A numerical study of an MPI/OpenMP implementation based on asynchronous threads for a three-dimensional splitting scheme in heat transfer problems

We present the results of a study of the parallel algorithms based on MPI and OpenMP for vector splitting schemes in heat transfer problems. We compare the three parallel implementations: MPI, “simple” MPI/OpenMP (#pragma omp directives applied to MPI-based code), and MPI/OpenMP with “postman” threads. The main idea of the last algorithm is to assign one thread within each computational node to perform the data transfer. This approach allows us to implement overlapping of useful computations and data transfer. The results show that the introducing postman threads can significantly improve the performance of an MPI/OpenMP implementation; nevertheless, for the considered class of numerical algorithms, it is more reasonable to use an MPI implementation.     

Averages of Ramanujan sums: note on two papers by E. Alkan

We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd’s, the Gamma function, the Bernoulli polynomials, and binomial coefficients.     

Ramanujan complexes and high dimensional expanders

Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last four decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various efforts made in recent years to generalize these notions from graphs to higher dimensional simplicial complexes.     

Acidity function in dipolar aprotic media

The H₀ acidity function has been determined for hydrochloric and trichloroacetic acids in dimethyl sulphoxide (DMSO) and acetonitrile using three amine class of indicators. The variation of H₀ with solvent composition at a fixed concentration of 0.1 M HCI in DMSO-water, acetonitrile-water and DMSO acetonitrile mixtures was also studied. Approximate medium effects on the proton in all these solvents were computed from the H₀ data and the results are discussed.     

An OpenMP version of the parallel algorithm for calculation of unsteady gas flow through porous objects with energy sources: Analysis and application

Gas flows in the gravity field through the porous objects with energy sources, which may originate from the natural or man-caused disasters, are investigated. An OpenMP version of the parallel algorithm has been developed for calculating unsteady 2D gas flows through porous self-heating media of complex subsurface geometries. The structure of the sequential algorithm and the transition from it to the OpenMP version are described; the performance and efficiency of parallelization are analyzed. Unsteady gas flows through axisymmetric porous self-heating objects with a partial closure of the object outlet (with a top cover) are investigated by means of the developed parallel algorithm. The influence of the partial closure of the object outlet on the cooling process of the porous objects with a nonuniform distribution of heat sources is analyzed.     

A cellular-automata model of population dynamics of three species of organisms in Lake Baikal

A cellular automata model of population dynamics of three species of organisms in Lake Baikal is proposed and investigated. Each species is subdivided into age and prey-predator groups. There are eight groups altogether. The model takes into account the spatial distribution of the organisms, seasonal birth rate variation, possible habitat pollution, and water streams. A computational experiment has been carried out for pollution in a southern area of Lake Baikal. It demonstrates that the population dynamics tends to an oscillating process with a period of one year. The minimum pollution at total extinction and maximum pollution not affecting the population dynamics are estimated. The model has been verified with production-to-biomass and occurrence frequency ratios.     

Thermodynamics of binary liquid mixtures

Excess volumes, V^E, of binary liquid mixtures (1) Toluene-Bromo-benzene, (2) Toluene-Nitrobenzene, (3) Toluene-Cyclohexanone, (4) Cyclo-hexane-Nitrobenzene, (5) Cyclohexane-Cyclohexanone were measured at 30° C. The results were analysed in terms of Flory’s theory. It is found that the theory, in general, is applicable to the mixtures studied.     

Sorption-desorption hysteresis in fibrous silica gel (Santocel C) with isomeric monohydric aliphatic alcohols

By employing the quartz fibre spring technique, sorption-desorption hysteresis at 35° has been studied of Iso-propyl, Iso-Butyl, Sec-Butyl, Tert-Butyl, Active Amyl and Iso-Amyl alcohols on fibrous silica gel (Santocel C) activated at 250°. The isotherms of all the alcohols have clearly defined “knees”. By the application of BET theory, the monolayer capacities are determined. Knowing the specific surface area of fibrous silica gel, assuming oriented sorption of the isomeric alcohols with the OH group attached to surface; the cross-sections of the alcohol molecules are calculated. Excepting Iso-Propyl and Sec-Butyl alcohols, all others have cross-sections greater than that of normal aliphatic alcohols. These higher values are to be expected in view of the side CH₃ groups. The exceptional behaviour of Iso-Propyl and Sec-Butyl alcohols is not clear. Permanent and reproducible hysteresis loops have been obtained in all the cases. Cohan’s theory of hysteresis cannot explain the observations satisfactorily. Cavity theory however explains all the cases of hysteresis. The shapes of the isotherms of the different alcohols in the high relative vapour pressure region indicate a variation in contact angles of the alcohols.     

