We construct an example of blow-up in a ”ow of min-plus linear operators arising as solution operators for a Hamilton…Jacobi equation @S/@t+|∇S|/ + U(x, t) = 0, where > 1 and the potential U(x, t) is uniformly bounded together with its gradient. The construction is based on the fact that, for a suitable potential de“ned on a time interval of length T, the absolute value of velocity for a Lagrangian minimizer can be as large as O(log T)2−2/. We also show that this growth estimate cannot be surpassed. Implications of this example for existence of global generalized solutions to randomly forced Hamilton…Jacobi or Burgers equations are discussed.
The 8th conference of the European Society for Fuzzy Logic and Technology, EUSFLAT-2013, took place in Milan, the industrial and business capital of Italy. The EUSFLAT 2013 Conference was hold at the premises of the University of Milano-Bicocca, Milan, Italy from September 11th to September 13th, 2013. The aim of the conference is to bring together theoreticians and practitioners working on fuzzy logic, fuzzy systems, soft computing and related areas. It provide a platform for the exchange of ideas among scientists, engineers and students.
Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.
Our approach to the problem of charge carrier transport in homogeneous polymers assumes carrier hopping on a densely packed manifold of transport (hopping) centers retaining the short-range order of the respective single crystal. The central idea, which distinguishes it from the Bassler’s disorder theory, is that the energy scatter concerns only a small fraction of hopping centers, which begin to act as traps. The majority of isoenergetic centers build up a transfer band with microscopic mobility µ0 equal to that in the respective single crystal. The origin of the energy scatter (and traps themselves) is ascribed to the elementary voids of the fluctuation free volume forming an association with the normal hopping centers.
В главе рассматривается установление дипломатических отношений между Испанией и Россией и оценивается роль Петра I в этом процессе. Особое внимание уделяется развитию торговых отношений между двумя странами. В тексте использованы новые архивные документы.
Each developing country tries to catch up with the developed world. Unfortunately, only few economies were able to reach this purpose during last sixty years. Well-known Gershenkonђs argument - «advantage of backwardness» - does not work properly in most cases [Gershenkon, 1962]. Though imitations of technologies and governance methods are much cheaper than innovations, the imitation process is also costly and requires sophisticated approaches of choosing and harmonizing different kinds of economic policies.
The presentation considers the problem of the academic heterogeneity among universities freshmen. This problem is widely discussed in circumstances of demographic decline when higher education becomes widespread. As a result differentiation of universities based on the quality of students' freshmen arises: some universities admit predominately high-scored students, while the others have a large variation in students’ preparation level. Universities have to work with non-uniform contingent of students. In Russia the Unified State Exam (USE) is used to admit students to the universities. There are two obligatory exams (Mathematics and Russian language) and different optional exams which students can choose depending on their future direction of study. Scores for USE are the only basis for students’ admission to universities. The points of interest are simultaneously the quality of admission and its heterogeneity. Heterogeneity implies differences in the student’s USE scores in one university. The data base includes USE scores of all students enrolled in all universities in 2011-2012 in the context of different majors. The procedure of academic heterogeneity investigation has been developed with the 5-points scale of heterogeneity levels. There are two types of issues in this research. The first one includes the analysis of academic heterogeneity indicators over years and the classification of universities based on their heterogeneity. The second issue concerns intra-university level and includes the following points: • Identification of factors that influence academic heterogeneity of enrolled students • Analysis of heterogeneity in the context of different majors • Analysis of the dynamics of academic heterogeneity over the years • The university contribution to the dynamics of heterogeneity during the period of education. • Recommendations for dealing with heterogeneous contingent of students. For assessing student’s heterogeneity traditional statistical methods were applied as well as mathematical modeling based on Item Response Theory (IRT). The use of IRT methods allows us to place all the data on the unique metric scale, construct classification of universities on the quality of admission and assess heterogeneity. Despite the differences in the systems of state exams and the academic selectivity in various countries the methods developed can be used to assess the heterogeneity of university freshmen in each country.