We prove the existence and nonexistence of solutions for the semilinear problem ∆u + K(r)f(u) = 0 with various boundary conditions on the exterior of the ball in R^N such that lim r→∞u(r) = 0. Here f : R → R is an odd locally lipschitz non-linear function such that there exists a β > 0 with f < 0 on (0, β), f > 0 on (β, ∞), and K(r) \equiv r^−α for some α > 0.

Call number: LD2668 .T4 1966 P595 / Master of Science

CIVINS / The United States Navy has taken a new interest in tumblehome hulls. While the stealth characteristics of these hull forms make them attractive to the Navy, their sea keeping characteristics have proven to be problematic. Normal approximations of sea keeping characteristics using linear differential equations with constant coefficients predict a very stable platform, while observations in model tests show a ship that is prone to extreme roll transients. This thesis examines a simple method of producing a non-linear simulation of roll motion using a tumblehome hull provided by the Office of Naval Research. This research demonstrates the significant difference that a variable restoring coefficient introduces into a hull's seakeeping characteristics. / Contract number: N62271-97-G-0026 / CIVINS

A research project submitted in partial fulfilment of the requirements of the degree of Masters of Science (Mathematics Education) University of the Witwatersrand Johannesburg, South Africa. 10 October 2016 / This research investigates three different kinds of errors made by learners using a discursive approach when dealing with equations in grade 10. The data for the study is made up of Grade 10 learners' responses to a pre-test and post-test, and is part of a much larger data set that was collected by the Wits Maths Connect Secondary Project (WMCS) in 2013. Questions like substitution and multiplying and simplifying as well as factorization are given attention as they are related to equations. The data for this study is collected by coding pre-test and post-test scripts. The data is analyzed using codes and using commognition. The role played by the equal sign in equations and operations that are performed on symbols as well as well as errors that creep in executing these operations are given attention in the study. Special attention is given to linear equations in this study. Errors identified by Brodie and Berger (2010) are confirmed. The finding is that extent to which errors made by grade 10 learners when dealing with equations stem from errors in arithmetic is substantial. The other finding is that extent to which grade 10 learners made errors related to basic algebra, when dealing with equations, is substantial. / TG2016

Ai Jun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 100-103). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In this thesis, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d'Alembertian equation. In particular, we prove the solution decays to a linearlized Kerr solution except for the angular mode l=2.

In order to introduce the investigation of the present thesis,let us consider the linear homogeneous differential equation:Z2 d3y/dz3 + Z (bo + Bi Zm + b2z2m) d2y/dz2 + (Co + CiZm + C2Z) dy/dZ+ (diZm-1 + d2Z2m-1) Y = 0Here, m is a positive integer, the variable Z is complex and the constants bi, Ci (i=0,1,2) and di (i=1,2) are complex with b2 ≠ 0. It is also assumed that the roots of the indicial equation are such that the difference of no two of them is congruent to zero modulo m.Ball State UniversityMuncie, IN 47306

In this master thesis, it is proposed to study the asymptotic behaviour of the solutions of the third order differential equation d3y d2y dyZ2 ____ + z (a0 + a1z) ____ + (b0+b1z+b2z2) ___ + (c0+c1z+c2z2)y = 0 dz3 dz2 dzHere, the variable z and the constants ai (i=0,1), bi, ci (i=0,1,2) are complex with b2 # 0. It is also assumed that no two roots of the indicial equation about the regular singular point z = 0 differ by an integer.Ball State UniversityMuncie, IN 47306

This thesis is concerned with the asymptotic solutions of the differential equationz(2) d(3)y/dz(3) + (a0z) d(2)y/dz(2) + [b0+b1z+b2z(2)] dy/dz + (c0+ c1z) y=0Here, the variable z is complex as are the constants ai, ci(i=O,1) and bi(i=O,1,2) with b2 does not equal 0. It is also assumed that the roots of the indicial equation about z = 0 are such that the difference of no two of them is congruent to zero modular 1.Ball State UniversityMuncie, IN 47306

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 129-133). Also available on the Internet.