Discussion of thermodynamic data obtained by adsorption gas chromatography of hydrocarbons on carbograph 4

Summary A new graphitized carbon black, Carbograph 4, with a specific surface area of 240 m² g⁻¹ was studied in terms of enthalpy, entropy and free energy of adsorption, determined by gas chromatographic method on a series of alkanes (C₂−C₆) and on benzene. The changes in the isosteric heat and entropy of adsorption when a non-polar stationary phase (squalane) was added to the adsorbent were also investigated. The data obtained are discussed and compared to those present in the literature for other graphitized carbon blacks. Some examples of separations obtained with Carbograph 4 are reported.     

Enzyme-mediated synthesis of EEHP and EMHP,useful pharmaceutical intermediates of PPAR agonists

A new scaleable synthetic route to the title compounds has been developed. The reaction pathway is based on the α-chymotrypsin-catalysed hydrolysis of the racemic ethyl 2-ethoxy-3-(p-methoxyphenyl)propanoate or of the racemic ethyl 2-methoxy-3-(p-methoxyphenyl)propanoate to give the corresponding resolved (S)-esters with excellent ee. The acids were easily separated from the (S)-esters by a simple acid–base work-up. The overall yields of 1 and 2 were 16% and 17%, respectively.     

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature ϑ, an evolution equation for the phase change parameter χ, including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable u. The main novelty of the model is that the equations for χ and u are coupled in such a way as to take into account the fact that the properties of the viscous and of the elastic parts influence the phase transition phenomenon in different ways. However, this brings about an elliptic degeneracy in the equation for u which needs to be carefully handled. First, we prove a global well-posedness result for the related initial-boundary value problem. Secondly, we address the long-time behavior of the solutions in a simplified situation. We prove that the ω-limit set of the solution trajectories is nonempty, connected and compact in a suitable topology, and that its elements solve the steady state system associated with the evolution problem. Dedicated to Jürgen Sprekels on the occasion of his 60th birthday     

The double cascade as a necessary mechanism for the instability of steady equivalent-barotropic flows

Summary In this paper we show that for a large class of steady solutions of the two-dimensional Euler equation and of the equation of conservation of potential vorticity for equivalent-barotropic flows, instabilities can grow only if their energy concentrates at length scales larger than that of the steady state. This possible growth of energy at large scales is accompanied by a corresponding growth of enstrophy at small scales. Such a distribution of energy and enstrophy, which is well known in the different context of two-dimensional turbulence, is therefore found to constitute a necessary mechanism for instability.

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Riassunto In questo lavoro mostriamo che, per una vasta classe di soluzioni stazionarie dell'equazione di Eulero bidimensionale e dell'equazione della conservazione della vorticità potenziale per flussi quasi geostrofici, le instabilità possono crescere solo se la loro energia si concentra a scale con lunghezza caratteristica piú grande di quella della soluzione stazionaria. Questa possibile crescita di energia a grande scale è accompagnata da una corrispondente crescita di enstrofia a piccola scala. Tale distribuzione di energia ed entrofia, ben nota in turbolenza bidimensionale, si dimostra essere un meccanismo necessario per l'instabilità.

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Резюме В этой работе мы показываем, что для большого класса стационарных решений двумерного уравнения Эйлера и уравнения сохранения потенциальной завихренности для эквивалентных баротропных потоков неустойчивости могут возрастатъ толъко в том случае, если их энергия концентрируется на масштабах с длинами, много большими, чем характерные длины стационарного состояния. Это возможное увеличение энергии на больших масштабах сопровождается соответствующим ростом ?энстрофии? на малых масштабах. Следовательно, указанное распределение энергии и ?энстрофии?, хорошо известное в двумерной турбулентости, представляет необходимый механизм для неустойчивости.

     

Bounds in Multistage Linear Stochastic Programming

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.     

Combining Gene Expression Profiles and Drug Activity Patterns Analysis: A Relational Clustering Approach

The combined analysis of tissue micro array and drug response datasets has the potential of revealing valuable knowledge about various relations among gene expressions and drug activity patterns in tumor cells. However, the amount and the complexity of biological data needs appropriate data mining models in order to extract interesting patterns and useful information. The ultimate goal of this paper is to define a model which, given the gene expression profile related to a specific tumor tissue, could help in selecting a set of most responsive drugs. This is accomplished through an integrated framework based on a constraint-based clustering algorithm, called Relational K-Means, which groups cell lines using drug response information and taking into account cell-to-cell relationships derived from their gene expression profiles.     

Discussion of thermodynamic data obtained by adsorption gas chromatography of hydrocarbons on a new graphitized carbon black with a high specific surface area

Summary A new graphitized carbon black (Carbograph 5) with a specific surface area (560 m² g⁻¹) greater than those of commerically available graphitized carbons was studied by gas chromatography to determine the enthalpy, entropy, and free energy of adsorption of a series of alkanes (C₂−C₆). The adsorption properties were also investigated by considering changes in the isosteric heats and entropies of adsorption when a nonpolar stationary phase (squalane) was added to the adsorbent. The data obtained are discussed and compared with literature values for other graphitized carbon blacks.     

Phase transitions for random walk asymptotics on free products of groups

Suppose we are given finitely generated groups Γ₁,…,Γ_m equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic or algebraic terms as singular terms up to sufficiently large order (except for some degenerate cases). We consider transient random walks on the free product Γ₁* … *Γ_m and give a complete classification of the possible asymptotic behaviour of the corresponding n‐step return probabilities. They either inherit a law of the form ?^nδn log n from one of the free factors Γ_i or obey a ?^nδn^?3/2‐law, where ? < 1 is the corresponding spectral radius and δ is the period of the random walk. In addition, we determine the full range of the asymptotic behaviour in the case of nearest neighbour random walks on free products of the form $\mathbb{Z}^{d_1}\ast \ldots \ast \mathbb{Z}^{d_m}Suppose we are given finitely generated groups Γ₁,…,Γ_m equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic or algebraic terms as singular terms up to sufficiently large order (except for some degenerate cases). We consider transient random walks on the free product Γ₁* … *Γ_m and give a complete classification of the possible asymptotic behaviour of the corresponding n‐step return probabilities. They either inherit a law of the form ?^nδn log n from one of the free factors Γ_i or obey a ?^nδn^?3/2‐law, where ? < 1 is the corresponding spectral radius and δ is the period of the random walk. In addition, we determine the full range of the asymptotic behaviour in the case of nearest neighbour random walks on free products of the form $\mathbb{Z}^{d_1}\ast \ldots \ast \mathbb{Z}^{d_m}$. Moreover, we characterize the possible phase transitions of the non‐exponential types n log n in the case Γ₁ * Γ₂. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012