Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD

ЄВРОПЕЙСЬКІ СТАНДАРТИ ОСВІТИ В СИМУЛЯЦІЙНІЙ МЕДИЦИНІ. ДОСВІД ОДЕСЬКОГО НАЦІОНАЛЬНОГО МЕДИЧНОГО УНІВЕРСИТЕТУ

The aim of the work – to highlight the experience of the Odesa National Medical University in the field of simulation medicine.The main body. In January 2014, on the basis of the Odesa National Medical University, the first in Ukraine Educational-Innovation Center of Practical Training of а Doctor was created on the territory of Ukraine, with the most modern equipment, analogues which do not exist in the country. The training uses techniques such as modeling scenarios of different difficulty levels, hybrid simulation, “standardized patient”, etc. The Center coordinates its work with the world’s leading centers of simulation training technology and rightly claims to be a basic status for improving skills, qualifications and retraining of doctors from all regions of Ukraine.Conclusions. The main task of modern secondary, higher and postgraduate medical education is to create conditions for students to develop a wide range of competences and firmly fixed practical skills without risking harm to the patient. Just these goals set forth a simulation medicine, which has been particularly active in recent years.Мета роботи – висвітлити досвід Одеського національного медичного університету в галузі симуляційної медицини.Основна частина. В січні 2014 року на базі Одеського національного медичного університету було створено перший на території України Навчально-інноваційний центр практичної підготовки лікаря, з найсучаснішим обладнанням, аналогів якому не існує в країні. В навчанні використовуються такі методики, як моделювання сценаріїв різного рівня складності, гібридна симуляція, “стандартизований пацієнт” та ін. Центр координує свою роботу з провідними у світі центрами симуляційних технологій навчання і по праву претендує на статус базового для підвищення навичок, кваліфікації та перепідготовки лікарів з усіх регіонів України.Висновки. Основним завданням сучасної середньої, вищої і післядипломної медичної освіти є створення умов для розвитку в учнів широкого спектра компетенцій і міцно закріплених практичних навичок без ризику нанесення шкоди пацієнту. Якраз такі цілі і ставить перед собою симуляційна медицина, яка отримала особливо активний розвиток в останні роки

High orders of perturbation theory: are renormalons significant?

According to Lipatov, the high orders of perturbation theory are determined by saddle-point configurations (instantons) of the corresponding functional integrals. According to t'Hooft, some individual large diagrams, renormalons, are also significant and they are not contained in the Lipatov contribution. The history of the conception of renormalons is presented, and the arguments in favor of and against their significance are discussed. The analytic properties of the Borel transforms of functional integrals, Green functions, vertex parts, and scaling functions are investigated in the case of \phi^4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of \phi^4 theory.Comment: 28 pages, 8 figures include

Повышение эффективности статистического подхода к обработке данных контроля технологического процесса транспорта нефти

Тема научной работы выбрана согласно стратегии совместного сотрудничества РФ и КНР, в которой возрастают требования к эффективности использования нефтетранспортных предприятий. Целью данной дипломной работы является изучение котроля техгологического процесса во времени на примере транспорта жидкости, при помощи метода контрольных карт Шухарта, метод главных компонент и стандарт статистика. В данной работе был произведен расчет и рассмотрена возможность осуществления технологического контроля при мониторинге многопараметрового процесса транспорта жидкости по трубопроводу.The theme of the scientific work is selected according to the strategy of joint cooperation between the Russian Federation and the PRC, in which the requirements to the effectiveness of the use of oil transportation enterprises are increasing. The purpose of this thesis is to study the control of the technological process in time using the example of fluid transport, using the method of Shewhart control charts, the method of main components and the standard statistic. In this paper, a calculation was made and the possibility of implementing technological control in monitoring a multi-parameter fluid transport process through a pipeline was considered

Magnetoresistivity in a Tilted Magnetic Field in p-Si/SiGe/Si Heterostructures with an Anisotropic g-Factor: Part II

The magnetoresistance components $\rho_{xx}$ and $\rho_{xy}$ were measured in two p-Si/SiGe/Si quantum wells that have an anisotropic g-factor in a tilted magnetic field as a function of temperature, field and tilt angle. Activation energy measurements demonstrate the existence of a ferromagnetic-paramagnetic (F-P) transition for a sample with a hole density of $p$=2$\times10^{11}$\,cm$^{-2}$. This transition is due to crossing of the 0$\uparrow$ and 1$\downarrow$ Landau levels. However, in another sample, with $p$=7.2$\times10^{10}$\,cm$^{-2}$, the 0$\uparrow$ and 1$\downarrow$ Landau levels coincide for angles $\Theta$=0-70$^{\text{o}}$. Only for $\Theta$ > 70$^{\text{o}}$ do the levels start to diverge which, in turn, results in the energy gap opening.Comment: 5 pages, 6 figure

On the classical capacity of quantum Gaussian channels

The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.Comment: 10 pages, IOP style. v2: minor corrections, close to the published versio