic algorithm II (NSGA-II), on eleven multi-objective benchmark functions and an optimal problem in the midwestern American electric power system which is integrated with wind power, respectively. The simulation results have shown that MOLA can obtain more accurate and evenly distributed Pareto fronts, in comparison with MOEA/D and NSGA-II.     

Preparation of 4-Vinyl-2(5H)-Furanoid Structural Unit via Organosilicon and - Selenium Intermediates

Two syntheses of the 2(5H)-furanoid structural unit (especially the 3-methyl derivative 1) have been reported from this laboratory.^1,2 The unit 1 is found in many naturally occurring compounds (especially sesqui terpenes). The 4-substi tuted d erivatives of 1 also occur frequently i n natural products, e.g. furospongolide³ 2.     

Regioselective Mono-<Emphasis Type="Italic">O</Emphasis>-Carboxymethylation of Polyhydroxyisoflavones

Optimized conditions are described for the regioselective mono-O-alkylation of daidzein 1a, genistein 1b, and biochanin A 1c with ethyl bromoacetate.