Results 21 to 30 of about 142,409 (160)
Factorization invariants in numerical monoids
, 2016 Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids of the natural
O'Neill, Christopher, Pelayo, Roberto
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Unit, Irreducible, and Prime Elements of The Integral Domain Z[sqrt (5)]
Jurnal MatematikaIn abstract algebra at the undergraduate level, the ring Z[sqrt(5)] is often used as a simple example of an integral domain that does not satisfy the unique factorization domain (UFD) but Z[sqrt(5)] is Halfway Factorial Domain (HFD).
Daisyah Alifian Fatahillaj
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A deterministic version of Pollard's p-1 algorithm
, 2009 In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's $p-1$ algorithm, which finds in random polynomial time the prime divisors $p$ of an ...
Zralek, Bartosz
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Deterministic elliptic curve primality proving for a special sequence of numbers
, 2013 We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm uses O(log N)
Everest +5 more
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Assessing Agricultural Green Total Factor Productivity in Latin America
Agribusiness, EarlyView.ABSTRACT The agricultural sector in Latin America plays a vital role in ensuring food security while impacting the environment. However, there remains a lack of analysis regarding the inputs responsible for pollution within its sub‐technologies. Hence, this article aims to assess agricultural green total factor productivity (TFP) through a novel ...
Tianxiang Li +2 more
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Acceleration detection of large (probably) prime numbers
, 2013 In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resort to trial division by a few initial prime numbers, since such a division take less time.
Nikolic, Olivera +2 more
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Trust‐region filter algorithms utilizing Hessian information for gray‐box optimization
AIChE Journal, EarlyView.Abstract Optimizing industrial processes often involves gray‐box models that couple algebraic glass‐box equations with black‐box components lacking analytic derivatives. Such systems challenge derivative‐based solvers. The classical trust‐region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous ...
Gul Hameed +4 more
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Where is the Primal Total Factor Productivity Index? [PDF]
SSRN Electronic Journal, 2010 A primal index of productivity change is introduced which decomposes exactly in three components: technical change, technical efficiency change and average scale economies (radial scale change). The proposed index is invariant to movement along indifference surfaces and it collapses to the Malmquist index if the technology is locally constant returns ...
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A trust‐region funnel algorithm for gray‐box optimization
AIChE Journal, EarlyView.Abstract Gray‐box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black‐box models lacking analytic derivatives, remains a challenge. Trust‐region (TR) methods provide a robust framework for gray‐box problems through local reduced models (RMs) for black‐box components, but they are ...
Gul Hameed +4 more
wiley +1 more source
What is the smallest prime? [PDF]
, 2012 What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers.
Caldwell, Chris K., Xiong, Yeng
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