다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

International Series in Operations Research and Management Science

J. Appl. Probab. © Applied 38A, 901-918 (2001) Printed in England Probability Trust 2001 ESTIMATION OF THE UPPER CUTOFF PARAMETER FOR TAPERED THE PARETO DISTRIBUTION Y. Y. KAGAN AND F. SCHOENBERG, University of California Abstract The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfor- tunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed. Keywords: Parameter estimation; tapered Pareto distribution; Gutenberg-Richter relation; maximum likelihood estimation; method of moments; earthquakes AMS 2000 Subject Classification: Primary 62F10 Secondary 62F12, 62F25, 62F15 Introduction In this paper, we investigate the problem of estimating the parameters used in models for the sizes of earthquakes. Such models are important for the investigation and quantification of seismic hazard, i.e. the risk of an earthquake exceeding a given size within a given time period in the future, which is a subject of concern not only in seismology but also in civil engineering, urban planning, and insurance. Our work was chiefly inspired by David Vere-Jones, who has been one of the principal architects of the general area of statistical seismology, in which the subject of our paper lies. In addition to his numerous significant advances on closely related themes, Vere- Jones has been a main proponent of the use of the tapered Pareto law in modeling earthquake sizes. This paper is addressed to both statisticians and seismologists, and in what fol- lows we provide more explanatory material than is customary. General properties of the earthquake process and its stochastic modelling, as well as some principles of sta- tistical analysis, have been discussed by Kagan [11] and Kagan and Vere-Jones [14]. Earthquake occurrences are most commonly modeled as point processes; Daley and Vere-Jones [2] provide a thorough introduction to such models. Extensive global catalogs of seismic moment tensor solutions with thousands of events have become available since 1977 (see [5], [6] and [24], and references therein). Received September 2000 Postal address: Dept of Earth and Space Sciences, University of California, Los Angeles CA 90095- 1567, USA. Email: ykagan@ucla.edu Postal address: Dept of Statistics, University of California, Los Angeles, CA 90095-1554, USA. Email: frederic@stat.ucla.edu

Estimation of the upper cutoff parameter for the tapered Pareto distribution

An expression of the extropy of a mixed system's lifetime was given firstly. Based on this expression, two mixed systems with same signature but with different components were compared. It was shown that the extropy of lifetime of a mixed system equals to that of its dual system if the lifetimes of the components have symmetric probability density function. Moreover, some bounds of the extropy of lifetimes of mixed systems were obtained and the concept of Jensen–extropy (JE) divergence of mixed systems was proposed. The JE divergence is non-negative and it can be used as an alternative information criteria for comparing mixed systems with homogeneous components. To illustrate the applications of JE divergence, some examples are addressed at the end of this paper.

On extropy properties of mixed systems

On the generalized cumulative residual entropy with applications in actuarial science

Recently, Rao et al. (2004) introduced an alternative measure of uncertainty known as the cumulative residual entropy (CRE). It is based on the survival (reliability) function F instead of the probability density function f used in classical Shannon entropy. In reliability based system design, the performance characteristics of the coherent systems are of great importance. Accordingly, in this paper, we study the CRE for coherent and mixed systems when the component lifetimes are identically distributed. Bounds for the CRE of the system lifetime are obtained. We use these results to propose a measure to study if a system is close to series and parallel systems of the same size. Our results suggest that the CRE can be viewed as an alternative entropy (dispersion) measure to classical Shannon entropy.

Some properties of the cumulative residual entropy of coherent and mixed systems

Recently, a new concept of entropy called generalized cumulative entropy of order $n$ was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.

/pdf/further-results-on-the-generalized-cumulative-entropy-vr0b869pxk.pdf

Further results on the generalized cumulative entropy

Recently, an alternative measure of uncertainty termed by extropy was proposed by Lad et al. Accordingly, a cumulative residual extropy is also introduced by replacing the survival function in plac...

On negative cumulative extropy with applications

Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazard rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated.

/pdf/extension-of-the-past-lifetime-and-its-connection-to-the-irefombjnt.pdf

Abdolsaeed Toomaj

Papers

On the generalized cumulative residual entropy with applications in actuarial science

Some properties of the cumulative residual entropy of coherent and mixed systems

Further results on the generalized cumulative entropy

On negative cumulative extropy with applications

Extension of the past lifetime and its connection to the cumulative entropy