On the two classes of high‐order convergent methods of approximate inverse preconditioners for solving linear systems

Two classes of methods for approximate matrix inversion with convergence orders p =3?2^k +1 (Class 1) and p =5?2^k ?1 (Class 2), k ≥1 an integer, are given based on matrix multiplication and matrix addition. These methods perform less number of matrix multiplications compared to the known hyperpower method or p th‐order method for the same orders and can be used to construct approximate inverse preconditioners for solving linear systems. Convergence, error, and stability analyses of the proposed classes of methods are provided. Theoretical results are justified with numerical results obtained by using the proposed methods of orders p =7,13 from Class 1 and the methods with orders p =9,19 from Class 2 to obtain polynomial preconditioners for preconditioning the biconjugate gradient (BICG) method for solving well‐ and ill‐posed problems. From the literature, methods with orders p =8,16 belonging to a family developed by the effective representation of the p th‐order method for orders p =2^k , k is integer k ≥1, and other recently given high‐order convergent methods of orders p =6,7,8,12 for approximate matrix inversion are also used to construct polynomial preconditioners for preconditioning the BICG method to solve the considered problems. Numerical comparisons are given to show the applicability, stability, and computational complexity of the proposed methods by paying attention to the asymptotic convergence rates. It is shown that the BICG method converges very quickly when applied to solve the preconditioned system. Therefore, the cost of constructing these preconditioners is amortized if the preconditioner is to be reused over several systems of same coefficient matrix with different right sides.     

Using a similarity measure for credible classification

This paper concerns classification by Boolean functions. We investigate the classification accuracy obtained by standard classification techniques on unseen points (elements of the domain, {0,1}ⁿ, for some n) that are similar, in particular senses, to the points that have been observed as training observations. Explicitly, we use a new measure of how similar a point x∈{0,1}ⁿ is to a set of such points to restrict the domain of points on which we offer a classification. For points sufficiently dissimilar, no classification is given. We report on experimental results which indicate that the classification accuracies obtained on the resulting restricted domains are better than those obtained without restriction. These experiments involve a number of standard data-sets and classification techniques. We also compare the classification accuracies with those obtained by restricting the domain on which classification is given by using the Hamming distance.     

γ-Hydroxypropyl-functionalised iron thiolate complexes: crystal and molecular structure of [{Fe2(CO)6(μ-SCH2CH2CH2OH)}2(μ4-S)]

The γ-hydroxypropyl-functionalised diiron dithiolate complex [Fe₂(CO)₆(μ-SCH₂CH₂CH₂OH)₂] is prepared upon thermolysis of Fe₃(CO)₁₂ and HO(CH₂)₃SH and further reaction with dppm (dppm = Ph₂PCH₂PPh₂) affords [Fe₂(CO)₄(μ-dppm)(μ-SCH₂CH₂CH₂OH)₂]. From the reaction of Fe₃(CO)₁₂ with dppm(S₂) a minor product is the tetrairon cluster, [{Fe₂(CO)₆(μ-SCH₂CH₂CH₂OH)}₂(μ⁴-S)], the mode of formation of which is unclear. It has been crystallographically characterised and adopts a μ⁴-S bridged double butterfly structure which is compared with other crystallographically characterised complexes of this type. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On strong unimodality of multivariate discrete distributions

A discrete function f defined on Zⁿ is said to be logconcave if for , , . A more restrictive notion is strong unimodality. Following Barndorff-Nielsen [O. Barndorff-Nielsen, Unimodality and exponential families, Commun. Statist. 1 (1973) 189-216] a discrete function is called strongly unimodal if there exists a convex function such that  if . In this paper sufficient conditions that ensure the strong unimodality of a multivariate discrete distribution, are given. Examples of strongly unimodal multivariate discrete distributions are presented.     

