In this note it is shown how closed sums of infinite series may be used to construct efficient economized formulas for microstrip electrical impedances. (Contains 1 figure.)

An explicit formula is established for the general solution of the homogeneous non-autonomous linear difference equation. The formula developed is then used to characterize globally periodic linear difference equations with constant coefficients.

This paper aims to explore some properties of certain third-order linear sequences which have some properties analogous to the better known second-order sequences of Fibonacci and Lucas. Historical background issues are outlined. These, together with the number and combinatorial theoretical results, provide plenty of pedagogical opportunities for…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

The connection between linear and 0-1 integer linear formulations has attracted the attention of many researchers. The main reason triggering this interest has been an availability of efficient computer programs for solving pure linear problems including the transportation problem. Also the optimality of linear problems is easily verifiable…

In this note, we introduce and discuss convolutions of two series. The idea is simple and can be introduced to higher secondary school classes, and has the potential of providing a good background for the well known convolution of function.

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…

We present a simulation tool to aid the study of basic pharmacology principles. By taking advantage of the properties of agent-based modeling, the tool facilitates taking a mechanistic approach to learning basic concepts, in contrast to the traditional empirical methods. Pharmacodynamics is a particular aspect of pharmacology that can benefit from…

A Monte Carlo investigation of six robust correlation estimators was conducted for data from distributions with longer than Gaussian tails: a bisquare coefficient, the Tukey correlation, the standardized sums and differences, a biweight standardized sums and differences, the transformed Spearman's rho and a bivariate trimmed Pearson. Evaluation of…

Describes a model for a front end query processor to deal with incomplete information in a database. The effectiveness of the processor in restricting the number of objects to be processed in a query and in aiding the interpretation of a query is discussed. (26 references) (Author/CLB)

A definition of test validity as the ratio of a covariance term to a variance term, analogous to the classical definition of test reliability, is proposed. When error scores on distinct tests are uncorrelated, the proposed definition coincides with the usual one, but it remains meaningful when error scores are correlated. (Author/BW)

A simple shortcut procedure for analysis of variance is presented using the means, standard deviations, and number of cases in each sample directly. (Author/NE)