Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Evaluation of solubility and partition properties of ampicillin-based ionic liquids

In order to overcome the problems associated with low water solubility, and consequently low bioavailability of active pharmaceutical ingredients (APIs), herein we explore a modular ionic liquid synthetic strategy for improved APIs. Ionic liquids containing l-ampicillin as active pharmaceutical ingredient anion were prepared using the methodology developed in our previous work, using organic cations selected from substituted ammonium, phosphonium, pyridinium and methylimidazolium salts, with the intent of enhancing the solubility and bioavailability of l-ampicillin forms. In order to evaluate important properties of the synthesized API-ILs, the water solubility at 25 °C and 37 °C (body temperature) as well as octanol–water partition coefficients (Kow's) and HDPC micelles partition at 25 °C were measured. Critical micelle concentrations (CMC's) in water at 25 °C and 37 °C of the pharmaceutical ionic liquids bearing cations with surfactant properties were also determined from ionic conductivity measurements.

Indenture for Partition Wall between William Woodruff and John Plimpton

Indenture regarding an agreement for a partition wall between William Woodruff and John Plimpton, June 24, 1829.

Factorisation de la fonction de partition du modèle d'Ising en deux dimensions défini sur deux régions contiguës

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Un calcul algébrique détaillé de la fonction de partition du modèle d'Ising bidimensionnel

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.

An integrated mathematical model to evaluate nutrient partition in dairy cattle between the animal and its environment

In the past decade, a number of mechanistic, dynamic simulation models of several components of the dairy production system have become available. However their use has been limited due to the detailed technical knowledge and special software required to run them, and the lack of compatibility between models in predicting various metabolic processes in the animal. The first objective of the current study was to integrate the dynamic models of [Brit. J. Nutr. 72 (1994) 679] on rumen function, [J. Anim. Sci. 79 (2001) 1584] on methane production, [J. Anim. Sci. 80 (2002) 2481 on N partition, and a new model of P partition. The second objective was to construct a decision support system to analyse nutrient partition between animal and environment. The integrated model combines key environmental pollutants such as N, P and methane within a nutrient-based feed evaluation system. The model was run under different scenarios and the sensitivity of various parameters analysed. A comparison of predictions from the integrated model with the original simulation models showed an improvement in N excretion since the integrated model uses the dynamic model of [Brit. J. Nutr. 72 (1994) 6791 to predict microbial N, which was not represented in detail in the original model. The integrated model can be used to investigate the degree to which production and environmental objectives are antagonistic, and it may help to explain and understand the complex mechanisms involved at the ruminal and metabolic levels. A part of the integrated model outputs were the forms of N and P in excreta and methane, which can be used as indices of environmental pollution. (C) 2004 Elsevier B.V All rights reserved.

Octanol-water partition coefficients for predicting the effects of tannins in ruminant nutrition

Tannins can cause beneficial or harmful nutritional effects, but their great diversity has until now prevented a rational distinction between tannin structures and their nutritional responses. An attempt has been made to study this problem by examining the octanol-water solubilities of tannins. A relatively simple HPLC method has been developed for screening mixtures of plant tannins for their octanol-water partition coefficients (K-ow coefficients). Tannins were isolated from the fruits and leaves of different Acacia, Calliandra, Dichrostachys, and Piliostigma species, which are known to produce beneficial or harmful effects. The K-ow coefficients of these tannins ranged from 0.061 to 13.9, average coefficients of variation were 9.2% and recoveries were 107%. Acacia nilotica fruits and leaves had the highest K-ow coefficients, that is, 2.0 and 13.9, respectively. These A. nilotica products also have high concentrations of tannins. The combined effects of high octanol solubilities and high tannin concentrations may explain their negative effects on animal nutrition and health. It is known that compounds with high octanol solubilities are more easily absorbed into tissues, and it is, therefore, proposed that such compounds are more likely to cause toxicity problems especially if consumed in large quantities. According to the literature, tannins in human foods tend to have low K-ow coefficients, and this was confirmed for the tannins in Piliostigma thonningii fruits. Therefore, unconventional feeds or browse products should be screened not only for their tannin concentrations but also for low octanol-water partition coefficients in order to identify nutritionally safe feeds and to avoid potentially toxic feeds.