Photochemical reactions of <Emphasis Type="Italic">cis</Emphasis>-[(η<Superscript>4</Superscript>-NBD)M(CO)<Subscript>4</Subscript>] (NBD = norbornadiene; M = Cr,Mo) olefin complex with ligand,containing S and N donor atoms

New complexes cis-[M(CO)₄-DABRd] (M = Cr(I), Mo(II) and fac-[M(CO)₃-SAT] (M = Cr(III), Mo(IV)) have been synthesized by the photochemical reactions of cis-[(η⁴-NBD)M(CO)₄] (NBD is norbornadiene; M=Cr, Mo) with 5-(4-dimethylaminobenzylidene) rhodanine (DABRd) and salicylidene-3-amino-1,2,4-triazole (SAT) ligands and characterized by elemental analysis, FT-IR and ¹H NMR spectroscopy, and mass spectrometry. The spectroscopic studies show that the DABRd ligand acts as a bidentate ligand coordinating via both NH-(S)C=S sulfur donor atoms in I and II and SAT ligand behaves as a tridentate ligand coordinating via its all imine nitrogen-C=N-donor atoms in III and IV to the metal center. The article was submitted by the authors in English.     

An experimental study on optimization of $${\mathbf{SiO}}_{2}$$ SiO 2 /water nanofluid flows in circular minichannels

Journal of Thermal Analysis and Calorimetry - An experimental research was performed to examine the effect of hydrodynamically and thermally developing distilled water-based SiO $$_2$$ nanofluid...     

Universal sound absorption in amorphous solids: A theory of elastically coupled generic blocks

Glasses are known to exhibit quantitative universalities at low temperatures, the most striking of which is the ultrasonic attenuation coefficient Q^?1. In this work we develop a theory of coupled generic blocks with a certain randomness property to show that universality emerges essentially due to the interactions between elastic blocks, regardless of their microscopic nature.     

One‐pot three‐component synthesis of novel 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid derivatives

A simple and easy synthesis of 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid ( 3 ) has been successfully developed through a one‐pot three‐component condensation reaction of (2‐amino‐phenyl)‐oxo‐acetic acid sodium salt ( 1 ) obtained from the hydrolysis of isatin with ammonium acetate and 3‐nitrobenzaldehyde. Some novel quinazoline‐ester derivatives 4‐7 were then obtained by the reaction between the new compound 3 and various alcohols. Then, quinazoline‐amide derivatives 10‐14 were synthesized from the reaction of various amines and 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carbonyl chloride ( 8 ), obtained by the reaction of compound 3 with SOCl₂. Finally, some novel quinazoline‐azo derivatives 17‐19 were synthesized by the coupling reaction between β‐dicarbonyl compounds and the novel amino‐quinazoline derivative compound 15 , obtained by reduction of nitro‐quinazoline derivative compound 11 . Thus, a new series of quinazoline‐4‐carboxylic acid, ester, amide, and azo derivatives was synthesized and fully characterized by ¹H NMR, ¹³C NMR, IR, and mass spectrometry analysis.     

A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm

Swarm intelligence is a research branch that models the population of interacting agents or swarms that are able to self-organize. An ant colony, a flock of birds or an immune system is a typical example of a swarm system. Bees’ swarming around their hive is another example of swarm intelligence. Artificial Bee Colony (ABC) Algorithm is an optimization algorithm based on the intelligent behaviour of honey bee swarm. In this work, ABC algorithm is used for optimizing multivariable functions and the results produced by ABC, Genetic Algorithm (GA), Particle Swarm Algorithm (PSO) and Particle Swarm Inspired Evolutionary Algorithm (PS-EA) have been compared. The results showed that ABC outperforms the other algorithms.     

Allyl palladium dithiocarbamates and related dithiolate complexes as precursors to palladium sulfides

Allyl-palladium dithiocarbamate complexes, [Pd(allyl)(S₂CNR₂)], have been prepared from the addition of dithiocarbamate salts to [Pd(allyl)(μ-Cl)]₂ and TGA and DSC studies have been carried out in order to assess their potential as MOCVD precursors to palladium sulfides. For comparison [(η³-C₄H₇)Pd(S₂PPh₂)] and [Pd(S₂CNMeR)₂] (R = Bu, Hex) have also been prepared and tested as precursors. The unsymmetrical dithiocarbamate complex, [(η³-C₃H₅)Pd(S₂CNMeHex)], which has a melting point of 65 °C was selected as the best single source precursor and thin films of predominantly Pd_2.8S were deposited on glass slides. The crystal structures of [(η³-C₄H₇)Pd(S₂CNMe₂)], [(η³-C₄H₇)Pd(S₂CNPr₂)], [(η³-C₄H₇)Pd(S₂PPh₂)] and [Pd(S₂CNMeBu)₂] are reported. All except [(η³-C₄H₇)Pd(S₂CNPr₂)] show weak intermolecular S?H or Pd?H interactions.