Thermodynamics of ionization of some substituted 4-methyl-thioanilines

Ionization constants of chloro, iodo and nitro substituted 4-methyl-thioanilines were determined over the range 30° to 50° using a spectro-photometric method. The results were analyzed in terms of the Harned-Robinson equation and values of heat, free energy and entropy of ionization were calculated. The free energies are additive, except in the case of 3, 5-diiodo-4-methylthioaniline, while the heats and the entropies are not.     

Magnetic susceptibilities of orthopyroxenes in the Frantz Isodynamic separator

Frantz Isodynamic Separator was calibrated with substances of known magnetic susceptibilities. From the calibration graph, magnetic susceptibilities of the orthopyroxenes were deduced. The investigated orthopyroxenes ranged in composition from En₈₇Fs₁₃ to En₅₁Fs₄₉ and varied in magnetic susceptibilities from 12·18 to 54·49 × 10^?6 e.m.u./gram at 30° C. Magnetic susceptibilities were found to decrease with increase in the En content. A graph drawn with current strengths and the compositions of the orthopyroxenes shows a linear relationship between them.     

Spectrophotometric studies of 6-methyl pyridine-2-aldoxime-iron (II) complex

6-Methyl pyridine-2-aldoxime produces with iron (II) solution a deep red complex soluble in 50% (by volume) aqueous acetone. The complex is stable at 10–45°C. and its colour intensity does not vary between pH 7·3 and 10·0. The complex obeys Lambert-Beer’s law at 520 mµ in the concentration range of 1·12 to 28·0 p.p.m. of iron.     

Overlapping restricted additive Schwarz method applied to the linear complementarity problem with?an?H-matrix

In this paper, a restricted additive Schwarz method is introduced for solving the linear complementarity problem that involves an H ₊-matrix. We show that the sequence generated by the restricted additive Schwarz method converges to the unique solution of the problem without any restriction on the initial point. Moreover, the comparison theorem is given between different versions of the restricted additive Schwarz method by using the weighted max-norm. We also show that the restricted additive Schwarz method is much better than the corresponding additive Schwarz variants in terms of the iteration number and the execution time.     

Ideal gas thermodynamic properties of xenon compounds

The ideal gas thermodynamic functions from 100° to 1500° K have been computed for three fluorides, three oxyfluorides, and three oxides of xenon using the published spectroscopic data. The thermodynamic properties for XeF₄ and XeF₆ were compared with those reported by Weinstocket al. S^o _298·15 calculated in this work for XeF₄ is higher by 1·5 cal than the third law entropy and that obtained by Weinstocket al. This difference is attributed to the large uncertainty in the third law entropy and the set of vibrational frequencies used by Weinstocket al. For XeF₆ a more reliable and consistent set of frequenices is suggested.     

Additive and hereditary properties of graphs are uniquely factorizable into irreducible factors

A hereditary property of graphs is any class of graphs closed under isomorphism and subgraphs. Let 𝒫₁, 𝒫₂,…, 𝒫_n be hereditary properties of graphs. We say that a graph G has property 𝒫_1°𝒫_2°···_°𝒫_n if the vertex set of G can be partitioned into n sets V₁, V₂,…, V_n such that the subgraph of G induced by V_i belongs to 𝒫_i; i = 1, 2,…, n. A hereditary property is said to be reducible if there exist hereditary properties 𝒫₁ and 𝒫₂ such that ℛ = 𝒫_1°𝒫₂; otherwise it is irreducible. We prove that the factorization of a reducible hereditary property into irreducible factors is unique whenever the property is additive, i.e., it is closed under the disjoint union of graphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 44–53, 2000     

Large Deviations for Stationary Measures of Stochastic Nonlinear Wave Equations\\with Smooth White Noise

The paper is devoted to the derivation of the large deviations principle for the family of stationary measures of the Markov process generated by the flow of the damped nonlinear wave equations with vanishing white noise. One of the main novelties here is that we do not assume that the deterministic equation possesses a unique equilibrium and we do not impose roughness on the noise. We introduce a new mathematical tool called the generalized stationary measure, which, informally speaking, is a stationary measure that is not necessarily σ‐additive. We show that any Markov operator admits such a measure and use this to develop the Freidlin‐Wentzell and Khasminskii approaches to the infinite‐dimensional setting. We also extend Sowers' method when establishing exponential tightness. Some ingredients of the proof rely on rather nonstandard techniques.© 2017 Wiley Periodicals, Inc.     