Analysis of Operator Models Arising in Problems of Hereditary Mechanics

The correct solvability of initial-value problems for integrodifferential equations with unbounded operator coefficients in Hilbert spaces is determined. Numerous problems of hereditary mechanics and thermal physics have motivated the study of such equations. Models taking into account a Kelvin–Voight friction are considered. A spectral analysis of the operator functions, which are the symbols of integro-differential equations considered in this paper, is made.     

Pure Cognitivism and Beyond

The article begins with Jonathan Dancy’s attempt to refute the Humean Theory of Motivation. It first spells out Dancy’s argument for his alternative position, the view he labels ‘Pure Cognitivism’, according to which what motivate are always beliefs, never desires. The article next argues that Dancy’s argument for his position is flawed. On the one hand, it is not true that desire always comes with motivation in the agent; on the other, even if this was the case, it would still not follow that desire is identical with the state of being motivated. When this negative work is done, the article turns to some positive, albeit admittedly tentative remarks about what sort of cognitivist theory of motivation one should endorse. The aim at this point is not to present a brand new theory, but rather to sketch an alternative that stems from what Dancy himself says and is in line with many of his endorsed commitments in other areas. In this way, by moving beyond Pure Cognitivism, the paper sketches a different, but still ‘Dancyesque’ theory of motivation.     

Faraday rotation tensor-extraction of components

This paper reports methods of obtaining the components of Faraday rotation tenser in anisotropic crystals, using longitudinal and transverse Faraday rotation along the optic axis. It is found that in crystals belonging to triclinic, monoclinic and orthorhombic symmetry, one can get 6 out of 9, 3 or 4 out of 5, and 2 out of 3 components respectively. In the case of uniaxial crystals only 1 component can be obtained. By measuring Faraday rotation in a randomly oriented polycrystal one more component in all the above classes can be obtained.     

(n + 1)-ary derivations of semisimple Filippov algebras

The structure of generalized and (n+1)-ary derivations of simple and semisimple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero is described. An example of a semisimple ternary Mal’tsev algebra is given which is not a Filippov algebra and admits a nontrivial 4-ary derivation.     

A branch-and-bound algorithm for the coupled task problem

The coupled task problem is to schedule jobs on a single machine where each job consists of two subtasks and where the second subtask has to be started after a given time interval with respect to the first one. The problem has several applications and is NP-hard. In this paper we present a branch-and-bound algorithm for this problem and compare its performance with four integer programming models.     

Integer valued means

In this paper, starting with the work of Kolmogorov on continuous means, we define the four properties, Symmetry, Internality, Monotonicity, and Associativity that a discrete mean should satisfy. An extremal mean is then a (discrete) mean whose output depends only on the maximum and minimum of the input set. We prove that any integer mean must be extremal.     

A simple proof of Ramanujan’s summation of the1ψ1

A simple proof by functional equations is given for Ramanujan’s₁ ψ ₁ sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.     

Viscosities of binary solutions of non-electrolytes

Viscosities and molar volumes of binary solutions,viz., Toluene-Nitrobenzene, Toluene-Bromobenzene, Toluene-Cyclohexanone, Cyclohexane-Cyclohexanone, Cyclohexane-Nitrobenzene, Cyclohexane-Acetic acid, Cyclohexane-Propionic acid and Cyclohexane-Butyric acid have been measured. The experimental results have been discussed in terms of viscosity-composition relations developed for binary solutions by Grunberg and Nissan and Katti and Chaudhri.     

Effect of UV irradiation on the structure of cotton fiber

The effect of UV irradiation on the structure of 5595-V brand cotton fiber was studied. Photodestruction was shown to be accompanied by a reduction in crystallinity.     

Approximation by Linear Combinations of Complex Phillips Operators in Compact Disks

In the present article we find direct quantitative estimate for approximation of complex valued functions by linear combinations of the complex Phillips operators. Here we extend the recent results of Gal and Gupta (Mathematics without boundaries; Surveys in Interdisciplinary Research, 2014). We have been able to achieve the better approximation for the complex Phillips operators.     

Solas cycle theory of pulsars

The plausibility of the Solar Cycle type of mechanism for pulsar phenomenon is examined. The relevant time scales are found to be within the range of the observed pulsar periods.