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47,633
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 688 (73 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
Data cube: A relational aggregation operator generalizing groupby, crosstab, and subtotals
, 1996
"... Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zerodimensional or onedimensional aggregates. Applications need the Ndimensional generalization of these op ..."
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Cited by 860 (11 self)
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Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zerodimensional or onedimensional aggregates. Applications need the Ndimensional generalization
Group formation in large social networks: membership, growth, and evolution
 IN KDD ’06: PROCEEDINGS OF THE 12TH ACM SIGKDD INTERNATIONAL CONFERENCE ON KNOWLEDGE DISCOVERY AND DATA MINING
, 2006
"... The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences — political movements, professional organizations, and religious denominations all provide fundamental examples of such communities. In the digital domain, ..."
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Cited by 496 (19 self)
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The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences — political movements, professional organizations, and religious denominations all provide fundamental examples of such communities. In the digital domain
Institutions as the Fundamental Cause of LongRun Growth
 IN HANDBOOK OF ECONOMIC GROWTH, ED. PHILIPPE AGHION AND STEPHEN DURLAUF
, 2005
"... This paper develops the empirical and theoretical case that differences in economic institutions are the fundamental cause of differences in economic development. We first document the empirical importance of institutions by focusing on two “quasinatural experiments” in history, the division of K ..."
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Cited by 458 (9 self)
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This paper develops the empirical and theoretical case that differences in economic institutions are the fundamental cause of differences in economic development. We first document the empirical importance of institutions by focusing on two “quasinatural experiments” in history, the division
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5631 (20 self)
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in the superconformal group (as opposed to just the superPoincare group). The ’t Hooft limit of 3+1 N = 4 superYangMills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various AntideSitter spacetimes is dual to various conformal
A large mass hierarchy from a small extra dimension
, 1999
"... We propose a new higherdimensional mechanism for solving the hierarchy problem. The weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of ..."
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Cited by 1077 (3 self)
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is fundamentally higher dimensional with 4+n spacetime dimensions, then the effective fourdimensional (reduced) Planck scale, MPl = 2 ×10 18 GeV, is determined by the fundamental (4+n)dimensional Planck scale, M, and the geometry of the extra dimensions.
Knowledge and Common Knowledge in a Distributed Environment
 Journal of the ACM
, 1984
"... : Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system&apo ..."
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Cited by 578 (55 self)
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: Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system
On limits of wireless communications in a fading environment when using multiple antennas
 Wireless Personal Communications
, 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (M ..."
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Cited by 2426 (14 self)
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to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signaltonoise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take
On the distribution of the length of the longest increasing subsequence of random permutations
 J. Amer. Math. Soc
, 1999
"... Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1 ..."
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Cited by 495 (33 self)
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Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1
On the geometric and algebraic rank of graph manifolds
, 2003
"... Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3ngenerated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M is call ..."
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Cited by 16 (1 self)
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Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3ngenerated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M
Results 1  10
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47,633