Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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05 Mar 2002
TL;DR: In this paper, a pseudo-random signal producing circuit includes a generator 110 for generating a first pseudo random signal having a bit width a (a being an integer not smaller than 1).
Abstract: A pseudo random signal producing circuit includes a generator 110 for generating a first pseudo random signal having a bit width a (a being an integer not smaller than 1), a generator 120 for generating a second pseudo random signal having a bit width b (b being an integer not smaller than 1 and different from a), a matrix calculator 130 for carrying out matrix calculation upon the first and the second pseudo random signals to produce a calculation result signal having a bit width (a*b), an N-bit shift register 200 responsive to the calculation result signal having the bit width (a*b) for producing an output pseudo random signal having a bit width N (N being a divisor of (a*b)), and a frequency-division clock generator 300 for driving a pseudo random data generator 100.
8 citations
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TL;DR: The concept of Okamoto-Painlev-e pair (S, Y) was introduced in this paper, which consists of a compact smooth complex surface S and an effective divisor Y on S satisfying certain conditions.
Abstract: In this paper, we introduce the notion of an Okamoto-Painlev\'e pair (S, Y) which consists of a compact smooth complex surface S and an effective divisor Y on S satisfying certain conditions. Though spaces of initial values of Painlev\'e equations introduced by K. Okamoto give examples of Okamoto-Painleve pairs, we find a new example of Okamoto-Painlev\'e pairs not listed in \cite{Oka}. We will give the complete classification of Okamoto-Painlev\'e pairs.
8 citations
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TL;DR: In this article, the existence of primes and primitive divisors in function field analogues of classical divisibility sequences was studied under various hypotheses, and it was shown that Lucas sequences and elliptic divisability sequences over function fields defined over number fields contain infinitely many irreducible elements.
Abstract: In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.
8 citations
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TL;DR: In this article, a single clock source drives a number of variable divisor frequency dividers to produce different musical tones at different times, and the exact value of the ratio varies from note to note within each octave so that the phase roll is not monotonously the same for all notes.
Abstract: In an electronic organ of the time-sharing type, a single clock source drives a number of variable divisor frequency dividers which are assigned different divisor values to produce different musical tones at different times. In order to prevent phase synchronism between two simultaneously operating dividers, and thus achieve a rolling phase relationship which is perceived as a chorus effect, divisor values are employed for the two frequency dividers which are not in a whole number relationship. If the two dividers are generating octavely related notes, the divisors used have a ratio not quite equal to the nominal 2:1 value which musical theory requires. Moreover, the exact value of the ratio varies from note to note within each octave so that the rate of phase roll is not monotonously the same for all notes. Alternatively, if the two dividers are both generating the same note, then the divisors used have a ratio which is not quite equal to the 1:1 value which musical theory requires.
8 citations
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TL;DR: A Riesz sum identity is established that generalizes Ramanujan's identity linked to the divisor problem and also investigates if identities exist for certain weighted sums, called RiesZ sums, that generalize Ramanujar's identities.
8 citations