Точки, прямі, площини,....аксіоми і теореми: введення в евклідову геометрію

Посилаючись на поняття математичної структури, доповнено істинно важливими аспектами, роз’яснено схему розбудови теорії евклідової геометрії на основі аксіоматики 0.В. Погорєлова, розкрито науковий стиль подання системи аксіом, продемонстровано методичні особливості строго логічного наповнення підручника фактами

Asymptotic behavior of Generalized Processor Sharing with long-tailed traffic sources

We analyze the asymptotic behavior of long-tailed traffic sources under the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing, have emerged as an important mechanism for achieving differentiated quality-of-service in integrated-services networks. Under certain conditions, we prove that in an asymptotic sense an individual source with long-tailed traffic characteristics is effectively served at a constant rate, which may be interpreted as the maximum feasible average rate for that source to be stable. Thus, asymptotically, the source is only affected by the traffic characteristics of the other sources through their average rate. In particular, the source is essentially immune from excessive activity of sources with 'heavier'-tailed traffic characteristics. This suggests that GPS-based scheduling algorithms provide an effective mechanism for extracting high multiplexing gains, while protecting individual connections

Nonparametric Analysis of Extremes on Web Graphs : PageRank Versus Max-Linear Model

We analyze the cluster structure in large networks by means of clusters of exceedances regarding the influence characteristics of nodes.As the latter characteristics we use PageRank and the Max-Linear model and compare their distributions and dependence structure. Due to the heaviness of tail and dependence of PageRank and Max-Linear model observations, the influence indices appear by clusters or conglomerates of nodes grouped around influential nodes. The mean size of such clusters is determined by a so called extremal index. It is related to the tail index that indicates the heaviness of the distribution tail. Wie consider graphs of Web pages and partition them into clusters of nodes by their influence

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Not AvailableCastor being a perennial, cross-pollinated, sexually polymorphic crop with high environmental sensitivity, initial plant breeding efforts were restricted to plant height and duration. Domestication of a wild, perennial crop to an annual crop of medium plant height and duration is the first success. Further, development of a two-line breeding system and standard seed production technology led to successful commercial exploitation of heterosis. Being a monotypic genus, diversification of parental base is restricted to intra-generic, intraspecific, or inter-varietal hybridization. Phenotypic expression is highly plastic and varies with locations and seasons. Majority of the morphological characters are monogenic, independently assorted with very limited linkages among the traits. However, information on genetics of major morphological characters is scattered in several old publications. Conventional breeding methods were successful in developing about 40 high-yielding hybrids and varieties with inbuilt resistance to major pests and diseases. An effort is made in the present chapter to consolidate the information on genetics and breeding methods followed in India and elsewhere.Not Availabl