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Modulo One Uniform Distribution of the Sequence of Logarithms of Certain Recursive Sequences
 Fibonacci Quarterly
"... Let {x.}° ° be a sequence of real numbers with corresponding fractional parts {/3.}°°, where 0. = x. [x.] and the bracket denotes the greatest integer function. For each n> 1, we define the function F on [ 0,1] so that F (x) is the number of those terms among /31 $ • • • , /3R whichlie in the in ..."
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Cited by 12 (0 self)
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Let {x.}° ° be a sequence of real numbers with corresponding fractional parts {/3.}°°, where 0. = x. [x.] and the bracket denotes the greatest integer function. For each n> 1, we define the function F on [ 0,1] so that F (x) is the number of those terms among /31 $ • • • , /3R whichlie in the interval [0,x), divided by n. Then {x.} is said to be uniformly distributed modulo one iff n lim oo—*n F (x) = x for all x € TO,
What is a Random Sequence
 The Mathematical Association of America, Monthly
, 2002
"... there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a ..."
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Cited by 4 (1 self)
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there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a
A TRANSFORMATION TO SOLVE INDEFINITE QUADRATIC EQUATIONS IN INTEGERS
"... Abstract. The paper proposes a new method, called the Fast Quadratic Transform (FQT), to solve the general indefinite twovariable quadratic equation in integers. The paper presents the new approach, discusses its properties, and provides a comparative evaluation with the classical technique. The FQ ..."
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Abstract. The paper proposes a new method, called the Fast Quadratic Transform (FQT), to solve the general indefinite twovariable quadratic equation in integers. The paper presents the new approach, discusses its properties, and provides a comparative evaluation with the classical technique. The FQT is demonstrated to be markedly superior for all cases in which it applies, including examples for more than sixty percent of the discriminants through two hundred. Consider the equation Prologue
Resource relocation on . . .
, 2010
"... The necessary information to optimally serve sequential requests at the vertices of an undirected, unweighted graph with a single mobile resource is a known result of Chung, Graham, and Saks; however, generalizations of this concept to directed and weighted graphs present unforeseen and surprising c ..."
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The necessary information to optimally serve sequential requests at the vertices of an undirected, unweighted graph with a single mobile resource is a known result of Chung, Graham, and Saks; however, generalizations of this concept to directed and weighted graphs present unforeseen and surprising changes in the necessary lookahead for strategic optimization. A pair of edges of unequal weights and opposite orientation can serve to simulate a communication or transportation connection with asymmetric costs, as may arise in a transportation network from prevailing winds or elevation changes, or in a communication network from aDSL or a similar technology. This research explores the complications introduced by asymmetric connections within even very small networks. We consider the dynamic relocation problem on a twovertex system and find that, even in this simplest possible asymmetric graph, the necessary lookahead for optimal relocation may be arbitrarily large. This investigation also gives rise to a lineartime algorithm to determine the optimizing realtime response to any request sequence which uniquely determines an optimal response.