Optimal packing of convex polytopes using quasi-phi-functions

We study a packing problem of a given collection of convex polytopes into a rectangular container of minimal volume. Continuous rotations and translations of polytopes are allowed. In addition a given minimal allowable distances between polytopes are taking into account. We employ radical free quasi-phi-functions and adjusted quasi-phi-functions to describe placement constraints. The use of quasi-phi-functions, instead of phi-functions, allows us to simplify non-overlapping, as well as, to describe distance constraints, but there is a price to pay: now the optimization has to be performed over a larger set of parameters, including the extra variables used by our new functions. We provide an exact mathematical model of the problem as a nonlinear programming problem. We also develop an efficient solution algorithm which involves a starting point algorithm, using homothetic trasformations of geometric objects and efficient local optimization procedure, which allows us to runtime and memory). We present here a number of examples to demonstrate the efficiency of our methodology.Рассматривается задача упаковки выпуклых многоранников в прямоугольном контейнере минимального объема. Допускаются непрерывные трансляции и повороты многогранников. Учитываются минимально допустимые расстояния, заданные между многогранниками. Для формализвации ограничений размещения применяются свободные от радикалов квази-phi-функции и псевдонормализованные квази-phi-функции. Использование квази-phi-функций, вместо phi-функций, позволяет упростить вид ограничений непересечения многогранников и описать в аналитическом виде ограничения на минимально допустимые расстояния, заданные между многогранниками. Однако процесс оптимизации требует большего числа параметров, включая дополнительные переменные для квази-phi-функций. Строится математическая модель в виде задачи нелинейного программирования. Предлагается эффективный метод решения, включающий: алгоритм, основанный на гомотетических преобразованиях геометрических объектов для построения допустимых стартовых точек, и процедура локальной оптимизации, которая позволила значительно уменьшить размерность задачи, а также сократить вычислительные ресурсы (время и память). Приводятся результаты численных экспериментов, которые демонстрируют эффективность предложенной методологии решения задачи упаковки выпуклых многогранников.Розглядається задача упаковки опуклих багатогранників у прямокутний контейнер мінімального об’єму. При цьому багатогранники припускають безперервні повороти та трансляції. Крім того, враховуються мінімально припустимі відстані між багатогранниками. Для побудови математичної моделі задачі як задачі нелінійного програмування використовуються вільні від радикалів квазі-phi-функції. Розроблено ефективний алгоритм розв’язання, який дозволяє зменшити розмірність задачі і обчислювальні витрати. Наведено числові приклади

Dynamics of acetylcholine receptors antibody titer in myasthenia gravis

The aim was to examine the longitudinal association between myasthenia gravis clinical severity and concentration of acetylcholine receptor (AChR) antibodies to evaluate if AChR-antibody variations correlate to disease severity. Material and Methods. Antibodies were determined by enzyme immunoassay. The International Clinical Classification (MGFA) was used to grade the severity of the disease. The level of antibodies was compared with the severity of the condition and the form of the disease at the stage of diagnosis in 65 patients, as well as in repeated studies in 26 patients. Results. The titer of AChR-antibodies did not correlate with the severity of the condition, however, a direct relationship between the change in the level of acetylcholine receptor antibodies and the change in the clinical state during the course of the disease was obtained. Conclusion. Repeated AChR-antibody measurements will help to predict the clinical state of the patient and can be used to correct immunosuppressive therapy.</p

High-rate Electrochemical Performance of Nanosized LiNi0,5Mn1,5O4

Structural and electrochemical characteristics of nanosized LiNi0,5Mn1,5O4 synthesized by means of a citric acid aided route are presented. It is found that materials treated at 800 °C consist of the maximal amount of the disordered face-centered cubic phase. Galvanostatic discharge curves registered at various discharge currents (147-5800 mA·g – 1 or 1-40 C) prove the excellent high-rate performance of the samples studied. Specifically, the sample treated at 800 °С endures a load of 40 C delivering the reversible specific capacity of 34 mAh·g – 1. Such results have never been attained with LiNi0,5Mn1,5O4 electrodes prepared using standard techniques and overwhelms all existing data published to date. This remarkable result makes evident excellent prospects of non-solid-state routes for obtaining electrode materials for heavy-duty lithium-ion batteries of new generation. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3550

Early detection of cognitive impairment in patients with multiple sclerosis

The aim of the study was to examine cognitive impairment in patients with multiple sclerosis with an emphasis on the speed and efficiency of information processing. It was supposed to reveal the patterns of these disorders depending on the duration and severity of the disease. Material and methods. The study included 50 patients with established diagnosis of clinically significant multiple sclerosis, a relapsing-remitting course. The EDSS score was evaluated. Cognitive functions were assessed using SDMT and PASAT-3 tests. All patients underwent a study of cognitive evoked potential. All examined patients were divided into 2 groups depending on the duration of the disease. Results. Cognitive screening tests PASSAT and SDMT showed no correlation with the duration of the disease severity and cannot serve as a tool for screening early signs of cognitive impairment in young patients with multiple sclerosis. A significant increase in latency of the P300 potential was obtained with increasing duration and severity of the disease, which correlates with the severity of cognitive dysfunction. Conclusion. This study is the initial step in the search for a tool for screening early manifestations of cognitive impairment in patients with multiple sclerosis. In the future it is planned to expand the research with the modernization of its design.</p

Новый подход в соединении абатмента и имплантата, особенности ортопедического этапа при использовании имплантационной системы Leone exacone

The article is described to advantages and disadvantages of cone- or screw-retained abutments. A new method of abutment fixation to implant is introduced. Due to self-locking properties of the Morse cone and to the internal hexagon's resistance to torsion movements, quality of treatment improves.В статье рассмотрены основные варианты соединения абатмента и имплантата, их недостатки и преимущества. Описана новая методика фиксации абатмента за счет самоблокирующего конуса Морзе с внутренним шестигранником

COMPUTER SIMULATION OF GAMMA-RAY DETECTOR BASED ON SCINTILLATION CRYSTALS AND SILICON PHOTOMULTIPLIERS

Subject of Research. The paper considers the principles of realization of the gamma-radiation detector based on a silicon photoelectron multiplier and a scintillation crystal with the use of an optical matching scheme. Method. For studying the possible variants of detector creation, computer models were developed in the ZEMAX Software environment, describing radiation propagation process of scintillation in the crystal volume in view of the main processes taking place in the scintillation detector. The model has the same optical characteristics as cesium iodide (CsI). Main Results. Quantitative parameters of the signal and radiation losses in modeled systems were obtained. The information on radiation distribution in the photodetector plane was obtained as well. The optimal sheme for detector creation from the registration effectiveness point of view was established and its geometric parameters were determined. Practical Relevance. The development of the approach gives the possibility to solve the problem of creating highly efficient and miniature scintillation detectors at the expense of a new class of photodetectors - silicon photoelectric multipliers. The results of the research will be useful in the development of scintillation gamma spectrometers and other devices with operating principles based on the methods of scintillation spectrometry and radiometr