We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere. 1. Introduction 1.1. In 1916, D. E. Menshov constructed an example of a nontrivial trigonometric series on the circle T
which converges to zero almost everywhere (a.e.). Such series are called nullseries. This result was the origin of the modern theory of uniqueness in Fourier analysis, see [Z59], [B64], [KL87], [KS94]. Clearly for such a series |c(n)|2 = ∞.
In this paper we describe a systematic approach for creating a dialog management system based on a Construct Algebra, a collection o f relations and operations on a task representation. These relations and operations are analytical components for building higher level abstractions called dialog motivators.
Chapter 2: Recurrence Relations concentrates on fundamental mathematical properties of various types of recurrence relations which arise frequently when analyzing an algorithm through a direct mapping from a recursive representation of a program to a recursive representation of a function describing its properties.
Many of the same organizations who provided me with data for the first edition of Stocks for the Long Run willingly updated their data for this second edition. I include Lipper Analytical Services and the Vanguard Group for their mutual funds data, Morgan Stanley for their Capital Market indexes,
Smithers & Co. for their market value data and Bloomberg Financial for their graphic representations.
SMOOTH AND DISCRETE SYSTEMS—ALGEBRAIC, ANALYTIC, AND GEOMETRICAL REPRESENTATIONS
ˇ FRANTISEK NEUMAN Received 12 January 2004
What is a diﬀerential equation? Certain objects may have diﬀerent, sometimes equivalent representations. By using algebraic and geometrical methods as well as discrete relations, diﬀerent representations of objects mainly given as analytic relations, diﬀerential equations can be considered.
Chapter 7: Permutations surveys combinatorial properties of permutations (orderings of the numbers 1 through N) and shows how they relate in a natural way to fundamental and widely-used sorting algorithms.
In modern high-performance liquid chromatography (HPLC), computers in a broad sense are used in every instrumental module and at every stage of analysis. Computers control the ﬂow rate, eluent composition, temperature, injection volume, and injection process. Detector output signal is converted from analog form into the digital representation to recognize the presence of peaks, and then at higher level of computer analysis a chromatogram is obtained. All these computer-based functions are performed in the background, and the chromatographer usually does not think about them.
Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Nhiễu loạn phân tích của $ \ bar \ một phần $-nhà điều hành và các công thức đại diện không thể thiếu trong không gian Hilbert...
PROCESS, QUANTUM, AND ANALYTICAL SENSORS
INTRODUCTION Automatic test systems, manufacturing process control, analytical instrumentation, and aerospace electronic systems all would have diminished capabilities without the availability of contemporary computer integrated data systems with multisensor information structures. This text develops supporting quantitative error models that enable a unified performance evaluation for the design and analysis of linear and digital instrumentation systems with the goal of compatibility of integration with other enterprise quality representations....
Public opinion and attitude is often the yardstick against which interventions are made. This collection synthesises and analyses the results and findings of some key policy areas investigated and will provide all stakeholders in South Africa with a set of factual information and derivative analytic insights. Such a representation informs choices and decisions to be made, policy dimensions to be investigated further and research to be commissioned in areas where voids are conspicuous.
We present some preliminary results of a Czech-English translation system based on dependency trees. The fully automated process includes: morphological tagging, analytical and tectogrammatical parsing of Czech, tectogrammatical transfer based on lexical substitution using word-to-word translation dictionaries enhanced by the information from the English-Czech parallel corpus of WSJ, and a simple rule-based system for generation from English tectogrammatical representation.