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The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 682 (76 self)
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.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R
Relations and their basic properties
 Journal of Formalized Mathematics
, 1989
"... Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions, ∪, ∩ and \ are ..."
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Cited by 1069 (6 self)
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Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions, ∪, ∩ and \ are redefined. Basic facts about the above mentioned notions are presented.
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 539 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query
An inventory for measuring clinical anxiety: Psychometric properties
 Journal of Consulting and Clinical Psychology
, 1988
"... The development ofa 2 litem selfreport inventory for measuring the severity of anxiety in psychiatric populations i described. The initial item pool f86 items was drawn from three preexisting scales: the Anxiety Checklist, the Physician's Desk Reference Checklist, and the Situational Anxiety ..."
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Cited by 719 (1 self)
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The development ofa 2 litem selfreport inventory for measuring the severity of anxiety in psychiatric populations i described. The initial item pool f86 items was drawn from three preexisting scales: the Anxiety Checklist, the Physician's Desk Reference Checklist, and the Situational
A LongMemory Property of Stock Market Returns and a New Model
 Journal of Empirical Finance
, 1993
"... A ‘long memory ’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return lrfl ” also has quite high autocorrelation for lo ..."
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Cited by 606 (21 self)
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A ‘long memory ’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return lrfl ” also has quite high autocorrelation
Panel Cointegration; Asymptotic and Finite Sample Properties of Pooled Time Series Tests, With an Application to the PPP Hypothesis; New Results. Working paper
, 1997
"... We examine properties of residualbased tests for the null of no cointegration for dynamic panels in which both the shortrun dynamics and the longrun slope coefficients are permitted to be heterogeneous across individual members of the panel+ The tests also allow for individual heterogeneous fixed ..."
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Cited by 499 (13 self)
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We examine properties of residualbased tests for the null of no cointegration for dynamic panels in which both the shortrun dynamics and the longrun slope coefficients are permitted to be heterogeneous across individual members of the panel+ The tests also allow for individual heterogeneous
A theory of communicating sequential processes
, 1984
"... A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account. ..."
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Cited by 4135 (17 self)
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A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen
Results 1  10
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