14 research outputs found
Comparison theorems for summability methods of sequences of fuzzy numbers
In this study we compare Ces\`{a}ro and Euler weighted mean methods of
summability of sequences of fuzzy numbers with Abel and Borel power series
methods of summability of sequences of fuzzy numbers. Also some results dealing
with series of fuzzy numbers are obtained.Comment: publication information is added, typos correcte
Approximation Theory and Related Applications
In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics
Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
We consider C^2 families of C^4 unimodal maps f_t whose critical point is
slowly recurrent, and we show that the unique absolutely continuous invariant
measure of f_t depends differentiably on t, as a distribution of order 1. The
proof uses transfer operators on towers whose level boundaries are mollified
via smooth cutoff functions, in order to avoid artificial discontinuities. We
give a new representation of the acim for a Benedicks-Carleson map f_t, in
terms of a single smooth function and the inverse branches of f_t along the
postcritical orbit. Along the way, we prove that the twisted cohomological
equation v(x)=\alpha (f (x)) - f'(x) \alpha (x) has a continuous solution
\alpha, if f is Benedicks-Carleson and v is horizontal for f.Comment: Typos corrected. Banach spaces (Prop 4.10, Prop 4.11, Lem 4.12,
Appendix B, Section 6) cleaned up: H^1_1 Sobolev space replaces C^1 and BV,
L^1 replaces C^0, and H^2_1 replaces C^2. Details added (e.g. Remark 4.9).
The map f_0 is now C^4. 61 page
A walk in the noncommutative garden
This text is written for the volume of the school/conference "Noncommutative
Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in
noncommutative geometry, based on a discussion of significant examples of
noncommutative spaces in geometry, number theory, and physics. The paper also
contains an outline (the ``Tehran program'') of ongoing joint work with Consani
on the noncommutative geometry of the adeles class space and its relation to
number theoretic questions.Comment: 106 pages, LaTeX, 23 figure