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The cutting and skiving stock problem (CSSP) as encountered in the paper industry is examined. CSSP is considered one of the most interesting generalizations of the uni-dimensional cutting stock problem. The MAJIQTRIM commercial software package is used to solve the problem using heuristic and linear techniques. The software has proven to be superior to manually generated solutions in terms of quality and performance.

Paper folding is one of the tasks that was chosen to teach children about multiplicative relationships. The act of operating on the paper itself will help students in articulating reasoning, testing and revising their conjectures and developing multiplicative reasoning.

Abstract. A model of a cone can be constructed from a piece of paper by removing a wedge and taping the edges together. The paper models discussed here expand on [...]

A brief overview of Tukey's paper, 'The Future of Data Analysis' after 40 years by various authors is discussed considering the debates regarding whether statistics is a science and ways to attract bright students by showing excitement and rewards of applied work. It is argued that beyond the ideas of data analysis, one should look at how data is analyzed by others and the key concept should be statistical thinking.

Byline: David E. Rowe (1) Author Affiliation: (1) Fachbereich 17--Mathematik, Johannes Gutenberg University, D55099, Mainz, Germany Article History: Registration Date: 07/11/2008

Byline: L.L. Stacho (1), Gy. Domotor (2), M.I. Ban (2) Keywords: Elber--Karplus procedures; reaction path-following; DDRP method Abstract: The flaws in the 'Reply' [1] to our paper [2] have been pointed out. Elber and Karplus (EK) have not disproved our irrefutable global statement that the energy average cannot be minimized which rebuts the theoretical background of EK-type calculations. Another statement of ours has shown that even a curve for which the average energy is locally minimal for all directional perturbations in the sense of classical variational calculus cannot be identical with the reaction path (RP) defined as a steepest descent path (SDP). EK found an error in the early preprint of our theoretical paper [3] and because of this error they qualified our correct variational statement as false for all the SDPs consisting of a straight line each. Mixing global and variational arguments, EK refuted our criticism in a logically incorrect manner. In this Comment we prove that both of our earlier statements invariably remain in force and the criticism included in those has been as well-established and solid as was before. Author Affiliation: (1) Bolyai Institute, JATE University of Szeged, H-6720, Szeged, Aradi Vertanuk tere 1, Hungary (2) Institute of Physical Chemistry, JATE University of Szeged, H-6720, Szeged, POB 105, Hungary Article History: Registration Date: 09/10/2004

The application of mathematical theorems to the paper folding techniques encountered in origami, the Japanese art of paper folding, reveals the shapes that can be constructed and those that cannot be constructed. Shapes such as cubes with double the volume of the given cube cannot be constructed. The mathematical characterization of origami is identical to the 17th problem developed by David Hilbert.

Kolmogorov-Arnold-Moser (or KAM) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori, and KAM theory establishes persistence results for such tori, which carry quasi-periodic motions. We sketch this theory, which begins with Kolmogorov's pioneering work.

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be [...]

An alternative approach to dealing with problems regarding disputed authorship is shown. The approach utilizes linear programming, a mathematical tool developed by mathematicians K.P. Bennett and O.L. Mangasarian. Applying the approach to the famous 'The Federalist' paper issue, where the authorship of several publications are being disputed, some of the steps involve the association of each paper with a point in 70-dimensional space, and the search for a hyperplane which separates the papers credited to Alexander Hamilton from those credited to James Madison.

Nikolai Nikolaevich Luzin's work on continuous functions in the early 20th century was influenced by French textbooks, especially the research of J. L. Lagrange and A. L. Cauchy. Attempts to restore infinitesimals derive directly from Luzin's thought.

Paper folding techniques used in combination with the computer simulation program The Geometer's Sketchpad as described in 'Exploring Conic Sections with The Geometer's Sketchpad' are an excellent way to teach students how to discover the underlying patterns in conics. By modeling the ellipse, hyperbola, and parabola, students can learn the underlying geometry needed to create models and can explore more possibilities. The Sketchpad models help students locate tangency points and connect the models to the concept of conics.

A solution to the non-existence of competitive equilibria in an economy where satiation is possible is presented. Based on an economic situation with many agents and where paper money is one of the commodities without transaction costs, it is concluded that competitive equilibrium may exist by using money as a net positive supply even if preferences may be satiated when the agents are permitted to select a consumption set within a given budget.

