# a-higher-dimensional-sieve-method

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## A Higher Dimensional Sieve Method

Author : Harold G. Diamond
ISBN : 9781139474917
Genre : Mathematics
File Size : 72. 77 MB
Format : PDF, ePub

Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica® which aid in the computation of such functions.

## Clustering Biological Data With Self Adjusting High Dimensional Sieve

Author : Josselyn Gonzalez
ISBN : 0438108183
Genre :
File Size : 30. 45 MB
Format : PDF, Docs

Data classification as a preprocessing technique is a crucial step in the analysis and understanding of numerical data. Cluster analysis, in particular, provides insight into the inherent patterns found in data which makes the interpretation of any follow-up analyses more meaningful. A clustering algorithm groups together data points according to a predefined similarity criterion. This allows the data set to be broken up into segments which, in turn, gives way for a more targeted statistical analysis. Cluster analysis has applications in numerous fields of study and, as a result, countless algorithms have been developed. However, the quantity of options makes it difficult to find an appropriate algorithm to use. Additionally, the more commonly used algorithms, while precise, require a familiarity with the data structure that may be resource-consuming to attain. Here, we address this concern by developing a novel clustering algorithm, the sieve method, for the preliminary cluster analysis of high-dimensional data. We evaluate its performance by comparing it to three well-known clustering algorithms for numerical data: the k-means, single-linkage hierarchical, and self-organizing maps. To compare the algorithms, we measure accuracy by using the misclassification or error rate of each algorithm. Additionally, we compare the within- and between-cluster variation of each clustering result through multivariate analysis of variance. We use each algorithm to cluster Fisher's Iris Flower data set, which consists of 3 ``true'' clusters and 150 total observations, each made up of four numerical measurements. When the optimal clustering structure is known, we found that the k-means and self-organizing maps are the more efficient algorithms in terms of speed and accuracy. When this structure is not known, we found that the sieve algorithm, despite higher misclassification rates, was able to obtain the optimal clustering structure through a truly blind clustering. Thus, the sieving algorithm functions as an informative and blind preliminary clustering method that can then be followed-up by a more refined algorithm. The existence of reliably efficient clustering process for numerical data means that more time, effort, and computational resources can be spent on a more rigorous and targeted statistical analysis.

## Sieve Methods

Author : Heine Halberstam
ISBN : 9780486320809
Genre : Mathematics
File Size : 42. 24 MB
Format : PDF, Docs

This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.

## Malliavin Calculus For L?vy Processes And Infinite Dimensional Brownian Motion

Author : Horst Osswald
ISBN : 9781107016149
Genre : Mathematics
File Size : 68. 32 MB
Format : PDF, Mobi

After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.

## Mathematics Of Two Dimensional Turbulence

Author : Sergei Kuksin
ISBN : 9781139576956
Genre : Mathematics
File Size : 73. 69 MB
Format : PDF, Docs

This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

## The Use Of High Intensity Ultrasonics

Author : Anton Puškár
ISBN : WISC:89008279309
Genre : Technology & Engineering
File Size : 85. 68 MB
Format : PDF, ePub, Mobi

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

## Dissertation Abstracts International

Author :
ISBN : STANFORD:36105121673201
File Size : 62. 30 MB
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## The American Mathematical Monthly

Author :
ISBN : UCAL:B3632257
Genre : Mathematicians
File Size : 56. 44 MB
Format : PDF

## Proceedings Ieee International Symposium On Information Theory

Author :
ISBN : PSU:000018396911
Genre : Information theory
File Size : 41. 78 MB
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## Ieee International Symposium On Information Theory

Author :
ISBN : CORNELL:31924051079071
Genre : Information theory
File Size : 28. 64 MB
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## Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards

Author :
ISBN : UOM:39015079680636
File Size : 29. 52 MB
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## Division Of Soils Technical Paper

Author :
ISBN : CHI:092012344
Genre : Soils
File Size : 50. 59 MB
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Author : National Research Council Canada
ISBN : NYPL:33433031712122
Genre : Engineering
File Size : 48. 14 MB
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## Mathematical Reviews

Author :
ISBN : UVA:X006180633
Genre : Mathematics
File Size : 43. 28 MB
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## ??????

Author :
ISBN : PSU:000067481835
Genre : Mathematical physics
File Size : 59. 16 MB
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## Proceedings Of The Annual Meeting

ISBN : UCAL:B3083162
Genre : Science
File Size : 81. 70 MB
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## 1990 Ieee International Symposium On Information Theory Isit

Author : Laurence B. Milstein
ISBN : UCSD:31822005230792
Genre : Information theory
File Size : 51. 93 MB
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## Bulletin New Series Of The American Mathematical Society

Author :
ISBN : UOM:39015085210089
Genre : Mathematics
File Size : 23. 91 MB
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## Cornell University Courses Of Study

Author : Cornell University
ISBN : CORNELL:31924089539732
Genre :
File Size : 78. 75 MB
Format : PDF, Kindle

## Medical Journal Of Shinshu University

Author :
ISBN : UCAL:B4313959
Genre : Medicine
File Size : 48. 81 MB
Format : PDF, Docs