No description available.

No description available.

No description available.

No description available.

No description available.

Accurate prediction of officer loss behavior is essential for the planning of personnel policies and executing the U.S. Army's Officer Personnel Management System (OPMS). Inaccurate predictions of officer strength affect the number of personnel authorizations, the Army's budget, and the necessary number of accessions. Imbalances of officer strength in the basic branches affect the Army's combat readiness as a whole. Captains and majors comprise a critical management population in the United States Army's officer corps. This thesis analyzes U.S. Army officer loss rates for captains and majors and evaluates the fit of several time series models. The results from this thesis validate the time series forecasting technique currently used by the Army G-1, Winters-method additive.

Summary The paper investigates the Gibbs’ phenomenon at a jump discontinuity for Fourier–Bessel series expansions. The unexpected thing is that the Gibbs’ constant for Fourier–Bessel series appears to be the same as that for Fourier series expansions. In order to compute the coefficients for Fourier–Bessel functionsefficiently, several integral formulasare derived and the Struve functions and their asymptotic expansions discussed, all of which significantly ease the computations. Three numerical examples are investigated. Findings suggest further investigations suitable for undergraduate research projects or small student group investigations.

Summary A result is discussed which permits the summing of series whose terms have more complicated sign patterns than simply alternating plus and minus. The Alternating Series Test, commonly taught in beginning calculus courses, is a corollary. This result, which is not difficult to prove, widens the series summable by beginning students and paves the way for understanding more advanced questions such as convergence of Fourier series. An elementary exposition is given of Dirichlet’s Test for the convergence of a series and an elementary example suitable for a beginning calculus class and a more advanced example involving a Fourier series which is appropriate for an advanced calculus class are provided. Finally, two examples are discussed for which Dirichlet’s Test does not apply and a general procedure is given for deciding the convergence or divergence of these and similar examples.

Summary Non-linear second-order differential equations whose solutions are the elliptic functions sn(t, k), cn(t, k) and dn(t, k) are investigated. Using Mathematica, high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these nonelementary functions that are correct to at least 11 decimal places. These formulas have the advantage over numerically generated data that they are computationally efficient over the entire real line. This approach is seen as further justification for the early introduction of Fourier series in the undergraduate curriculum, for by doing so, models previously considered hard or advanced, whose solution involves elliptic functions, can be solved and plotted as easily as those models whose solutions involve merely trigonometric or other elementary functions.

The purpose of this paper is to develop some of the more basic Fourier transforms which are the outgrowth of the Fourier theorem. Although often approached from the stand-point of the series, this paper will approach the theorem from the standpoint of the integral.