[Opt-Net] Two new books from Prof. Yaroslav D. Sergeyev, the winner of , the 2010 Pythagoras International Prize in Mathematics

[Opt-Net]

1. Yaroslav D. Sergeyev, Arithmetic of Infinity, E-book, 2013.

http://www.amazon.co.uk/Arithmetic-Infinity-Yaroslav-D-Sergeyev-ebook/dp/B00G7RB1FS/ref=sr_1_2?s=books&ie=UTF8&qid=1384278559&sr=1-2

This book presents a new type of arithmetic that allows one to execute
arithmetical operations with infinite numbers in the same manner as we
are used to do with finite ones. The problem of infinity is considered
in a coherent way different from (but not contradicting to) the famous
theory founded by Georg Cantor. Surprisingly, the introduced
arithmetical operations result in being very simple and are obtained as
immediate extensions of the usual addition, multiplication, and division
of finite numbers to infinite ones. This simplicity is a consequence of
a newly developed positional numeral system used to express infinite
numbers. In order to broaden the audience, the book was written as a
popular one. This is the second revised edition of the book (the first
paperback edition has been published in 2003, available at European
Amazon sites).

Opinions of some experts:
"Mathematicians have never been comfortable handling infinities, such as
those that crop up in the area of a Sierpinski carpet. But an entirely
new type of mathematics looks set to by-pass the problem", MIT
Technology Review, 03.19.2012.
" We will mention here the timely proposal of an enlarged numerical
system advanced recently by Yaroslav D. Sergeyev. This is simpler than
non standard enlargements in its conception, it does not require
infinitistic constructions and affords easier and stronger computation
power." Lolli G. Infinitesimals and infinites in the history of
mathematics: A brief survey, Applied Mathematics and Computation, 2012,
218(16), 7979--7988.
"He shows that it is possible to effectively work with infinite and
infinitesimal quantities and to solve many problems connected to them in
the field of applied and theoretical mathematics." De Cosmis S., De
Leone R. The use of Grossone in Mathematical Programming and Operations
Research, Applied Mathematics and Computation, 2012, 218(16), 8029-8038.
"I am sure that the new approach presented in this book will have a very
deep impact both on Mathematics and Computer Science." From the review
written by D. Trigiante in Computational Management Science, 2007, 4(1),
85-86.
"These ideas and future hardware prototypes may be productive in all
fields of science where infinite and infinitesimal numbers (derivatives,
integrals, series, fractals) are used." From the review written by A.
Adamatzky, Editor-in-Chief of the International Journal of
Unconventional Computing, 2006, 2(2), 193-194.
"The expressed viewpoint on infinity gives possibilities to solve new
applied problems using arithmetical operations with infinite and
infinitesimal numbers that can be executed in a simple and clear way."
  From the review written by P.M. Pardalos, Editor-in-Chief of the
Journal of Global Optimization, 2006, 34, 157--158.

At the web page of the author, the interested reader can find a number
of reviews and technical articles of several researches.

2. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera, Introduction
to Global Optimization Exploiting Space-Filling Curves, 2013, Springer,
E-book and paperback editions.

http://www.amazon.co.uk/Introduction-Optimization-Exploiting-Space-Filling-SpringerBriefs/dp/1461480418/ref=sr_1_1?s=books&ie=UTF8&qid=1384363092&sr=1-1

/Introduction to Global Optimization Exploiting Space-Filling
Curves/provides an overview of classical and new results pertaining to
the usage of space-filling curves in global optimization.  The authors
look at a family of derivative-free numerical algorithms applying
space-filling curves to reduce the dimensionality of the global
optimization problem; along with a number of unconventional ideas, such
as adaptive strategies for estimating Lipschitz constant, balancing
global and local information to accelerate the search. Convergence
conditions of the described algorithms are studied in depth and
theoretical considerations are illustrated through numerical examples.
This work also contains a code for implementing space-filling curves
that can be used for constructing new global optimization algorithms.
Basic ideas from this text can be applied to a number of problems
including problems with multiextremal and partially defined constraints
and non-redundant parallel computations can be organized. Professors,
students, researchers, engineers, and other professionals in the fields
of pure mathematics, nonlinear sciences studying fractals, operations
research, management science, industrial and applied mathematics,
computer science, engineering, economics, and the environmental sciences
will find this title useful.

Yaroslav D. Sergeyev, Ph.D., D.Sc., D.H.C. is Distinguished Professor at
the University of Calabria, Italy and Professor at N.I. Lobachevski
Nizhniy Novgorod State University, Russia. He has been awarded several
national and international research awards (Pythagoras International
Prize in Mathematics, Italy, 2010; Outstanding Achievement Award from
the 2010 World Congress in Computer Science, Computer Engineering, and
Applied Computing, USA; Lagrange Lecture, Turin University, Italy, 2010;
MAIK Prize for the best scientific monograph published in Russian,
Moscow, 2008, etc.). His list of publications contains more than 200
items, among them 5 books. He is a member of editorial boards of 4
international scientific journals. He has given more than 30 keynote and
plenary lectures at prestigious international congresses in mathematics
and computer science. Software developed under his supervision is used
in more than 40 countries of the world. Numerous magazines, newspapers,
TV and radio channels have dedicated a lot of space to his research.