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Relations defined on sets
 Journal of Formalized Mathematics
, 1989
"... Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse ima ..."
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Cited by 517 (0 self)
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Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse
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
Functions from a set to a set
 Journal of Formalized Mathematics
, 1989
"... function from a set X into a set Y, denoted by “Function of X,Y ”, the set of all functions from a set X into a set Y, denoted by Funcs(X,Y), and the permutation of a set (mode Permutation of X, where X is a set). Theorems and schemes included in the article are reformulations of the theorems of [1] ..."
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Cited by 1094 (23 self)
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function from a set X into a set Y, denoted by “Function of X,Y ”, the set of all functions from a set X into a set Y, denoted by Funcs(X,Y), and the permutation of a set (mode Permutation of X, where X is a set). Theorems and schemes included in the article are reformulations of the theorems of [1
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
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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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Shape modeling with front propagation: A level set approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods ..."
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Cited by 804 (20 self)
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is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. Index Terms Shape modeling, shape recovery, interface motion, level sets, hyperbolic conservation laws, HamiltonJacobi
Some Evidence on the Importance of Sticky Prices
 JOURNAL OF POLITICAL ECONOMY
, 2004
"... We examine the frequency of price changes for 350 categories of goods and services covering about 70 % of consumer spending, based on unpublished data from the BLS for 1995 to 1997. Compared with previous studies we find much more frequent price changes, with half of goods' prices lasting less ..."
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Cited by 734 (15 self)
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We examine the frequency of price changes for 350 categories of goods and services covering about 70 % of consumer spending, based on unpublished data from the BLS for 1995 to 1997. Compared with previous studies we find much more frequent price changes, with half of goods' prices lasting less than 4.3 months. Even excluding the role of temporary price cuts (sales), we find that half of goods' prices last 5.5 months or less. The frequency of price changes differs dramatically across categories. We exploit this variation to ask how inflation for "flexibleprice goods" (goods with frequent changes in individual prices) differs from inflation for "stickyprice goods" (those displaying infrequent price changes). Compared to the predictions of popular sticky price models, actual inflation rates are far more volatile and transient, particularly for stickyprice goods.
Results 1  10
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4,188,585