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This 4-th edition of the leading reference volume on distance
metrics is characterized by updated and rewritten sections on some
items suggested by experts and readers, as well a general
streamlining of content and the addition of essential new topics.
Though the structure remains unchanged, the new edition also
explores recent advances in the use of distances and metrics for
e.g. generalized distances, probability theory, graph theory,
coding theory, data analysis. New topics in the purely mathematical
sections include e.g. the Vitanyi multiset-metric, algebraic
point-conic distance, triangular ratio metric, Rossi-Hamming
metric, Taneja distance, spectral semimetric between graphs,
channel metrization, and Maryland bridge distance. The
multidisciplinary sections have also been supplemented with new
topics, including: dynamic time wrapping distance, memory distance,
allometry, atmospheric depth, elliptic orbit distance, VLBI
distance measurements, the astronomical system of units, and
walkability distance. Leaving aside the practical questions that
arise during the selection of a 'good' distance function, this work
focuses on providing the research community with an invaluable
comprehensive listing of the main available distances. As well as
providing standalone introductions and definitions, the
encyclopedia facilitates swift cross-referencing with easily
navigable bold-faced textual links to core entries. In addition to
distances themselves, the authors have collated numerous
fascinating curiosities in their Who's Who of metrics, including
distance-related notions and paradigms that enable applied
mathematicians in other sectors to deploy research tools that
non-specialists justly view as arcane. In expanding access to these
techniques, and in many cases enriching the context of distances
themselves, this peerless volume is certain to stimulate fresh
research.
This 4-th edition of the leading reference volume on distance
metrics is characterized by updated and rewritten sections on some
items suggested by experts and readers, as well a general
streamlining of content and the addition of essential new topics.
Though the structure remains unchanged, the new edition also
explores recent advances in the use of distances and metrics for
e.g. generalized distances, probability theory, graph theory,
coding theory, data analysis. New topics in the purely mathematical
sections include e.g. the Vitanyi multiset-metric, algebraic
point-conic distance, triangular ratio metric, Rossi-Hamming
metric, Taneja distance, spectral semimetric between graphs,
channel metrization, and Maryland bridge distance. The
multidisciplinary sections have also been supplemented with new
topics, including: dynamic time wrapping distance, memory distance,
allometry, atmospheric depth, elliptic orbit distance, VLBI
distance measurements, the astronomical system of units, and
walkability distance. Leaving aside the practical questions that
arise during the selection of a 'good' distance function, this work
focuses on providing the research community with an invaluable
comprehensive listing of the main available distances. As well as
providing standalone introductions and definitions, the
encyclopedia facilitates swift cross-referencing with easily
navigable bold-faced textual links to core entries. In addition to
distances themselves, the authors have collated numerous
fascinating curiosities in their Who's Who of metrics, including
distance-related notions and paradigms that enable applied
mathematicians in other sectors to deploy research tools that
non-specialists justly view as arcane. In expanding access to these
techniques, and in many cases enriching the context of distances
themselves, this peerless volume is certain to stimulate fresh
research.
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Stirling Numbers
Elena Deza
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R4,178
Discovery Miles 41 780
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Ships in 10 - 15 working days
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Stirling numbers are one of the most known classes of special
numbers in Mathematics, especially in Combinatorics and Algebra.
They were introduced by Scottish mathematician James Stirling
(1692-1770) in his most important work, Differential Method with a
Tract on Summation and Interpolation of Infinite Series (1730).
Stirling numbers have rich history; many arithmetic,
number-theoretical, analytical and combinatorial connections;
numerous classical properties; as well as many modern
applications.This book collects together much of the scattered
material on the two subclasses of Stirling numbers to provide a
holistic overview of the topic. From the combinatorial point of
view, Stirling numbers of the second kind S(n,k) count the number
of ways to partition a set of n different objects (i.e., a given
n-set) into k non-empty subsets. Stirling numbers of the first kind
s(n, k) give the number of permutations of n elements with k
disjoint cycles. Both subclasses of Stirling numbers play an
important role in Algebra: they form the coefficients, connecting
well-known sets of polynomials.This book is suitable for students
and professionals, providing a broad perspective of the theory of
this class of special numbers, and many generalizations and
relatives of Stirling numbers, including Bell numbers and Lah
numbers. Throughout the book, readers are presented with exercises
to test and cement their understanding.
This book comes out of need and urgency (expressed especially in
areas of Information Retrieval with respect to Image, Audio,
Internet and Biology) to have a working tool to compare data.