On stability in the classical linear theory of fluid mixures

Summary In this paper we study the stability(1) of linear inviscid fluid mixtures. In particular, we show that thestatical stability criterion of Gibbs is both necessary and sufficient for thedynamical stability of the mixture(2), using, as our main hypotheses, only those inequalities and symmetries which are consequences of the second law of thermodynamics(3). A Dario Graffi nel suo 70° compleanno Entrata in Redazione il 28 giugno 1975.     

Oxidation of aldehydes by aqueous Ce (IV) in nitric acid

The kinetics of oxidation of acetaldehyde (at 20°, 31° and 40° C.), propionaldehyde (at 15°, 25° and 35° C.) and chloral hydrate (40°, 50° and 60° C.) by ceric nitrate in nitric acid medium [(H⁺) ≈ 0 · 5?1 · 5 M] were studied. The reactions were followed by determining rates of ceric disappearance for variations in [Ce⁴⁺], [RCHO], [H⁺], μ, temperature, etc. The stoichiometry, ΔCe⁴⁺ / Δ CH₃CHO ≈ 2 was established. The reactions were found to be 2nd Order—first order each with respect to [Ce⁴⁺] and [RCHO]. No complex formation between Ce⁴⁺ and aldehydes was observed. Neutral Ce (NO₃)₄ (H₂O)₂ and diol of the aldehyde were assumed the active species. The rate and thermodynamic data were calculated and discussed. The rates of oxidation were correlated with the structures of the aldehydes.     

Asymptotic normality of fringe subtrees and additive functionals in conditioned Galton–Watson trees

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offspring distribution defining the random tree is assumed to have expectation 1 and finite variance; no further moment condition is assumed. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 57–101, 2016     

Application of Lennard-Jones Devonshire equation of state to detonation of PETN

Kirkwood’s extension of Lennard-Jones Devonshire model for liquids, to multicomponent fluid mixtures, has been used to find out the various parameters of detonation of pentaerythritol tetranitrate (PETN), for various loading densities. The exponent of the law of adiabatic expansion of hot dense products has been determined.     

Lyapunov exponents of free operators

Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended Fuglede-Kadison determinant. We establish the existence of Lyapunov exponents, derive formulas for their calculation, and show that Lyapunov exponents of free variables are additive with respect to operator product. We illustrate these results using an example of free operators whose singular values are distributed by the Marchenko-Pastur law, and relate this example to C.M. Newman's “triangle” law for the distribution of Lyapunov exponents of large random matrices with independent Gaussian entries. As an interesting by-product of our results, we derive a relation between the extended Fuglede-Kadison determinant and Voiculescu's S-transform.     

Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven

The drying kinetics of maltodextrin DE 12 in a convection oven are modeled using Fick's second law of diffusion and following the William, Landel and Ferry (WLF) equation for the moisture and temperature dependence of the effective diffusivity. An experimental design with a temperature range from 70°C to 140°C and sample amount varying from 4 to 12 ml is used. The resulting diffusion equation describing the dynamics of moisture content is highly nonlinear and possesses Dirichlet and Neumann boundary conditions. Ordinary differential equations are added to take the time-dependent variation of temperature into account. The method of lines is applied to discretize the partial differential equation w.r.t. the space variable leading to a highly stiff and numerically unstable system of ordinary differential equations. The data fitting problem is formulated to estimate some unknown model parameters simultaneously for 18 data sets under consideration.     

Pressure and flow in two dimensional numerical bifurcation models

The finite element method has been used to solve the Navier-Strokes equations for steady flow conditions in bifurcations. The results are presented as pressure, velocity and streamline plots at different Reynolds number. The three bifurcations considered have rigid walls and bifurcation angles of 0°, 20° and 180°. For the bifurcation with branch angles 0° and 20° there is flow separation along the inner wall of the outlet branches and large spatial pressure variations, these phenomena being more pronounced at the higher Reynolds numbers. For the bifurcation with a branch angle of 180° the high pressure gradients occured at the outer corner and for the high Reynolds number a vortex formation developed downstream of this corner.     

