14 research outputs found
On Jordan type inequalities for hyperbolic functions
This paper deals with some inequalities for trigonometric and hyperbolic
functions such as the Jordan inequality and its generalizations. In particular,
lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are
proved.Comment: 16 page
A Lower Bound on the Sinc Function and Its Application
A lower bound on the sinc function is given. Application for the sequence { } ∞ =1 which related to Carleman inequality is given as well
On the approximation of quasiperiodic functions with Diophantine frequencies by periodic functions
We present an analysis of the approximation error for a -dimensional
quasiperiodic function with Diophantine frequencies, approximated by a
periodic function with period . When the -dimensional ()
periodic function containing has certain regularity, the global
behavior of can be described by a finite number Fourier components. The
dominant part of periodic approximation error is bounded by .
Meanwhile, we discuss the optimal approximation rate. Finally, these analytical
results are verified by some examples
Gratings: Theory and Numeric Applications
International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers
Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984
There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another.
IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory
Gratings: Theory and Numeric Applications, Second Revisited Edition
International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11