The book will provide powerful resource for all researchers using
Mathematics as well as for mathematicians themselves. In the time
when over-specialization and terminology fences isolate
researchers, this Dictionary try to be "centripedal" and
"oikoumeni," providing some access and altitude of vision but
without taking the route of scientific vulgarisation. This
attempted balance is the main philosophy of this Dictionary which
defined its structure and style.
Key features:
- Unicity: it is the first book treating the basic notion of
Distance in whole generality.
- Interdisciplinarity: this Dictionary is larger in scope than
majority of thematic dictionaries.
- Encyclopedicity: while an Encyclopedia of Distances seems now too
difficult to produce, this book (by its scope, short introductions
and organization) provides the main material for it and for future
tutorials on some parts of this material.
- Applicability: the distances, as well as distance-related notions
and paradigms, are provided in ready-to-use fashion.
- Worthiness: the need and urgency for such dictionary was great in
several huge areas, esp. Information Retrieval, Image Analysis,
Speech Recognition and Biology.
- Accessibility: the definitions are easy to locate by subject or,
in Index, by alphabetic order; the introductions and definitions
are reader-friendly and maximally independent one from another;
still the text is structured, in the 3D HTML style, by
hyperlink-like boldfaced references to similar definitions.
* Covers a large range of subjects in pure and applied
mathematics
* Designed to be easily applied--the distances and distance-related
notions and paradigms are ready to use
* Helps users quickly locate definitions by subject or in
alphabetical order; stand-alone entries include references to other
entries and sources for further investigation
Perfect and amicable numbers, as well as a majority of classes of
special numbers, have a long and rich history connected with the
names of many famous mathematicians. This book gives a complete
presentation of the theory of two classes of special numbers
(perfect numbers and amicable numbers) and gives much of their
properties, facts and theorems with full proofs of them, as well as
their numerous analogue and generalizations.
This book contains a complete detailed description of two classes
of special numbers closely related to classical problems of the
Theory of Primes. There is also extensive discussions of applied
issues related to Cryptography.In Mathematics, a Mersenne number
(named after Marin Mersenne, who studied them in the early 17-th
century) is a number of the form Mn = 2n - 1 for positive integer
n.In Mathematics, a Fermat number (named after Pierre de Fermat who
first studied them) is a positive integer of the form Fn = 2k+ 1,
k=2n, where n is a non-negative integer.Mersenne and Fermat numbers
have many other interesting properties. Long and rich history, many
arithmetic connections (with perfect numbers, with construction of
regular polygons etc.), numerous modern applications, long list of
open problems allow us to provide a broad perspective of the Theory
of these two classes of special numbers, that can be useful and
interesting for both professionals and the general audience.
This book introduces oriented version of metrics and cuts and their
multidimensional analogues, as well as partial metrics and weighted
metrics. It is a follow-up of Geometry of Cuts and Metrics by Deza
and Laurent which presents rich theory of classical binary and
symmetric objects - metrics and cuts.Many research publications on
this subject are devoted to different special aspects of the theory
of generalized metrics. However, they are disconnected one from
other, often written in different mathematical language, consider
the same objects from different points of view without analysis of
possible connections, etc. In this book we will construct full
theory of main classes of finite generalized metrics and their
polyhedral aspects.
Figurate numbers have a rich history with many applications. The
main purpose of this book is to provide a thorough and complete
presentation of the theory of figurate numbers, giving much of
their properties, facts and theorems with full proofs. This book is
the first of this topic written in unified systematic way. It also
contains many exercises with solutions.
This updated and revised third edition of the leading reference
volume on distance metrics includes new items from very active
research areas in the use of distances and metrics such as
geometry, graph theory, probability theory and analysis. Among the
new topics included are, for example, polyhedral metric space,
nearness matrix problems, distances between belief assignments,
distance-related animal settings, diamond-cutting distances,
natural units of length, Heidegger's de-severance distance, and
brain distances. The publication of this volume coincides with
intensifying research efforts into metric spaces and especially
distance design for applications. Accurate metrics have become a
crucial goal in computational biology, image analysis, speech
recognition and information retrieval. Leaving aside the practical
questions that arise during the selection of a 'good' distance
function, this work focuses on providing the research community
with an invaluable comprehensive listing of the main available
distances. As well as providing standalone introductions and
definitions, the encyclopedia facilitates swift cross-referencing
with easily navigable bold-faced textual links to core entries. In
addition to distances themselves, the authors have collated
numerous fascinating curiosities in their Who's Who of metrics,
including distance-related notions and paradigms that enable
applied mathematicians in other sectors to deploy research tools
that non-specialists justly view as arcane. In expanding access to
these techniques, and in many cases enriching the context of
distances themselves, this peerless volume is certain to stimulate
fresh research.
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