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A new mechanism of neutron acceleration is studied experimentally in detail for cold neutrons passing through the accelerated perfect crystal with the energies close to the Bragg one. The effect arises due to the following reason. The crystal refraction index (neutron–crystal interaction potential) for neutron in the vicinity of the Bragg resonance sharply depends on the parameter of deviation from the exact Bragg condition, i.e. on the crystal–neutron relative velocity. Therefore the neutrons enter into the accelerated crystal with one neutron–crystal interaction potential and exit with the other. Neutron kinetic energy cannot vary inside the crystal due to its homogeneity. So, after passage through such a crystal, neutrons will be accelerated or decelerated because of the different energy change at the entrance and exit crystal boundaries.

A class of model-robust optimal designs, based on an extension of the standard optimality criteria to cases where there exist some prior information on the validity of a response function, is considered. Under this set-up, the concept of the “model validity range” is introduced and explored. A necessary condition for optimality is obtained for the determinant criterion ( D -optimality in the classical case). A modified version of this criterion is proposed and discussed. The corresponding results provide upper and low bounds for the original problem and help to construct approximate solutions, when contamination is relatively small. Optimal designs for simple but commonly used regression models are obtained and studied.

Russian Abstract: В результате выполнения данной работы были выполнены следующие задачи:1. Выполнен краткий обзор законодательства в части функционирования корпоративных пенсионных систем в Российской Федерации;2. Рассмотрены основные термины и определения, используемые в сфере корпоративного пенсионного обеспечения;3. Проанализированы корпоративные пенсионные системы таких стран, как США, Великобритания, Германия, Франция, Бельгия, Ирландия, Новая Зеландия, Южная Корея, Китай, Гонконг, Тайвань, Япония, Мексика и Бразилия;4. Выделены и рассмотрены ключевые мировые тенденции в развитии корпоративных пенсионных систем;5. Проведен анализ развития корпоративных пенсионных систем в Российской Федерации в 1990-2000-ые гг., в т. ч. изменение основных характеристик;6. Выполнен анализ рынка корпоративных пенсионных систем в Российской Федерации;7. Рассмотрены и проанализированы основные проблемы, препятствующие развитию корпоративных пенсионных систем в Российской Федерации;8. Сформулированы ключевые предложения по развитию корпоративных пенсионных систем в Российской Федерации, с учетом мирового опыта и рекомендаций авторитетных международных организаций, таких как Организация экономического сотрудничества и развития, Международная организация по стандартизации, Международная ассоциация страховых надзоров и др.9. Основные результаты проведенной работы будут применяться при формировании предложений по созданию механизмов и стимулов для создания и развития корпоративных пенсионных систем в Российской Федерации. English Abstract: This paper focused on the analysis of the following tasks:1. An overview of legislation in terms of the functioning of the corporate pension system in the Russian Federation was performed;2. The basic terms and definitions used in corporate pension schemes were overviewed;3. Review of corporate pension schemes in countries such as USA, UK, Germany, France, Belgium, Ireland, New Zealand, South Korea, China, Hong Kong, Taiwan, Japan, Mexico and Brazil were analyzed;4. Review of key global trends in the development of corporate pension systems were highlighted and addressed;5. Analysis of the corporate pension system in the Russian Federation in 1990-2000-s was performed, including the change of the basic characteristics;6. Analysis of the corporate pension system in the Russian Federation;7. Analysis os issues hindering the development of the corporate pension system in the Russian Federation;8. Provide key proposals for the development of the corporate pension system in the Russian Federation, taking into account international experience and recommendations of international organizations such as the Organization for Economic Cooperation and Development, the International Organization for Standardization, International Association of Insurance Supervisors and others.9. Main results of this work will be used in the formation of proposals for the establishment of mechanisms and incentives for the creation and development of the corporate pension system in the Russian Federation.

Russian Abstract: Цель настоящей научно-исследовательской работы - разработка и обоснование предложений по модернизации пенсионной формулы для расчета страховой части трудовой пенсии по старости с учетом стимулирования более позднего выхода на пенсию, совершенствованию системы формирования соответствующих пенсионных прав и связанных с этим мер, позволяющих повысить эффективность пенсионной системы в рамках имеющихся социально-демографических, экономических и институциональных ограничений. В результате выполненной работы была разработана и обоснована новая пенсионная формула для расчета страховой пенсии учетом стимулирования более позднего выхода на пенсию, разработаны предложения совершенствованию механизму финансирования пенсионной системы, также сформулированы меры, направленные на ее оптимизацию. English Abstract: The goal of this study is a development and a justification of proposals for the modernization of pension formula for calculation of the insurance part of retirement pension based on stimulation of later retirement, improvement of system that forms pension rights and linked measures allowing to increase of effectiveness of pension system within given social, demographic, economical and institutional restrictions. The main result of this study is a development of new pension formula for calculation of pension based on stimulation of the later retirement, proposals for improvement of financing of pension system and formulating of measures for its optimization.

A new class of model-robust optimality criteria, based on the mean squared error, is introduced in this paper. The motivation is to find designs when the researcher is more concerned with controlling the variance than the bias, or vice versa. The set of criteria proposed here is also appealing from a mathematical perspective in the sense that, unlike the Box and Draper (1959, J. Amer. Statist. Assoc. 54, 622–654), criterion, they can be imbedded in the framework of convex design theory and, hence, facilitate the search for globally optimal designs. The basic idea is to minimize a convex function of the bias part of the mean squared error subject to a convex constraint on the variance part, or vice versa. Equivalence theorems are derived and examples for the linear and quadratic regression problems are provided.

In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their “classical” treatment.

This is an attempt to discuss various approaches developed in experimental design when constraints are imposed. These constraints may be on the total cost of the experiment, the location of the supporting point, the value of auxiliary objective functions, and so on. The basic idea of the paper is that all corresponding optimization problems can be imbedded in the convex theory of experimental design. Part 1 is concerned with the properties of optimal designs, while Part 2 is devoted mainly to numerical methods. We have tried to avoid details, emphasizing ideas rather than technicalities. This is not intended as a literature review. The authors subjectively surely left many excellent papers behind.

The shape of the plaque pH-profile after consumption of a food item determines the food's potential caries risk. This and related facts have caused an increased interest in measurements of plaque pH-profiles during the last decade. A standard design for these measurements is to take equally spaced observations over a certain period of time. The theory of optimal experimental design gives methods for positioning the measurements of a pH-profile in an optimized way. The objective is to minimize the effort given a desired precision of the estimated profile characteristics or to maximize the precision given the number of measurements. We show that a reduction in the number of measurements up to 50 per cent or a respective improvement in precision of the estimates as compared to standardly applied designs is possible. This implies less inconvenience for the subjects and better compliance with the needs of investigation. Our study is intended to demonstrate the applicability of the theory of optimal experimental design which has the potential to improve the efficiency of medical research.

The purpose of this paper is to investigate methods for the design of optimal dynamic experiments. In Section 2, we introduce notation and a determinant criterion for dynamic experiments. In Section 3, optimal dynamic designs are constructed analytically in a number of simple cases. As will be seen, the dimension of the design problem increases with the dimension of the control vectors (equivalently, the response vector). In Section 4, we discuss the use of suitable parameterizations of the control variable trajectories to reduce the dimensionality of the optimization problem. The relationship between the design of optimal dynamic experiments and the results developed for marginally restricted designs is considered in Section 5. Numerical methods are discussed in Section 6. We close, in Section 7, with an extension of the methodology to the case where one or more linear combinations of the response trajectory is observed for each control trajectory.