Asymptotic distributions for a class of generalized LL-statistics

We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ240 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the Conditions for the Introducing Distance Learning in Russian Universities

Modern computer and Internet technologies make it possible not only to transfer educational materials to digital media, but also to implement in a remote format various teaching methods,  diagnostics,  individualization  of  educational  interests  and  trajectories,  and  much  more. In addition, modern technologies in this area allow us to do what was simply impossible within the framework of the conventional education system. But the issue of a reasonable measure of the use of these technologies and the adequate setting and implementation of tasks in this direction requires special work. The article presents the results of this kind of work carried out on the basis of a program-project approach. Although the work was carried out within the framework of the assignment of  the  FEMU  to  classical  universities  for  mathematical  education,  the  specifics  of  universities  and mathematical education were not significant. The assignment was to determine the readiness of the mathematical faculties of universities for the systematic use of distance learning through an expert survey  of  FEMU  members.  The  relevance  of  the  question  of  the  timeliness  of  the  introducing  distance learning in a particular situation, on the one hand, and the problematic nature of this issue, due to the lack of proper systemic, logical grounds for its solution, prompted the author to apply his own method, which is conceptually different from the numerous surveys and “experiences” available in literature. The application of this method (“double inversion of position” or, in other words, “double negation”: intent   – objections  – withdrawal of objections), made it possible to formulate three principal lists. The first contains an explicitly formulated framework in which the introducing distance learning makes sense; the second and third represent the research and development program necessary for the implementation of distance learning. And already on the basis of the first list, related to the current situation, a survey of experts was conducted, which made it possible to formulate the main conclusions on the problem under discussion. The results obtained fix a logical necessity that does not depend on private opinions or specific features of the situation

Cost management of a construction company based on functional cost analysis

In conditions of environmental instability and uncertainty, one of the factors for the effective functioning and development of a construction company is high-quality and continuous cost management. The cost management process is aimed at maximizing profits by increasing the efficiency of the use of all resources. It requires constant monitoring to make adjustments to the planned costs and their amounts. Cost management is impossible without careful analysis. Along with the traditional methods of cost management, it is advisable for construction companies to apply functional cost analysis, which is an effective tool for optimizing costs and the quality of production functions performance. The research studies a construction company. Particular attention in the study is paid to indirect costs due to an increase in their share in the structure of the construction products cost. Within the framework of the functional cost analysis, an ABC analysis was carried out and a Pareto curve was modelled. It allowed us to focus on the allocated cost areas and classify the processes into main, basic and supportive ones. The significance of the identified processes was determined using the paired comparisons method. The results obtained allow us to draw a conclusion about the correspondence of the share of cost items and their significance for the analyzed construction company. The research materials are of interest and practical importance for the CEOs of construction companies

Anti-criminal Education and Modern Criminalistics (According to the Materials of the International Summer Baikal Legal School)

The Author analyzes a number of documents defining the basis of the state policy of the Russian Federation in the development of legal literacy and legal awareness of citizens, in which legal education and legal information of citizens are indicated as one of the main directions for implementing such a policy. It is noted that such methods of forming a high level of legal culture of the population, traditions of respect for the law, law and order and court, honesty and integrity in general are implemented by law enforcement and judicial authorities, other state authorities and local self-government. It is emphasized that the means of legal education and legal information of the general population can be actively developed by representatives of the forensic science, including by creating a variety of printed and electronic memos, manuals, lectures, videos, posters, booklets, as well as electronic applications, multimedia presentations. Outlines the legal, theoretical and conceptual basis of this issue. Presented several proven and implemented in the practice of modern means of legal (anti-crime) education in the format of electronic mobile applications. It is emphasized that the new approach to the implementation of the above-mentioned direction of state policy is able to ensure the solution of such tasks as: synergy in the development of the sciences of the anti-criminal cycle (criminal law, criminal procedure, criminalistics, criminology, etc.); overcoming the notorious barrier between science and practice, the creation of scientifically based recommendations of an applied nature; legal education of citizens; increasing the effectiveness of countering crimes

Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities

A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements. For the class under consideration the complete group classification is performed with respect to convenient equivalence groups (generalized extended and conditional ones) and with respect to the set of all point transformations. Usage of different equivalences and coefficient gauges plays the major role for simple and clear formulation of the final results. The corresponding set of admissible transformations is described exhaustively. Then, using the most direct method, we classify local conservation laws. Some exact solutions are constructed by the classical Lie method.Comment: 23 pages, minor misprints are correcte

Improving the quality of materials for highway construction

© Medwell Journals, 2016.The study is devoted to studying the possibility of improving the quality of asphalt concrete and cement concrete for road surfaces. We have shown the interaction which occurs between the components of mixed thermoplastic elastomer and matrix of petroleum bitumen for road building. We have proved a presence of a chemical reaction between mixed thermoplastic elastomer and a bitumen matrix on unsaturated C = C bonds with formation of a lightly crosslinked polymer within polymeric-bitumen binder. We have established that an introduction of polycarboxylate superplasticizers in cement concrete composition reduces chemical shrinkage and thereby increase its physical-mechanical characteristics

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

In the paper we consider singular spectral Sturm--Liouville problem $-(py')'+(q-\lambda r)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function $p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$ is diagonal. The main goal is to prove that well-known (for smooth case) facts about number and distribution of zeros of eigenfunctions hold in general case.Comment: 7 page

Creating an interactive simulator for practicing catecholamine pathway skills

The purpose of the study is to introduce multi-stage tasks into the curriculum for a more holistic understanding of the material being studied by students.Цель исследования – введение в программу обучения многоступенчатых задач для более целостного понимания изучаемого материала