Download Equations of Phase-Locked Loops: Dynamics on Circle, Torus by Jacek Kudrewicz, Stefan Wasowicz PDF

By Jacek Kudrewicz, Stefan Wasowicz

Phase-Locked Loops (PLLs) are digital structures that may be used as a synchronized oscillator, a driving force or multiplier of frequency, a modulator or demodulator and as an amplifier of section modulated signs. This ebook updates the tools utilized in the research of PLLs by way of drawing at the effects got within the final forty years. Many are released for the 1st time in ebook shape. Nonlinear and deterministic mathematical versions of continuous-time and discrete-time PLLs are thought of and their simple homes are given within the kind of theorems with rigorous proofs. The ebook shows very attractive dynamics, and indicates a number of actual phenomena saw in synchronized oscillators defined through entire (not averaged) equations of PLLs. in particular chosen mathematical instruments are used the speculation of differential equations on a torus, the phase-plane pix on a cyclinder, a perturbation idea (Melnikov s theorem on heteroclinic trajectories), imperative manifolds, iterations of one-dimensional maps of a circle and two-dimensional maps of a cylinder. utilizing those instruments, the houses of PLLs, specifically the areas of synchronization are defined. Emphasis is on bifurcations of assorted kinds of periodic and chaotic oscillations. unusual attractors within the dynamics of PLLs are thought of, similar to these chanced on by means of RÃ¶ssler, Henon, Lorenz, might, Chua and others.

Download Sophus Lie: a sketch of his life and work by Fritschze B. PDF

By Fritschze B.

Sophus Lie (1842-1899) was once the most vital mathematicians of the 19th century. His paintings on line-sphere transformation and the construction of the idea of constant teams and his program of those to different parts of arithmetic used to be ground-breaking and has had a long-lasting influence at the additional improvement within the box. certainly, a brand new self-discipline of arithmetic often called Lie idea at the present time has resulted. This exact mathematician Sophus Lie summarized his existence and paintings within the draft of an highbrow testimonial as follows.

Download Seminaire Bourbaki vol 1978 79 Exposes 525-542 by A. Dold, B. Eckmann PDF

By A. Dold, B. Eckmann

In view that 1984, a sequence of local meetings on mathematical physics has been equipped via physicists from Iran, Pakistan and Turkey to advertise the study in mathematical and theoretical physics within the quarter. This quantity, which derives from the XI neighborhood convention on Mathematical Physics, contains eight overview and forty four study articles at the most vital issues in mathematical and theoretical physics comparable to astrophysics and cosmology, conformal box thought, excessive strength physics, basic relativity and plasma physics. The overview articles are complete and self-contained and file at the most crucial advancements within the corresponding topics. every one evaluation article presents an entire record of references, that is particularly necessary for graduate scholars who're simply beginning their examine actions; even formidable undergraduates in physics can use those evaluate papers as priceless history fabric to head extra into the topic and discover the learn literature. they're contributed by way of fashionable senior scientists: M Moniez (Laboratoire de l'Accelerateur Lineare, France) and V Sahni (Inter-University Centre for Astronomy and Astrophysics (IUCAA), India) in Astrophysics and Cosmology, W Nahm (Dublin Institute for complicated experiences (DIAS), eire) in Conformal box idea, J Lukierski (University of Wroclaw, Poland) in Mathematical Physics, Riazuddin and Fayyazuddin (Quaid-i-Azam collage, Pakistan) in excessive power Physics, N Dadhich (Inter-University Centre for Astronomy and Astrophysics (IUCAA), India) and A Qadir (National collage of technology and know-how, Pakistan) generally Relativity, and N Tsintsadze (Tbilisi nation college, Georgia) in Plasma Physics.

Download The history of mathematics from antiquity to the present: A by Joseph W. Dauben PDF

By Joseph W. Dauben

By Frédéric Pham

Bringing jointly primary texts from Frédéric Pham’s study on singular integrals, the 1st a part of this booklet specializes in topological and geometrical facets whereas the second one explains the analytic procedure. utilizing notions built by way of J. Leray within the calculus of residues in numerous variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational learn of the singularities of integrals lies on the interface among research and algebraic geometry, culminating within the Picard-Lefschetz formulae. those mathematical buildings, enriched through the paintings of Nilsson, are then approached utilizing tools from the idea of differential equations and generalized from the viewpoint of hyperfunction idea and microlocal analysis.

Providing a ‘must-have’ advent to the singularities of integrals, a couple of supplementary references additionally supply a handy advisor to the themes covered.

This e-book will entice either mathematicians and physicists with an curiosity within the quarter of singularities of integrals.

By Edmund Landau

Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the legislation of algebra carry? and the way can we turn out those legislation? What are the houses of the numbers on which the Differential and essential Calculus relies? In different phrases, What are numbers? And why have they got the homes we characteristic to them? because of the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now accept a passable resolution. This English translation of Landau's well-known Grundlagen der Analysis-also to be had from the AMS-answers those very important questions.