Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.
Robert R. McLaughlin is the pastor of Grace Bible Church in Somerset, Massachusetts and the President of Robert McLaughlin Bible Ministries. Both ministries are non-denominational grace ministries dedicated to teaching the Word of God from the original languages and making it available at no charge throughout the world. For over 30 years Pastor McLaughlin has taught from the original languages of scripture, The Ministry is dedicated to equipping the believers in the Lord Jesus Christ to live the life that the Lord has designed for them. This is a life of contentment and strength as we go through the inevitable problems and challenges that life brings. Like it or not, believe it or not, we are all a part of an Angelic Conflict. One can hardly live in today’s society and not come across the concept of good versus evil. Books, movies, video games, news, it is found everywhere. It is actually a measure of Satan’s genius that he uses all of these things to disguise, obscure, and pervert the truth. This book explains why most people, including many Christians, are unable to associate the events of their lives with the big picture, the Angelic Conflict itself. The Bible teaches that before the creation of man, a conflict arose between God and His angels, when Satan attempted to ascend to the Mount of Heaven and wrestle God’s ruler-ship away from Him. The resulting battle left the surface of the earth in ruins, at this point the earth was packed in ice. Presumably it was at this time that the trial occurred in which Satan and the angels that followed him were found guilty and sentenced to the Lake of Fire. Since Satan is obviously not yet in the Lake of Fire, the logical conclusion is that he appealed his sentence. We can speculate a number of grounds on which he is making this appeal. One is an accusation against God’s character that we hear often enough in life: How can a loving God cast His creatures into hell? To answer this appeal, God created man, a lower being, and set him in the great stadium of earth for all the angels to observe. God would take on the form of this lower being Himself. He would allow sinful man to abuse and mock Him, and finally to nail Him to a Roman Cross in an attempt to destroy Him. Our Lord Jesus Christ would then bear the penalty for the sins of all mankind. By doing so He neutralized the claims His justice had against us, so that we could live with Him and fellowship with Him forever. This book unlocks the secrets of the Angelic Conflict!
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
The author argues that there are conflicting traditions with regard to the question of what is the moral standing of animals according to Christianity. The dominant tradition maintains that animals are primarily resources but there are alternative strands of Christian thought that challenge this view.
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