A cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two- or three-way dominance data (e.g., preference, choice, consideration) measured on ordered successive category rating scales. The technical description of the proposed model and estimation procedure are discussed, as well as the…

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

Defined mathematically, the internal rate of return (IRR) of a cash-flow stream is the discount rate at which its net present value is 0. What is the significance or meaning of such a measure? Using simple example problems and illustrative calculations, the author explains a technically correct but, at the same time, intuitively meaningful…

Reports an error in "Confidence intervals for gamma-family measures of ordinal association" by Carol M. Woods (Psychological Methods, 2007[Jun], Vol 12[2], 185-204). The note corrects simulation results presented in the article concerning the performance of confidence intervals (CIs) for Spearman's r-sub(s). An error in the author's C++ code…

Motivated by centaurs jumping around a circular stadium, we derive Kronecker's Approximation Theorem, which in turn provides elementary solutions to difficult problems in the theory of Diophantine approximations.

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the "Tractable Cognition thesis": Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational-level theories…

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

Professional astronomers use specialized software not normally available to students to determine the rotation periods of asteroids from fragmented light curve data. This paper describes a simple yet accurate method based on Microsoft Excel[R] that enables students to find periods in asteroid light curve and other discontinuous time series data of…

This article studies various holiday distributions, the most interesting one being Easter. Gauss' Easter algorithm and Microsoft Excel are used to determine that the Easter distribution can be closely approximated by the convolution of two well-known uniform distributions. (Contains 8 figures.)

A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…

The aim of this study was to examine students' performance calibration in physical education. One hundred fifth and sixth grade students provided estimations regarding their performance in a dribbling test after practicing dribbling for 16 minutes under different self-regulatory conditions (i.e., receiving feedback, setting goals, self-recording).…

The purpose of this study was to investigate the formal mathematics educational training of elementary grade teachers as well as their perceived levels of self-efficacy regarding the Georgia Performance Standards for mathematics. This study investigated 129 first through fifth grade teachers in Northeast Georgia. The researcher administered a…

High school students from disadvantaged high schools in Toronto were invited to take two surveys, about three weeks apart. Half of the students taking the first survey were also shown a 3 minute video about the benefits of post secondary education (PSE) and invited to try out a financial-aid calculator. Most students' perceived returns to PSE were…