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Quadratic residues of certain types
 Rocky Mountain J. Math
"... ABSTRACT. The main purpose of the paper is to show that if p is a prime different from 2, 3, 5, 7, 13, 37, then there exists a prime number q smaller than p, q ≡ 1 (mod 4), which is a quadratic residue modulo p. Also, it is shown that if p is a prime number which is not 2, 3, 5, 7, 17, then there ex ..."
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Cited by 2 (0 self)
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ABSTRACT. The main purpose of the paper is to show that if p is a prime different from 2, 3, 5, 7, 13, 37, then there exists a prime number q smaller than p, q ≡ 1 (mod 4), which is a quadratic residue modulo p. Also, it is shown that if p is a prime number which is not 2, 3, 5, 7, 17, then there exists aprimenumberq ≡ 3 (mod 4), q<p, which is a quadratic residue modulo p. 1. Introduction. In [2] it is shown that any n ∈ N, n>3, could be written as n = a + b, a, b being positive integers such that Ω(ab) is an even number. If m ∈ N, m ≥ 2, has the standard decomposition m = p a1
InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
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Cited by 821 (23 self)
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In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "
Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks
 IEEE Transactions on Automatic Control
, 1992
"... AbstructThe stability of a queueing network with interdependent servers is considered. The dependency of servers is described by the definition of their subsets that can be activated simultaneously. Multihop packet radio networks (PRN’s) provide a motivation for the consideration of this system. We ..."
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Cited by 949 (19 self)
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region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. I.
Short signatures from the Weil pairing
, 2001
"... We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures ar ..."
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Cited by 755 (25 self)
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We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures
Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms
, 1998
"... This article reviews five approximate statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These tests are compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type I err ..."
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Cited by 723 (8 self)
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error). Two widely used statistical tests are shown to have high probability of type I error in certain situations and should never be used: a test for the difference of two proportions and a paireddifferences t test based on taking several random traintest splits. A third test, a paired
PVM: A Framework for Parallel Distributed Computing
 Concurrency: Practice and Experience
, 1990
"... The PVM system is a programming environment for the development and execution of large concurrent or parallel applications that consist of many interacting, but relatively independent, components. It is intended to operate on a collection of heterogeneous computing elements interconnected by one or ..."
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Cited by 788 (27 self)
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of various types of algorithms (and their interactions), while the underlying infrastructure permits the execution of applications on a virtual computing environment that supports multiple parallel computation models. PVM contains facilities for concurrent, sequential, or conditional execution of application
Learning and development in neural networks: The importance of starting small
 Cognition
, 1993
"... It is a striking fact that in humans the greatest learnmg occurs precisely at that point in time childhood when the most dramatic maturational changes also occur. This report describes possible synergistic interactions between maturational change and the ability to learn a complex domain (language ..."
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Cited by 531 (17 self)
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(language), as investigated in connectionist networks. The networks are trained to process complex sentences involving relative clauses, number agreement, and several types of verb argument structure. Training fails in the case of networks which are fully formed and ‘adultlike ’ in their capacity. Training
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out
CIL: Intermediate language and tools for analysis and transformation of C programs
 In International Conference on Compiler Construction
, 2002
"... Abstract. This paper describes the CIntermediate Language: a highlevel representation along with a set of tools that permit easy analysis and sourcetosource transformation of C programs. Compared to C, CIL has fewer constructs. It breaks down certain complicated constructs of C into simpler ones, ..."
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Cited by 533 (11 self)
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Abstract. This paper describes the CIntermediate Language: a highlevel representation along with a set of tools that permit easy analysis and sourcetosource transformation of C programs. Compared to C, CIL has fewer constructs. It breaks down certain complicated constructs of C into simpler ones
ASYMPTOTIC EQUILIBRIUM FOR CERTAIN TYPE OF DIFFERENTIAL EQUATIONS WITH MAXIMUM ∗
"... In this work we obtain asymptotic representations for the solutions of certain type of differential equations with maximum. We deduce the asymptotic equilibrium for this class of differential equations. ..."
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In this work we obtain asymptotic representations for the solutions of certain type of differential equations with maximum. We deduce the asymptotic equilibrium for this class of differential equations.
Results 1  10
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