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Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031641892
Category :
Languages : en
Pages : 731
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Book Description
Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031641892
Category :
Languages : en
Pages : 731
Get Book Here
Book Description
Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031178378
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Author: Shouchuan Hu
Publisher: Springer Science & Business Media
ISBN: 1461546656
Category : Mathematics
Languages : en
Pages : 941
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Book Description
In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.
Author: Lixin Cheng
Publisher: Frontiers Media SA
ISBN: 283253175X
Category : Science
Languages : en
Pages : 757
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Book Description
This Research Topic is part of a series with, "Bioinformatics Analysis of Omics Data for Biomarker Identification in Clinical Research - Volume I" (https://www.frontiersin.org/research-topics/13816/bioinformatics-analysis-of-omics-data-for-biomarker-identification-in-clinical-research) The advances and the decreasing cost of omics data enable profiling of disease molecular features at different levels, including bulk tissues, animal models, and single cells. Large volumes of omics data enhance the ability to search for information for preclinical study and provide the opportunity to leverage them to understand disease mechanisms, identify molecular targets for therapy, and detect biomarkers of treatment response. Identification of stable, predictive, and interpretable biomarkers is a significant step towards personalized medicine and therapy. Omics data from genomics, transcriptomics, proteomics, epigenomics, metagenomics, and metabolomics help to determine biomarkers for prognostic and diagnostic applications. Preprocessing of omics data is of vital importance as it aims to eliminate systematic experimental bias and technical variation while preserving biological variation. Dozens of normalization methods for correcting experimental variation and bias in omics data have been developed during the last two decades, while only a few consider the skewness between different sample states, such as the extensive over-repression of genes in cancers. The choice of normalization methods determines the fate of identified biomarkers or molecular signatures. From these considerations, the development of appropriate normalization methods or preprocessing strategies may promote biomarker identification and facilitate clinical decision-making.
Author: Georg Polya
Publisher: Springer Science & Business Media
ISBN: 1475762925
Category : Mathematics
Languages : en
Pages : 400
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Book Description
Author: Willem E Saris
Publisher: Springer
ISBN: 1349190543
Category : Social Science
Languages : en
Pages : 242
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Book Description
Author: Helena Chmura Kraemer
Publisher: SAGE
ISBN: 9780803929494
Category : Mathematics
Languages : en
Pages : 128
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Book Description
How Many Subjects? is a practical guide to sample size calculations and general principles of cost-effective research. It introduces a simple technique of statistical power analysis which allows researchers to compute approximate sample sizes and power for a wide variety of research designs. Because the same technique is used with only slight modifications for different statistical tests, researchers can easily compare the sample sizes required by different designs and tests to make cost-effective decisions in planning a study. These comparisons, emphasized throughout the book, demonstrate important principles of design, measurement and analysis that are rarely discussed in courses or textbooks.
Author: Stanley Wasserman
Publisher: SAGE Publications
ISBN: 1452253919
Category : Social Science
Languages : en
Pages : 320
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Book Description
Social network analysis, a method for analyzing relationships between social entities, has expanded over the last decade as new research has been done in this area. How can these new developments be applied effectively in the behavioral and social sciences disciplines? In Advances in Social Network Analysis, a team of leading methodologists in network analysis addresses this issue. They explore such topics as ways to specify the network contents to be studied, how to select the method for representing network structures, how social network analysis has been used to study interorganizational relations via the resource dependence model, how to use a contact matrix for studying the spread of disease in epidemiology, and how cohesion and structural equivalence network theories relate to studying social influence. It also offers statistical models for social support networks. Advances in Social Network Analysis is useful for researchers involved in general research methods and qualitative methods, and who are interested in psychology and sociology.
Author: Pankaj Choudhary
Publisher: Springer
ISBN: 3319254332
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This volume presents an eclectic mix of original research articles in areas covering the analysis of ordered data, stochastic modeling and biostatistics. These areas were featured in a conference held at the University of Texas at Dallas from March 7 to 9, 2014 in honor of Professor H. N. Nagaraja’s 60th birthday and his distinguished contributions to statistics. The articles were written by leading experts who were invited to contribute to the volume from among the conference participants. The volume is intended for all researchers with an interest in order statistics, distribution theory, analysis of censored data, stochastic modeling, time series analysis, and statistical methods for the health sciences, including statistical genetics.
Author: Răzvan Gelca
Publisher: Springer
ISBN: 3319589881
Category : Mathematics
Languages : en
Pages : 857
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Book Description
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
