The metric

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: On the determining number and the metric dimension of graphs...

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fixed Points for Multivalued Mappings and the Metric Completeness

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  • Any sphere S n admits a metric of constant sectional curvature. These canonical metrics are homogeneous and Einstein, that is the Ricci curvature is a constant multiple of the metric. The spheres S 4m+3 , m 1, are known to have another Sp(m + 1)-homogeneous Einstein metric discovered by Jensen [Jen73]. In addition, S 15 has a third Spin(9)-invariant homogeneous Einstein metric discovered by Bourguignon and Karcher [BK78]. In 1982 Ziller proved that these are the only homogeneous Einstein metrics on spheres [Zil82]. ...

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  • Before entering upon our subject proper, we think it advisable to explain a few points, simple though they are, which might cause confusion to some readers. Our experience has shown us that as soon as we use the words "millimeter" and "degree," perplexity is the result. "What is a millimeter?" is propounded to us very often in the course of a year; nearly every new acquaintance is interested in having the metric system of measurement, together with the fine gauges used, explained to him.

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  • This brief paper, which is itself an extended abstract for a forthcoming paper, describes a metric that can be easily computed during either b o t t o m - u p or top-down construction of a parse tree for ranking the desirability of alternative parses. In its simplest form, the metric tends to p r e f e r trees in which constituents are pushed as far down a s possible, but by appropriate modification of a c o n s t a n t in the formula other behavior can be obtained also. This paper includes an...

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  • Chapter 3, Systems of measurement and weight, reviews weights and measures. It introduces the metric system as well as apothecary and household systems. Time and temperature conversions are included. Special attention is given to conversion factors, and the procedures for ratio proportion, fraction proportion, and dimensional analysis methods are introduced as building blocks for later chapters.

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  • BS 449 was first issued in 1932 and was revised in December 1935, July 1937, July 1948 and May 1959. It was reset and reprinted in February 1965 incorporating amendments Nos. 1 to 5 and reprinted in October 1967 incorporating amendments Nos. 6 and 7. When a programme of Codes of Practice for Buildings was drawn up in 1942 under the aegis of the Ministry of Works, a Code of Practice for the structural use of steel in buildings was included in a series for all types of building construction: this was later (1948) issued as CP 113....

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  • Trong toán học, một không gian mêtric (tiếng Anh: metric space) là một tập hợp mà trong đó khái niệm về khoảng cách giữa các phần tử được định nghĩa. Không gian mêtric gần nhất với hiểu biết trực quan của con người là không gian Euclid ba chiều. Mêtric Euclid của không gian này định nghĩa khoảng cách giữa hai điểm là độ dài đoạn thẳng nối chúng.

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  • Hellos – Identifies neighbors Used by the neighbor discovery and recovery process. Multicast Unreliable delivery Acknowledgements (ACK) – Acknowledges receipt Hello packets with no data Unicast Unreliable delivery Updates – Advertises routes Transmitted only when necessary Unicast when sent to a specific router Multicast when sent to multiple routers Reliable delivery Queries – Ask about a route (DUAL) Reliable delivery Multicast or Unicast Queries and Replies – Ask about a route and answer a query (DUAL) Reliable delivery Replies: Unicast...

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  • It is interesting to look at the major sources of waste from within the chemical industry. Bulk chemical production is normally thought of as a ‘dirty’ industry and historically this has been the case. As the industry became more competitive, more economic processes needed to be developed and it became unacceptable (and non- viable) to produce the same amount of waste as 30 years ago. Today it is the speciality and pharmaceutical industries which produce most waste (at least...

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  • This book has been written to help professionals, students, and lay people identify the increasing number of terms in the fields of environmental engineering and science. More than 8000 terms, acronyms, and abbreviations applying to wastewater, potable water, industrial water treatment, seawater desalination, air pollution, incineration, and hazardous waste remediation have been defined. The most unique feature of this book is the inclusion of more than 3000 trademarks and brand names.

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  • Surveying a vast theory like Teichmüller theory is like surveying a land, and the various chapters in this Handbook are like a collection of maps forming an atlas: some of them give a very general overview of the field, others give a detailed view of some crowded area, and others are more focussed on interesting details. There are intersections between the chapters, and these intersections are necessary.

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  • The goal of this book is to show how usability metrics can be a powerful tool for successfully evaluating the user experience for any product. When some people think about usability metrics, they feel overwhelmed by complicated formulas, contradictory research, and advanced statistical methods. We hope to demystify much of the research and focus on the practical application of usability metrics. We’ll walk you through a step-by-step approach to collecting, analyzing, and presenting usability metrics.

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  • We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe’s theorem, settling a long standing open problem in the nonlinear theory of Banach spaces. We apply our results to several problems in metric geometry. Namely, we use metric cotype in the study of uniform and coarse embeddings, settling in particular the problem of classifying when Lp coarsely or uniformly embeds into Lq . We also prove a nonlinear analog of the Maurey-Pisier theorem, and use it to...

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  • This is the second volume containing examples from Functional analysis. The topics here are limited to Topological and metric spaces, Banach spaces and Bounded operators. Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

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  • This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstr¨m data, o the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose. ...

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  • We classify the measure theoretic attractors of general C 3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry. 1. Introduction 1.1. Statement of results. The study of measure theoretical attractors occupied a central position in the theory of smooth dynamical systems in the 1990s. Recall that a forward invariant compact set A is called a (minimal) metric attractor for some dynamics if the basin of attraction B(A) := {x : ω(x) ⊂ A} of A has positive Lebesgue measure and B(A ) has Lebesgue measure zero for every forward invariant compact set...

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  • This paper is a continuation of Fefferman’s program [7] for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg¨ kernels of the domains as o analogs of the heat kernel of Riemannian manifolds. In Riemannian (or conformal) geometry, the coefficients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric; by integrating the coefficients one obtains index theorems in various settings. ...

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  • Let p 1 and let (X, d, μ) be a complete metric measure space with μ Borel and doubling that admits a (1, p)-Poincar´ inequality. Then there exists e ε 0 such that (X, d, μ) admits a (1, q)-Poincar´ inequality for every q p−ε, e quantitatively. 1. Introduction Metric spaces of homogeneous type, introduced by Coifman and Weiss [7], [8], have become a standard setting for harmonic analysis related to singular integrals and Hardy spaces. Such metric spaces are often referred to as a metric measure space with a doubling measure. An advantage of working...

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  • The Oracle Enterprise Manager Metric Reference Manual (hereafter referred to as the Metric Reference Manual) lists all the target metrics that Enterprise Manager monitors. This manual compiles in one place all the target metric help available online, eliminating the need to have the Grid Control Console up and running.

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