A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices

Summary In this paper we describe a block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts. The method is accelerated via Chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum. A parallel implementation of this method is investigated on the eight processor Alliant FX/80. Numerical results and comparisons with simultaneous iteration on some Harwell-Boeing matrices are reported.     

Existence of positive periodic solutions of nonlinear neutral differential systems with variable delays

In this work we use some mixed techniques of the Mawhin coincidence degree theory and fixed point theorem to prove the existence of positive periodic solutions of delay systems. As a consequence, we offer existence criteria and sufficient conditions for existence of periodic solutions to the systems with feedback control. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved.     

Robust fuzzy fault detection and isolation approach applied to surge in centrifugal compressor modeling and control

This work presents the results of applying an advanced fault detection and isolation technique to centrifugal compressor; this advanced technique uses physics models of the centrifugal compressor with a fuzzy modeling and control solution method. The fuzzy fault detection and isolation has become an issue of primary importance in modern process engineering automation as it provides the prerequisites for the task of fault detection. In this work, we present an application of this approach in fault detection and isolation of surge in compression system. The ability to detect the surge is essential to improve reliability and security of the gas compressor plants. We describe and illustrate an alternative implementation to the compression systems supervision task using the basic principles of fuzzy fault detection and isolation associated with fuzzy modeling approach. In this supervision task, the residual generation is obtained from the real input-output data process and the residual evaluation is based on fuzzy logic method. The results of this application are very encouraging with relatively low levels of false alarms and obtaining a good limitation of surge in natural gas pipeline compressors.     

Regular path decompositions of odd regular graphs

Kotzig asked in 1979 what are necessary and sufficient conditions for a d‐regular simple graph to admit a decomposition into paths of length d for odd d>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable to a decomposition of the graph into paths of length 3 where the middle edges of the paths coincide with the 1‐factor. We conjecture that existence of a 1‐factor is indeed a sufficient condition for Kotzig's problem. For general odd regular graphs, most 1‐factors appear to be extendable and we show that for the family of simple 5‐regular graphs with no cycles of length 4, all 1‐factors are extendable. However, for d>3 we found infinite families of d‐regular simple graphs with non‐extendable 1‐factors. Few authors have studied the decompositions of general regular graphs. We present examples and open problems; in particular, we conjecture that in planar 5‐regular graphs all 1‐factors are extendable. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 114–128, 2010     

Sufficient Condition for the Existence of an Even [a, b]-Factor in Graph

Let a, b, be two even integers. In this paper, we get a sufficient condition which involves the stability number, the minimum degree of the graph for the existence of an even [a, b]-factor.     

Direct oxidation of methane to oxygenates over heteropolyanions

Partial oxidation of methane to formaldehyde and methanol was studied at atmospheric pressure in the temperature range of 700-750 °C using heteropolycompound catalysts （NH4）6HSiMo11FeO40, （NH4）4PMo11FeO39, and H4PMo11VO40, which were prepared and characterized by various analysis techniques such as infrared, visible UV, XRD and DTA. O2 or N2O was used as the oxidizing agent, and the principal products of the reaction were CH3OH, CH2O, CO, CO2, and water. The conversion and the selectivity of products depend strongly on the reaction temperature, the nature of oxidizing agent, and the composition of catalyst.     

Synthesis,X-ray structure and theoretical study of benzazole thioether and its zinc complex as corrosion inhibitors for steel in acidic medium

A ligand, 2-((benzo[d]thiazol-2-ylthio)methyl)-1H-benzo[d]imidazole, and its zinc complex have been synthesized. The structure of these compounds have been determined by spectroscopic techniques and single crystal X-ray diffraction. The corrosion inhibition study of these compounds for steel in 0.5 M H₂SO₄ medium has also been investigated using potentiodynamic polarization and EIS techniques. The quantum calculations were applied to investigate the relationship between the electronic properties and the corrosion inhibition efficiency of the two benzazoles derivatives. Surface analysis (XRF) indicated that the rust layer formed on the Cu-containing steels was enriched with Cu compounds. Polarization curves revealed that both inhibitors acted as a mixed-type inhibitor.     

An Optimal L∞–error Estimate for an Approximation of a Parabolic Variational Inequality

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L^∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions.     

Neighborhoods and Covering Vertices by Cycles

G =(V,E) is a 2-connected graph, and X is a set of vertices of G such that for every pair x,x' in X, , and the minimum degree of the induced graph <X> is at least 3, then X is covered by one cycle. This result will be in fact generalised by considering tuples instead of pairs of vertices. Let be the minimum degree in the induced graph <X>. For any , . If , and , then X is covered by at most (p-1) cycles of G. If furthermore , (p-1) cycles are sufficient. So we deduce the following: Let p and t () be two integers. Let G be a 2-connected graph of order n, of minimum degree at least t. If , and , then V is covered by at most cycles, where k is the connectivity of G. If furthermore , (p-1) cycles are sufficient. In particular, if and , then G is hamiltonian. Received April 3, 1998