Algorithmes stochastiques à bruit dépendant

We introduce different ways of modeling the dependency of the input noise of stochastic algorithms. We are aimed to prove that such innovations allow us to use the ODE (ordinary differential equation) method. Illustrations in the linear regression framework and in the law of the large number for triangular arrays of weighted dependent random variables are also given. We have aimed to provide results easy to check in practice. To cite this article: P. Doukhan, O. Brandière, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Thermal noise engines

In this paper, electrical heat engines driven by the Johnson-Nyquist noise of resistors are introduced. They utilize Coulomb’s law and the fluctuation–dissipation theorem of statistical physics. In these engines, resistors, capacitors and switches are the building elements. For best performance, a large number of parallel engines must be integrated to run in a synchronized fashion, and the size of an elementary engine must be at the 10 nm scale. At room temperature, in the most idealistic case, a two-dimensional ensemble of engines of 25 nm size integrated on a 2.5 × 2.5 cm silicon wafer with 10 °C temperature difference between the warm-source and the cold-sink would produce a power of about 0.5 W. Regular and coherent (correlated-cylinder states) versions of these engines are shown and both of them can operate in either four-stroke or two-stroke modes. In the idealistic case, all these engines have Carnot efficiency, which is the highest efficiency possible in any heat engine without violating the second law of thermodynamics.     

A comparison of abstract versions of deflation,balancing and additive coarse grid correction preconditioners

In this paper we consider various preconditioners for the conjugate gradient (CG) method to solve large linear systems of equations with symmetric positive definite system matrix. We continue the comparison between abstract versions of the deflation, balancing and additive coarse grid correction preconditioning techniques started in (SIAM J. Numer. Anal. 2004; 42 :1631–1647; SIAM J. Sci. Comput. 2006; 27 :1742–1759). There the deflation method is compared with the abstract additive coarse grid correction preconditioner and the abstract balancing preconditioner. Here, we close the triangle between these three methods. First of all, we show that a theoretical comparison of the condition numbers of the abstract additive coarse grid correction and the condition number of the system preconditioned by the abstract balancing preconditioner is not possible. We present a counter example, for which the condition number of the abstract additive coarse grid correction preconditioned system is below the condition number of the system preconditioned with the abstract balancing preconditioner. However, if the CG method is preconditioned by the abstract balancing preconditioner and is started with a special starting vector, the asymptotic convergence behavior of the CG method can be described by the so‐called effective condition number with respect to the starting vector. We prove that this effective condition number of the system preconditioned by the abstract balancing preconditioner is less than or equal to the condition number of the system preconditioned by the abstract additive coarse grid correction method. We also provide a short proof of the relationship between the effective condition number and the convergence of CG. Moreover, we compare the A‐norm of the errors of the iterates given by the different preconditioners and establish the orthogonal invariants of all three types of preconditioners. Copyright © 2008 John Wiley & Sons, Ltd.     

Adhesive ability of a heat-resistant double-chain polymer and the strength of CFRP based on it

The adhesive ability of a heat-resistant polyiminoquinazolindione (PIQD) binder, based on a double-chain polymer, and the physicomechanical characteristics of unidirectional CFRPs made with it are investigated. It is shown that, at room temperature, the strength of model adhesive joints (PIQD-steel wire) and of the CFRPs in shear and bending is rather low — about half of that of similar specimens based on an epoxy binder. At the same time, all their mechanical characteristics, to a large measure (50%), are retained at temperatures up to 450°C, which considerably exceeds the heat resistance of all polymer matrices used at the present time. The elastic modulus of the CFRPs in bending practically remains the same up to 450°C. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 535–546, July–August, 2008.     

Durability of polymers subjected to stretching and twisting

The durability upon subjection to stretching and twisting is compared for polymethyl methacrylate, polyethylene, and ebonite in the temperature range from ?196° to 50°C. It was shown that to an accuracy of ±10%, the maximum tensile stress may be considered responsible for decomposition.     

Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms

We consider multiclass Markovian polling systems with feedback and analyze their average performance measures. Scheduling in polling systems has many applications in computer and communication systems. We utilize the framework that has been effectively used to analyze various composite scheduling algorithms in many types of multiclass queues systematically in conjunction with the functional computation method (Hirayama in Naval Research Logistics 50:719?C741, 2003; Journal of the Operations Research Society of Japan 48:226?C255, 2005; Advances in queueing theory and network applications, pp. 119?C146, Springer, New?York, 2009a; Journal of Industrial and Management Optimization 6:541?C568, 2010). We define the conditional expected values of the performance measures such as the sojourn times as functions of the system state and find their expressions by solving some equations. Then from these expressions, we derive the average numbers of customers and the average sojourn times for all service stages of customers circulating the system. We consider their application to a packet scheduling problem where multiple categories of packets share a resource.