A Sparse-Sparse Iteration for Computing a Sparse Incomplete Factorization of the Inverse of an SPD Matrix

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a preconditioner for solving symmetric positive definite linear systems of equations by using the preconditioned conjugate gradient algorithm. Some numerical experiments on test matrices from the Harwell-Boeing collection for comparing the numerical performance of the presented method with one available well-known algorithm are also given.Comment: 15 pages, 1 figur

Robust Dropping Criteria for F-norm Minimization Based Sparse Approximate Inverse Preconditioning

Dropping tolerance criteria play a central role in Sparse Approximate Inverse preconditioning. Such criteria have received, however, little attention and have been treated heuristically in the following manner: If the size of an entry is below some empirically small positive quantity, then it is set to zero. The meaning of "small" is vague and has not been considered rigorously. It has not been clear how dropping tolerances affect the quality and effectiveness of a preconditioner $M$. In this paper, we focus on the adaptive Power Sparse Approximate Inverse algorithm and establish a mathematical theory on robust selection criteria for dropping tolerances. Using the theory, we derive an adaptive dropping criterion that is used to drop entries of small magnitude dynamically during the setup process of $M$. The proposed criterion enables us to make $M$ both as sparse as possible as well as to be of comparable quality to the potentially denser matrix which is obtained without dropping. As a byproduct, the theory applies to static F-norm minimization based preconditioning procedures, and a similar dropping criterion is given that can be used to sparsify a matrix after it has been computed by a static sparse approximate inverse procedure. In contrast to the adaptive procedure, dropping in the static procedure does not reduce the setup time of the matrix but makes the application of the sparser $M$ for Krylov iterations cheaper. Numerical experiments reported confirm the theory and illustrate the robustness and effectiveness of the dropping criteria.Comment: 27 pages, 2 figure

The generalized monotonicity property of the Perron root

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov's theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles. © 2007 Springer Science+Business Media, Inc

FIRST DATA ON THE CONCENTRATIONS AND DISTRIBUTION OF NOBLE METALS IN NI-CU SULFIDE ORES OF THE SOUTH MAKSUT DEPOSIT (EAST KAZAKHSTAN)

The magmatic sulfide deposits in the Central Asian orogenic belt are hosted in a series of mafic–ultramafic intrusions in the Maksut zone (E Kazakhstan), the Kalatongke and the Huangshan zones in Xinjiang (NW China) and the Hongqiling zone in NE China. In the Maksut zone there are several intrusions, the best studied from which is the South Maksut intrusion with Cu–Ni–PGE mineralization.The magmatic sulfide deposits in the Central Asian orogenic belt are hosted in a series of mafic–ultramafic intrusions in the Maksut zone (E Kazakhstan), the Kalatongke and the Huangshan zones in Xinjiang (NW China) and the Hongqiling zone in NE China. In the Maksut zone there are several intrusions, the best studied from which is the South Maksut intrusion with Cu–Ni–PGE mineralization

Generalized Sharp Bounds on the Spectral Radius of Digraphs

The spectral radius {\rho}(G) of a digraph G is the maximum modulus of the eigenvalues of its adjacency matrix. We present bounds on {\rho}(G) that are often tighter and are applicable to a larger class of digraphs than previously reported bounds. Calculating the final bound pair is particularly suited to sparse digraphs. For strongly connected digraphs, we derive equality conditions for the bounds, relating to the outdegree regularity of the digraph. We also prove that the bounds hold with equality only if {\rho}(G) is the r-th root of an integer, where r divides the index of imprimitivity of G.Comment: 12 pages and 1 figure. Nov. 30, 2012 revisio

LYSAN ALKALINE-ULTRABASIC COMPLEX (EASTERN SAYAN): AGE AND GEODYNAMIC CONSEQUENCES

This paper presents new ideas about the formational identity, as well as the first data on the age of formation of rocks within the Lysan intrusive complex located at junction of the Derbin block and the Sisim-Kazyr zone of the Central Asian folded belt. The study identified the similarities between the Lysan complex and intrusions of the alkaline-ultrabasic formation. It formed during the period of maximum intraplate activity along the edge of the Siberian craton