Ideas for using dot paper in the teaching of geometry are presented. Dot paper has wider uses than geoboards, although geoboards are useful for younger pupils. Dot paper allows students to learn about geometrical properties and relationships for themselves. Dot paper is particularly suited to learning about triangles, non-square parallelograms and squares, and to area calculations. Perimeters, medians and altitudes, congruent and similar figures are appropriate items for study.

The University of Texas at Austin has the papers of the mathematician Francis Louis Miksa. He lived from 1901 to 1975 and contributed to recreational mathematics such as with his invention of dyad squares. Miksa also worked in the areas of magic squares, number theory, combinatorics and Pythagorean triangles. The papers are kept in the Archives of American Mathematics, and they include correspondence with other problem solvers and mathematicians.

The construction in a way that enables the description of other related paper folding constructions as alternative geometrical front-ends to the sound mathemathetical base created by Peter Hilton and Jean Pederson is summarized. It is recommended to try the constructions presented with real paper.

The rock-paper-scissors problem is an entertaining methods to developm students' understanding of the principle of probability. How to use the rock-paper-scissors problem for math instruction is discussed.

A break symmetry-based recursive investigation of Catalan number parenthesization reveals a direct link between CG-arrangements and bracketings by providing recursive mappings between the two at the break point. Each of the arrangements is then mapped to a bracketing, and a final manipulation process reassembles these bracketings. The break point of alpha in any CG-arrangement is the first point after the beginning of alpha, going from left to right, where every pair of parenthesis that has been opened is again closed. An inductive process gives one-to-one correspondences.

Problems that offer multiple revelations during its investigations and that can be approached mathematically in more than one way often involve paper folding and conic sections. These problems can be easily demonstrated with a sheet of wax paper or emulated by the geometer's sketchpad.

The popular children's game of Scissors, Paper and Stone is extended to games with any number of opposing objects. Thus, the optimal strategy for each type of game is obtained. A game is first symbolized by a tournament, which is a directed graph with nodes representing objects and an arc between each pair of nodes pointing towards the winner. Thus, the games qualify as tournament games. These games are played many times, with their optimal strategies random in nature. However, this study is able to derive a unique strategy that uses an odd number of nodes.

Charles Jeffries' claim that Poynting's vector for energy transfer in static electromagnetic fields gives incorrect results is due to a misunderstanding of Poynting's identity. The new vector which he proposes as a replacement predicts values and diverges considerably from experimental results. Poynting's vector is directly derived from Maxwell's equations and remains valid even in static fields. Engineers and scientists can continue to use this method with confidence.

The goal of the elementary mathematics program is to create an environment that supports the active exploration of mathematical ideas while demonstrating the connections between mathematics and everyday life. Many [...]

A comment on a study of forecasting ability of the ARIMA model is presented. The central point made by the study is said to be misleading since the cross-corellations between estimated trend and irregular disturbances are predicted by theory and should be expected. Thus the conclusions on the ARIMA model should be studied more extensively since the model may not give a good fit as reported.

T. S. FERGUSON, L. S. SHAPLEY, and J. B. MACQUEEN (Eds.). Hayward, CA: Institute of Mathematical Statistics, 1996. ISBN 0-940600-42-0. xiv + 407 PP. $32 (P). This book is a [...]

A description is presented of an exercise which can be given to students of mathematics which involves an investigation of the limit of angle measures which can be formed through repeatedly folding a piece of paper.

Congruences mod p for a prime p and partial products of the numbers 1, ..., p - 1 are obtained. Bibliography: 2 titles., UDC 511 1. FULL FACTORIALS In accordance with the Wilson theorem, for a positive rational prime number p, the factorial of p - 1 satisfies the congruence (p - 1)! [...]

A comment on a paper exploring the forecasting ability of the ARIMA and BSM models of trend extraction is presented. A paper by Andrew HArvey is presented in contrast to the original paper by Garcia-Ferrer and Del Hoyo. The original paper is vague in the definition of orthogonality and discuss resduals of the trend. The contrasting paper argues by adding random white-noise inputs into the entire equation. Characterization of the trend component is required for the forecasting analysis.