Progressive Internal Gravity Waves With Bounded Upper Surface Climbing a Triangular Obstacle

TL;DR: In this paper, the general equation of steady-state motion derived in Part I is integrated to yield the flow of a stratified fluid over an obstacle of finite dimensions, and the results indicate a more or less complicated laminar wave motion for obstacles of maximum height below a certain value.

Abstract: The last chapter of the book is chiefly concerned with Post's theory of normal languages, and Post's theorem on the existence of a normal extension of any canonical language (quoted without proof) is made the basis of 9, proof of Church's theorem that the decision problem for the first order predicate calculus is not recursively solvable, and serves also to exhibit Godel's theorem that no consistent language adequate for mathematics is capable of proving every true statement in Arithmetic. The Elements of 1Tfathematical Logic is intended to serve as a teaching text, and each section concludes with a set of graded exercises. The style is vigorous and stimulating, and the illustrations often as apt as they are unexpected. Regarding the axiom of choice, we learn that some political observers regard Ilr. Truman as a test case " when i t comes to understanding political questions . . if Truman can understand a given political question, then anyone can. The axiom of choice implies that we can always find a test caSe ". Professor Rosenbloom has spared no pains to make his book as reliable and up-to-the-minute as possible. The bibliographical appendix is itself impressive evidence of familiarity with an extensive range of recent discoveries, but in addition to his reading the author travelled widely in the Cnited Statesand visited Scandinavia and England as well-to keep himself informed of forthcoming works and to clarify his oun ideas by personal discussions with the leading workers in the field. Professor Rosenbloom and the Dover Press are both to be warmly congratulated on a sincere, timely and instructive book. R. L. GOODSTEIN.

TL;DR: In this article, the effect of an uneven bottom on the long gravity waves is investigated by using a nonlinear perturbation method, to the lowest order of perturbations, for the free-surface elevation h (1) :

TL;DR: In this article, the authors derived the Airy equations as the first approximation for an uneven bottom, and then transformed them to a set of first order quasi-linear hyperbolic equations with the characteristic curves in the x-t plane directly related to the bottom profile.