Minimal-Time Ship Routing

A recently theory of minimal-time ship routing through time-dependent ocean wave height and direction fields is put to a numerical test by using a series of semidaily analyses furnished by the U.S. Navy Fleet Numerical Weather Facility. The interpolations and integrations required are found to be feasible. A resume of the theory is given.http://archive.org/details/minimaltimeshipr00bleiN

Identification and Validation of Touring Competencies for Volunteer Docents in Art Museums

The purpose of the study was to (1) identify pedagogical touring competencies needed by volunteer docents in art museums, (2) catalog the competency statements into major competency categories, (3) validate the list of competency statements, and (4) compare priority designations awarded each statement by the individuals within the two major subgroups: museum staff and volunteer docents. In conclusion, many of the needs represented by the highest ranking competencies in each category are seldom addressed in the traditional volunteer docent training program. This study showed that abilities to help the child feel comfortable in the museum and combinations of abilities to help the docent make judgments regarding the presentation of the material require attention and, at the very least , special training. It is recommended that training personnel in art museums identify the needs of volunteer trainees and design training programs less on traditional guidelines and more on the specific needs appropriate to the task

Use of long-range weather forecasts in ship routing

Naval Air Systems Command (AIR 051) under the administration of Naval Weather Research Facility Norfolk, VA.http://archive.org/details/useoflongrangewe09hal

Calculating machine solution of quadratic and cubic equations by the odd number method

The article of record as published may be found at http://dx.doi.org/10.2307/2002231Eastlack has published a method for the solution of quadratic equations by means of a calculating machine. His process is ex­tended here to the solution of cubic equations. In the ordinary manual operation of calculating machines, the use of the method of solving cubic equations presented here will not be found to be as convenient as the use of certain other methods, such as that of Newton. The method is described here, however, in the belief that it may find application in large scale, automatic computing machines (such as the IBM Sequence Controlled Calculator or the ENIAC) where a large number of operations is not objec­tionable, provided that the operations are repetitive and sufficiently simple. We limit our discussion to real roots. Eastlack's method of solving quadratic equations is first reviewed so that the extension of the method to cubic equations may be clearer

Oblateness-perturbed orbits by velocity correspondence variations

This paper presents an elementary treatment of the first order differential effects of the earth's oblateness on a close satellite using the simple notion of a varied orbit. The usual result of this approach is that the radial variation contains a secular term which is unbounded for infinite time. The standard method of celestial mechanics for removing this difficulty is to analyse the perturbed orbit as an ellipse whose shape and space orientation are functions of time. It is shown here that the secular term may be avoided more simply by relating points on the varied and unvaried orbits by a type of radial velocity correspondence instead of the usual time correspondence, and by making the varied orbit osculate at a latus rectum chord end point of the unvaried orbit.http://archive.org/details/oblatenesspertur00ble

Asymptotic Representation of Stirling Numbers of the Second Kind

The distribution of the Stirling numbers S(n,k) of the second kind with respect to k has been shown to be asymptotically normal near the mode. A new single-term asymptotic representation of S(n,k), more effective for large k, is given here. It is based on Hermite's formula for a divided difference and the use of sectional areas normal to the body diagonal of a unit hypercube in k-space. A proof is given that the distribution of these areas is asymptotically normal. A numerical comparison is made with the Harper representation for n=200Office of Naval Research (Dr. Bruce McDonald), Statistics and Probability Branch, Arlington, VAhttp://archive.org/details/asymptoticrepres00bleiNR-042-286, NSWSES-56953, NISC-56969N

Unique maximum property of the Stirling numbers of the second kind

Letting f(n) and (n) be the first and last maxim of the graph S(n,k); k = 1, 2, ... , n, Kanold [J. Reine Angew. Math 230 (1968), 211-212] shows that, for sufficiently large n, n/log n /= 3 remains unsolved. It is the purpose of this paper to provide the complete solution of this classical problemOffice of Naval Research Contract No. NR-042-286http://archive.org/details/uniquemaximumprope00ble

Asymptotics of stirling numbers of the second kind

A complete asymptotic development of the Stirling numbers S(N, K) of the second kind is obtained by the saddle point method previously employed by Moser and Wyman.This work was partially supported by the Office of Naval Research under Contract Number NR 042-286 at the Naval Postgraduate School