In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval 0; 1]. There are only denu-merable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathemat...

When people use mathematics to model real-life situations, their modeling is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric “contain” relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/...

Long number multiplications (n ≥ 128-bit) are a primitive in most cryptosystems. They can be performed better by using Karatsuba-Ofman technique. This algorithm is easy to parallelize on workstation network and on distributed memory, and it’s known as the practical method of choice. Multiplying long numbers using Karatsuba-Ofman algorithm is fast but is highly recursive. In this paper, we propo...

The notion of the ‘mathematical impossibility’ of group decision making is founded on errors in microeconomics, game theory, and related disciplines. We highlight mathematical errors that have been committed by von Neumann and Morgenstern, Pareto, Hicks, Samuelson, and Debreu which have been propagated throughout the social sciences. 1 Applicability of Mathematical Operations 1.1 Mathematical S...

Can mathematical competence be measured by analyzing the patterns of pauses between written elements in the freehand copying of mathematical equations? Twenty participants of varying levels of mathematical competence copied sets of equations and sequences of numbers on a graphics tablet. The third quartile of pauses is an effective measure, because it reflects the greater number of chunks and t...

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval 0; 1]. There are only denu-merable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathemat...

Monte Carlo (MC) technique is a numerical method that makes use of random numbers to solve mathematical problems for which an analytical solution is not known. The first article, “The Monte Carlo Method” by Metropolis and Ulam, has appeared for the first time in 1949 [9], even though well before that certain statistical problems were solved using random numbers. Since the simulation of random n...

Polyenoid systems (or polyenoids) are trees which can be embedded in a hexagonal lattice and represent CnHn+2 polyene hydrocarbons. Complete mathematical solutions in terms of summations and in terms of a generating function are deduced for the numbers of polyenoids when overlapping edges and/or vertices are allowed. Geometrically planar polyenoids (without overlapping vertices) are enumerated ...

Sloane’s influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community. The sequence A001611 listing the “Fibonacci numbers + 1” contains a very large number of references and links. The sequence A000071 for the “Fibonacci numbers −1” contains an even larger number. Strangely, resentment seems to prevail between the two sequ...

A mathematical model is developed to analyze the transmission of inhalational anthrax through the postal system by cross-contamination of mail. The model consists of state vectors describing the numbers of cross-contaminated letters generated, the numbers of anthrax spores on these letters, the numbers of resulting infections in recipients, and matrices of transition probabilities acting on the...