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This volume explores the many different meanings of the notion of
the axiomatic method, offering an insightful historical and
philosophical discussion about how these notions changed over the
millennia.
The author, a well-known philosopher and historian of
mathematics, first examines Euclid, who is considered the father
of the axiomatic method, before moving onto Hilbert and Lawvere.
He then presents a deep textual analysis of each... more...

This two-volume work presents a systematic theoretical and
computational study of several types of generalizations of
separable matrices. The main attention is paid to fast algorithms
(many of linear complexity) for matrices in semiseparable,
quasiseparable, band and companion form. The work is focused on
algorithms of multiplication, inversion and description of
eigenstructure and includes a large number of illustrative examples
throughout the... more...

Group inverses for singular M-matrices are useful tools not only
in matrix analysis, but also in the analysis of stochastic
processes, graph theory, electrical networks, and demographic
models. Group Inverses of M-Matrices and Their
Applications highlights the importance and utility of
the group inverses of M-matrices in several application areas.
After introducing sample problems associated with Leslie matrices
and stochastic... more...

Newtonian Nonlinear Dynamics for Complex Linear and Optimization
Problems explores how Newton's equation for the motion of one
particle in classical mechanics combined with finite difference
methods allows creation of a mechanical scenario to solve basic
problems in linear algebra and programming. The authors present a
novel, unified numerical and mechanical approach and an important
analysis method of optimization.

This practical treatise is an introduction to the mathematics and
physics of affine Kac-Moody algebras. It is the result of an
unusual interdisciplinary effort by two physicists and two
mathematicians to make this field understandable to a broad
readership and to illuminate the connections among seemingly
disparate domains of mathematics and physics that are
tantalizingly suggested by the ubiquity of Lie theory. The book
will be useful... more...

This book features survey and research papers from The Abel
Symposium 2011: Algebras, quivers and representations, held in
Balestrand, Norway 2011. It examines a very active research area
that has had a growing influence and profound impact in many
other areas of mathematics like, commutative algebra, algebraic
geometry, algebraic groups and combinatorics. This volume
illustrates and extends such connections with algebraic geometry,... more...

This work covers three important aspects of monomials ideals in the
three chapters "Stanley decompositions" by Jürgen Herzog, "Edge
ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez
Montaner. The chapters, written by top experts, include computer
tutorials that emphasize the computational aspects of the
respective areas. Monomial ideals and algebras are, in a sense,
among the simplest structures in commutative algebra and the main... more...

The book deals with the representation in series form of compact
linear operators acting between Banach spaces, and provides an
analogue of the classical Hilbert space results of this nature that
have their roots in the work of D. Hilbert, F. Riesz and E.
Schmidt. The representation involves a recursively obtained
sequence of points on the unit sphere of the initial space and a
corresponding sequence of positive numbers that correspond to the... more...