Large-scale Ferrofluid Simulations on Graphics Processing Units

We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the performance of the optimized AP algorithm on the GPU. The accuracy of the scheme is corroborated by comparing the results of numerical simulations with theoretical predictions

On factorization hierarchy of equations for banana Feynman amplitudes

We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with $\delta$-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First, we review the properties of the corresponding differential operators themselves, mainly their factorization properties at the equal mass locus and their form at special values of the dimension. Then we study the relation between the Fourier transform of the coordinate space equations and the Picard-Fuchs equations and show that they are related by factorization as well. The equations in question are the counterparts of the Virasoro constraints in the much-better studied theory of eigenvalue matrix models and are the first step towards building a full-fledged theory of Feynman integrals, which will reveal their hidden integrable structure.Comment: 13 page

Irreducible representations of simple Lie algebras by differential operators

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented as first order differential operators in $\frac{1}{2} \left(\dim \mathfrak{g} - \text{rank} \, \mathfrak{g}\right)$ variables. All rising generators ${\bf e}$ are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators ${\bf f}$. We present explicit formulas of this kind for the simple root generators of all classical Lie algebras

Finding a point of growth for domestic producers : focus on food products with a short shelf life

The article proves the relevance of the production of food products with a short shelf life by domestic producers, analyzes the findings of theoretical works related to the study of consumer choice and the formation of consumer habits, presents examples of successful competition between regional producers in various regions of the country with federal players. The significance of food production with a short shelf life as a point of growth for domestic business is substantiated and the opportunities and advantages of production of these types of products and the possibility of their promotion in various territories are shown.peer-reviewe

Secretory activity of gastroduodenal zone before and after cholecystectomia

Вивчено функціональні особливості секреторної активності гастродуоденальної зони до та піс­ля холецистектомії. Встановлено пригнічення ферментовидільної функції шлунка у хворих із постхолецистектомічним синдромом. З’ясовано, що наявність дуодено-гастрального рефлюксу свідчить про дуоденостаз і недостатність замикальної функції пілоричного сфінктера. У хворих видалення жовчного міхура призводить до аритмії циркадних і ультрадіадних ритмів усієї травної системи й, у тому числі, до порушень активності секреторних залоз шлунка.Изучены функциональные особенности секреторной активности гастродуоденальной зоны до и пис¬ля холецистэктомии. Установлено угнетение ферментовыводящей функции желудка у больных с постхолецистэктомический синдромом. Выяснено, что наличие дуодено- гастральной рефлюкса свидетельствует о дуоденостаз и недостаточность замыкательной функции пилорического сфинктера. У больных удаление желчного пузыря приводит к аритмии циркадных и ультрадиадних ритмов всей пищеварительной системы и, в том числе, к нарушениям активности секреторных желез желудка.Functional features of the gastroduodenal zone secretory activity before and after cholecystectomia were studied. The oppression of the stomach enzymatic secretion in patients with postcholecystectomia syndrome was established. The presence of duodeno-gastral reflux testifies to the duodenostasis and incompetence of closing function of the pyloric sphincter. Cholecystectomia entails the arrhythmia of circadian and ultradian rhythms of the whole digestive apparatus, including the derangements of the stomach secretory glands