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Several pseudorandom number generators are described and compared on the basis of cost of generation and length of period of the sequences that are produced. The major statistical tests, which are used to obtain a measure of randomness for the different generators are discussed and compared. Four pseudorandom number generators are programmed in GPSS and are used to generate interarrival and service times for an M/M/1 queuing system. The results of each of the trials are compared to the theoretical results which can be obtained from queuing theory.

Random numbers are a basic part in a Simulation Model, and they are also used in random sampling. These techniques are employed by quality engineers in the successful execution of their jobs. The every-day use of random numbers, however, often leads to a sense of complacency in he mind of engineers toward the exacting requirements that should be satisfied by the random number process to generate a genuine random number. Microcomputers have become a common and powerful tool that helps managers and engineers in their simulation experiments by providing sequences of random numbers. This research presents a sequence of eight tests to test the Radio Shack microcomputer system random number generator for uniformity and randomness; then, this Radio Shack random number generator is used to generate uniform and non-uniform deviates and a non-parametric test is performed to test these deviates for randomness. Two computer programs written in the BASIC language are used to test for randomness. The first one to test the Radio Shack random number generator and the second one to test the uniform and non-uniform deviates.

Nazirites are a well-documented phenomenon within the context of the Hebrew Bible. The bulk of research has focused mainly on the role of Samson as a life long Nazirite, but little has been done concerning the role of women within the context of the Nazirite Vow. The goal of this paper will be to examine the role of women within the Nazirite Vow, as well as examining the constraints that might arise when one takes into account the purity laws. The Nazirite Vow is the only vow within the Bible that explicitly mentions the inclusion of women. The question I am interested in addressing is, are there circumstances that might exclude the woman? The idea behind the Nazirite vow is that one is consecrating oneself to YHWH, or setting oneself apart. If one were setting oneself apart then these rules that they would have to follow would not supersede the purity laws. I would suggest that beyond the regular constraints, avoiding dead bodies, grape products, and cutting ones hair, one would still be responsible to keep the purity laws. Therefore, when one takes an issue like menstruation into account, this severely limits the amount of time a woman has to complete the Nazirite Vow. As I will detail in this paper, this leads to the conclusion that if the vow lasted for more than thirty days the only women who would be able to complete the Nazirite Vow successfully would be pregnant women or a woman who is postmenopausal. This could suggest a certain amount of restriction regarding the woman's ability to perform this vow and may suggest why the inclusion of women is made explicit within the context of Numbers 6. Furthermore, this could suggest that fertility might be an aspect of the Nazirite Vow. / Religion

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No description available.

M.S.

The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²). / Master of Science

Perfect, abundant, and deficient numbers are defined in terms of the sum of the divisors function. The history and the discovery of perfect numbers is discussed, and the question of the existence of an odd perfect number is considered. There is a discussion of amicable pairs and multiply perfect numbers. Other numbers which are defined by the sum of their divisors are also introduced. / M.S.

Early in the thirteenth century, Leonardo de Pisa, or, Fibonacci, introduced his famous rabbit problem, which may be stated simply as follows: assume that rabbits reproduce at a rate such that one pair is born each month from each pair of adults not less than two months old. If one pair is present initially, and if none die, how many pairs will be present after one year? The solution to the problem gives rise to a sequence {U_n} known as the Classical Fibonacci Sequence. {U_n} is defined by the recurrence relation U_n = U_n-1 + U_n-2, n ≥ 2, U₀ = 0, U₁ = 1 Many properties of this sequence have been derived. A generalized sequence {F_n} can be obtained by retaining the law of recurrence and redefining the first two terms as F₁ = p', F₂ = p' + q' for arbitrary real numbers p' and q'. Moreover, by defining H₁ = p+iq, H₂ = r+is, p,q,r and s real, a complex sequence is determined. Hence, all the properties of the classical sequence can be extended to the complex case. By reducing the classical sequence by a modulus m, many properties of the repeating sequence that results can be derived. The Fibonacci sequence and associated golden ratio occur in communication theory, chemistry, and in nature. / Master of Science