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22,090
Average Order in Cyclic Groups
, 2002
"... For each natural number n we determine the average order #(n) of the elements in a cyclic group of order n. We show that a large fraction of the contribution to #(n) comes from the #(n) primitive elements of order n. It is therefore of interest to study also the function #(n) = #(n)/#(n). We determi ..."
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Cited by 6 (1 self)
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For each natural number n we determine the average order #(n) of the elements in a cyclic group of order n. We show that a large fraction of the contribution to #(n) comes from the #(n) primitive elements of order n. It is therefore of interest to study also the function #(n) = #(n)/#(n). We
The Average Order of a Permutation
 Electronic J. Combinatorics
, 1998
"... . We show that the average order n of a permutation in Sn satisfies log n = C r n log n +O `# n log log n log n ' , which refines earlier results of Erdos and Turan, Schmutz, and Goh and Schmutz. 1. Introduction. For # # S n let N(#) be the order of # in the group S n . Erdos and Tu ..."
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Cited by 6 (0 self)
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. We show that the average order n of a permutation in Sn satisfies log n = C r n log n +O `# n log log n log n ' , which refines earlier results of Erdos and Turan, Schmutz, and Goh and Schmutz. 1. Introduction. For # # S n let N(#) be the order of # in the group S n . Erdos
Average Order in Cyclic Groups
 JOURNAL DE THÉORIE DES NOMBRES
, 2004
"... For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We determi ..."
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For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We
Average Orders of Certain Arithmetical Functions
, 2006
"... ABSTRACT. We consider the functions M(n), the maximum exponent of any prime power dividing n and m(n), the minimum exponent of any prime power dividing n. The sums ∑ n≤x M(n) and n≤x m(n) have been well investigated in the literature. In this note, we will improve known estimates of both the above s ..."
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ABSTRACT. We consider the functions M(n), the maximum exponent of any prime power dividing n and m(n), the minimum exponent of any prime power dividing n. The sums ∑ n≤x M(n) and n≤x m(n) have been well investigated in the literature. In this note, we will improve known estimates of both the above sums under the assumption of the Riemann hypothesis. We will also obtain Ωtype estimates for these sums unconditionally.
A note on the average order of the gcdsum function
 J. Integer Seq
"... We prove an asymptotic formula for the average order of the gcdsum function by using a new convolution identity. 1 Introduction and main result In 2001, Broughan [1] studied the gcdsum function g defined for any positive integer n by g (n) = n∑ (k,n), ..."
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Cited by 11 (2 self)
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We prove an asymptotic formula for the average order of the gcdsum function by using a new convolution identity. 1 Introduction and main result In 2001, Broughan [1] studied the gcdsum function g defined for any positive integer n by g (n) = n∑ (k,n),
Liquidity Risk and Expected Stock Returns
, 2002
"... This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related crosssectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individualsto ..."
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Cited by 629 (6 self)
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stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. Over a 34year period, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 % annually, adjusted
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside ..."
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Cited by 558 (14 self)
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It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We
Random Early Detection Gateways for Congestion Avoidance.
 IEEELACM Transactions on Networking,
, 1993
"... AbstractThis paper presents Random Early Detection (RED) gateways for congestion avoidance in packetswitched networks. The gateway detects incipient congestion by computing the average queue size. The gateway could notify connections of congestion either by dropping packets arriving at the gatewa ..."
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Cited by 2716 (31 self)
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. However, it would clearly be undesirable to have large queues (possibly on the order of a delay bandwidth product) that were full much of the time; this would significantly increase the average delay in the network. Therefore, with increasingly highspeed networks, it is increasingly important to have
Scalable Application Layer Multicast
, 2002
"... We describe a new scalable applicationlayer multicast protocol, specifically designed for lowbandwidth, data streaming applications with large receiver sets. Our scheme is based upon a hierarchical clustering of the applicationlayer multicast peers and can support a number of different data deliv ..."
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Cited by 731 (21 self)
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endtoend latencies and similar failure recovery properties. More importantly, it is able to achieve these results by using orders of magnitude lower control traffic. Finally, we present results from our widearea testbed in which we experimented with 32100 member groups distributed over 8 different
A comparison of event models for Naive Bayes text classification
, 1998
"... Recent work in text classification has used two different firstorder probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multivariate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey ..."
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Cited by 1025 (26 self)
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Recent work in text classification has used two different firstorder probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multivariate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e
Results 1  10
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22,090