Combination of Gilbert's syndrome and gastrointestinal diseases

The aim of review. To detect relation between Gilbert's syndrome (GS) and other diseases of a gastrointestinal tract (GIT).Key points. Gilbert's syndrome - hereditary, unconjugated jaundice related to decrease of activity of uridinediphosphate glucuronosyltransferase 1А1 (UGT 1А1) in the liver. The prevalence in European countries of reaches 9 %. Mutation of encoding gene — A (TA) 7TAA A is the principal cause of insufficiency of this enzyme, however development of clinical syndrome and severity of symptoms is related to other factors as well (male gender, additional genetic mutations, et al.). Provoking factors of jaundice attacks include fasting, infectious diseases, overstrain, effect of drugs and xenobiotics. Patients demonstrate various complaints related to disorders — nausea, decrease of appetite, heartburn, epigastric pain, defecation disorders. Gilbert's syndrome quite often is combined to of the upper gastro-intestinal diseases (gastroduodenitis, esophagitis, sphincter disorders). Recent studies have demonstrated, that this hereditary syndrome is a risk factor of gallbladder diseases, including biliary sludge, gallstone disease. Lower gastro-intestinal disorders often have functional origin. In the literature publications on rare frequency of colorectal cancer and Crohn's disease in patients with GS have appeared. The protective role of unconjugated bilirubin in relation to various diseases - cardio-vascular, autoimmune, oncologic is studied.Conclusion. The reasons of development of symptoms related to gastro-intestinal organs in patients with Gilbert's syndrome are investigated insufficiently. It can be assumed, that there is combination to other gastro-intestinal diseases. Diseases of the esophagus, stomach, duodenum and biliary tracts decelop most frequently at GS. To author’s opinion and literature data, it is caused by embryogenetic affinity and functional relation between liver, biliary tract and upper gastro-intestinal tract, disorder of structure and rheologic properties of bile, characteristic for GS, and also decrease of detoxification liver function. Doctors should be concerned in relation of gastro-intestinal diseases GS

PALEOGEODYNAMICS OF MAGMATIC AND METAMORPHIC PROCESSES OF FORMATION OF ULTRAMAFIC ROCKS OF CHAGAN-UZUN MASSIF (OPHIOLITES OF GORNY ALTAI)

The Geochemical and mineralogical studies showed, that harzburgites of the Chagan-Uzun massif are restites with a degree of partial melting 15–20 %, which formed at temperatures 1520–1420 °С under the conditions of the mid-oceanic ridge and transformed during the evolution of paleooceanic structures under the influence of magmatic processes at the initial stages of subduction and manifestation of boninite magmatism. The combined use of data on the geochemistry of rare and rare earth elements, as well as on the compositions of pyroxenes, Cr-spinels, melt inclusions in Cr-spinels and computational modeling, indicates the formation of clinopyroxenites of Chagan-Uzun ophiolites at the mid-oceanic ridge during crystallization of picrite and picrobasalt melts at temperatures 1315–1245 °C and pressures 4–2 kbar. The study of amphiboles showed high metamorphic parameters of transformation of harzburgites (5.1–1.9 kbar, 820–700 °С) and clinopyroxenites (2.6–1.4 kbar and 740–680 °С) of the Chagan-Uzun massif, typical for ultrabasites from the modern mid-oceanic ridges. In general, results of comprehensive studies made it possible to determine the sequence of paleogeodynamic processes of formation of ultramafic rocks of the Chagan-Uzun massif. Initial formation of harzburgites in the course of partial melting of mantle and crystallization of clinopyroxenites in the magma chamber occurred under the conditions of the mid-oceanic ridge. At the next stage, ultramafic rocks fell within the subduction-zone initiation area, where they were exposed to the influence of boninite melts

THE PROBLEM OF IMPROVING THE NORMATIVE FRAMEWORK FOR STANDARDIZING THE CHEMICAL INDUSTRY

В настоящей статье рассматривается проблема совершенствования нормативной базы стандартизации химической промышленности. Разработана модель исследования проблемы этой комплексной проблемы. Результаты системного анализа проблемы создания комплексной программы стандартизации для химической продукции, предназначенной для машиностроения, показали, что данная проблема актуальна и требует определенных системных подходов к разработке модели и методики комплексной программы стандартизации для продукции.This article discusses the problem of improving the regulatory framework for standardization of the chemical industry. A research model for this complex problem has been developed. The results of a system analysis of the problem of creating a comprehensive standardization program for chemical products intended for mechanical engineering showed that this problem is relevant and requires certain systematic approaches to the development of a model and methodology for a comprehensive standardization program for products