On cross-ratio distortion and Schwarz derivative

We prove asymptotic estimates for the cross-ratio distortion with respect to a smooth or holomorphic function in terms of its Schwarz derivative.Comment: the spelling of the name `Schwarz' correcte

Invariant measures for Burgers equation with stochastic forcing

In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts all other solutions with the same forcing. This is done by studying the so-called one-sided minimizers. We also give a detailed description of the structure and regularity properties for the stationary solutions. In particular, we prove, under some non-degeneracy conditions on the forcing, that almost surely there is a unique main shock and a unique global minimizer for the stationary solutions. Furthermore the global minimizer is a hyperbolic trajectory of the underlying system of characteristics.Comment: 84 pages, published version, abstract added in migratio

Sensitive detection of photoexcited carriers by resonant tunneling through a single quantum dot

We show that the resonant tunnel current through a single energy level of an individual quantum dot within an ensemble of dots is strongly sensitive to photoexcited holes that become bound in the close vicinity of the dot. The presence of these holes lowers the electrostatic energy of the quantum dot state and switches the current carrying channel from fully open to fully closed with a high on/off ratio (> 50). The device can be reset by means of a bias voltage pulse. These properties are of interest for charge sensitive photon counting devices.Comment: 5 pages, 4 figure

Particle dynamics inside shocks in Hamilton-Jacobi equations

Characteristics of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. For nonsmooth "viscosity" solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that for any convex Hamiltonian there exists a uniquely defined canonical global nonsmooth coalescing flow that extends particle trajectories and determines dynamics inside the shocks. We also provide a variational description of the corresponding effective velocity field inside shocks, and discuss relation to the "dissipative anomaly" in the limit of vanishing viscosity.Comment: 15 pages, no figures; to appear in Philos. Trans. R. Soc. series

Perfect retroreflectors and billiard dynamics

We construct semi infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability the exit velocity is exactly opposite to the entrance velocity, and the particle's exit point is arbitrarily close to its initial position. The method is based on asymptotic analysis of statistics of entrance times to a small interval for irrational circle rotations. The rescaled entrance times have a limiting distribution in the limit when the length of the interval vanishes. The proof of the main results follows from the study of related limiting distributions and their regularity properties. © 2011 AIMSciences

Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

Core acid treatment influence on well reservoir properties in Kazan oil-gas condensate field

The research involves investigation of the influence of hydrochloric acid (HCI-12%) and mud acid ( mixture: HCl - 10 % and HF - 3 %) treatment on the Upper-Jurassic reservoir properties in Kazan oil-gas condensate field wells. The sample collection included three lots of core cylinders from one and the same depth (all in all 42). Two lots of core cylinders were distributed as following: first lot - reservoir properties were determined, and, then thin sections were cut off from cylinder faces; second lot- core cylinders were exposed to hydrochloric acid treatment, then, after flushing the reservoir properties were determined, and thin sections were prepared. Based on the quantitative petrographic rock analysis, involvin 42 thin sections, the following factors were determined: granulometric mineral composition, cement content, intergranular contacts and pore space structure. According to the comparative analysis of initial samples, the following was determined: content decrease of feldspar, clay and mica fragments, mica, clay and carbonate cement; increase of pore spaces while in the investigated samples- on exposure of rocks to acids effective porosity and permeability value range is ambiguous

Вивчення продуктів деградації хлоропромазину гідрохлориду методом рідинної мас-спектроскопії у ін’єкційних препаратах

The analysis of model samples of the drug Aminazin has been performed, its active substance is chlorpromazine hydrochloride. These model solutions were subjected to sterilization with previous exposure at room temperature. It has been found that depending on duration of the exposure during sterilization the degradation of the drug occurs in two possible ways – with formation of opalescence or without it. The schemes of degradation with formation of either one product – chlorpromazine sulfoxide, or some products – chlorpromazine sulfoxide, chlorpromazine N-oxide, nor-chlorpromazine and others have been proposed. It has been found that opalescence of solutions is caused by formation of degradation products – chlorpromazine N-oxide and norchlorpromazine that are slightly soluble in water. The analysis of model samples was performed using the liquid chromatography/mass spectrometry methods developed by the authors. In the course of analysis the molecular weights corresponding to the abovementioned products were obtained. Therefore, the experimental confirmation of the chemes of degradation proposed has been obtained. As the result of the research conducted the chromatographic method for detection of impurities using liquid chromatography/mass spectrometry has been developed, and the main ways of degradation of chlorpromazine hydrochloride in aqueous solutions have been determined. According to the result of the research the recommendations to the manufacturing process have been developed, and measures for optimizing the composition of the drug have been proposed.Проведен анализ модельных образцов препарата Аминазин, действующим веществом которого является хлорпромазина гидрохлорид. Данные модельные растворы были подвергнуты стерилизации с предварительной выдержкой при комнатной температуре. Установлено, что в зависимости от длительности экспозиции при стерилизации деградация препарата происходит по двум возможнымпутям – с образо ванием опалесценции либо без нее. Были предложены схемы деградации с образоанием либо одного продукта хлорпромазина сульфоксида, либо нескольких – хлорпромазина сульфоксида, хлорпромазина N-оксида, нор-хлорпромазина и пр. Было установлено, что опалесценция растворов вызывается образованием мало растворимых в воде продуктов деградации –хлорпромазина N-оксида, нор-хлопромазина. Анализ модельных образцов проводился методом жидкостной хроматомасс-спектрометрии по методике, разработанной авторами статьи. В ходе анализа были получены молекулярные массы, соответствующие указанным выше продуктам. Таким образом, было получено эспериментальное подтверждение предложенных схем деградации. В результате проведенной работы нами была разработана хроматографическая методика обнаружения примесей методом жидкостной хроматомасс-спектрометрии и определены основные пути деградации хлорпромазина гидрохлорида в водных растворах. Также в результате проведенных исследований были разработаны рекомендации к производственному процессу и предложены меры по оптимизации состава препарата.Проведений аналіз модельних зразків препарату Аміназин, діючою речовиною якого є хлоропромазину гідрохлорид. Вказані модельні розчини пройшли стерилізацію з попередньою витримкою при кімнатній температурі. Встановлено, що залежно від тривалості експозиції при стерилізації деградація препарату проходить за двома можливими шляхами – з утворенням опалесценції або без неї. Були запропоновані схеми деградації з утворенням або одного продукту хлоропромазину сульфоксиду, або декількох – хлоропромазину сульфоксиду, хлоропромазину N-оксиду, норхлопромазину та ін. Було встановлено, що опалесценція розчинів викликається утворенням водонерозчинних продуктів деградації – хлоропромазину N-оксиду, нор-хлопромазину. Аналіз модельних зразків проводився методом рідинної хроматомас-спектрометрії за методикою, розробленою авторами статті. Під час аналізу були отримані молекулярні маси, що відповідають вказаним вище продуктам. Таким чином, було отримано експериментальне підтвердження запропонованих схем деградації. У результаті проведеної роботи нами була розроблена хроматографічна методика виявлення домішок методом рідинної хроматомас-спектрометрії та визначені головні шляхи деградації хлоропромазину гідрохлориду у водних розчинах. Також у результаті проведених досліджень були розроблені рекомендації до виробничого процесу та запропоповані заходи з оптимизації складу препарату