On Anomalous Dissipation in the Plasma of the Dusty Lunar Exosphere

JETP Letters - One of the main features of the dusty plasma compared to the conventional plasma (without charged dust particles is anomalous dissipation that is caused by the charging of dust...     

Nondiffusive weak localization in two-dimensional systems with spin-orbit splitting of the spectrum

The effect of spin splitting caused by structural asymmetry (Rashba’s contribution) and bulk asymmetry (Dresselhaus’s contribution) on the magnetoconductance of two-dimensional structures with high mobility of charge carriers is studied. The theory of weak localization with regard to both of the contributions is developed. The theory is valid in the entire region of classically low magnetic fields for arbitrary relations between the frequencies of spin precession and elastic collisions. The suppression of the correction for antilocalization is demonstrated in the case of equal contributions of structural anisotropy and bulk anisotropy to the spin splitting. The effect of the contribution, cubic in the wave vector, to the spin splitting on the quantum magnetoresistance is studied.     

Estimating the largest singular values of large sparse matrices via modified moments

We describe a procedure for determining a few of the largest singular values of a large sparse matrix. The method by Golub and Kent which uses the method of modified moments for estimating the eigenvalues of operators used in iterative methods for the solution of linear systems of equations is appropriately modified in order to generate a sequence of bidiagonal matrices whose singular values approximate those of the original sparse matrix. A simple Lanczos recursion is proposed for determining the corresponding left and right singular vectors. The potential asynchronous computation of the bidiagonal matrices using modified moments with the iterations of an adapted Chebyshev semi-iterative (CSI) method is an attractive feature for parallel computers. Comparisons in efficiency and accuracy with an appropriate Lanczos algorithm (with selective re-orthogonalization) are presented on large sparse (rectangular) matrices arising from applications such as information retrieval and seismic reflection tomography. This procedure is essentially motivated by the theory of moments and Gauss quadrature.This author's work was supported by the National Science Foundation under grants NSF CCR-8717492 and CCR-910000N (NCSA), the U.S. Department of Energy under grant DOE DE-FG02-85ER25001, and the Air Force Office of Scientific Research under grant AFOSR-90-0044 while at the University of Illinois at Urbana-Champaign Center for Supercomputing Research and Development.This author's work was supported by the U.S. Army Research Office under grant DAAL03-90-G-0105, and the National Science Foundation under grant NSF DCR-8412314.     

Scaling by Binormalization

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.     

Generalized moment representations of basis hypergeometric series

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 803–808, June, 1989.     

Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Functional analysis and boundary-value problems: An introductory treatment

Book Review

Functional analysis and boundary-value problems: An introductory treatmentB. Dayanand Reddy: Pitman Monographs and Survey in Pure and Applied Mathematics, Longman Scientific and Technical, 1986, 333 pp., £45.00 net     

Properties of Monocarboxy Cellulose Containing Sorbed Fe(III), Al(III), and Cr(III) Cations

Sorption of Fe(III), Al(III), and Cr(III) on monocarboxy cellulose at various pH, concentrations of metal chloride or sulfate in solution, and time was studied. The effect of type and amount of the cation sorbed on the physicomechanical properties, swelling, and stability in phosphate buffer of monocarboxy cellulose fibers was considered.     

Anionische Nickel-Pseudohalogenid-Komplexe der Typen [Ni{N(CN)2}3]− und [Ni{N(CN)2}2(NCS)2]2−

Anionie Nickel Pseudohalide Complexes of the Types [Ni{N(CN)₂}₃]^? and [Ni{N(CN)₂}₂(NCS)₂]^2? The preparation of a new type of anionic pseudohalide complexes of nickel [Ni{N(CN)₂}₃]^? and of mixed thiocyanate-dicyanamide complexes [Ni{N(CN)₂}₂(NCS)₂]^2? is reported. The structures of the complexes are discussed on the basis of IR- and magnetic measurements. The new compounds are representing polymer octahedral complexes with a bridging function of the dicyanamide ligands.