Results 1  10
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92
Computing iceberg queries efficiently
 In Proc. of the 24th VLDB Conf
, 1998
"... Many applications compute aggregate functions... ..."
Mellin transforms and asymptotics: Finite differences and Rice's integrals
, 1995
"... High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combin ..."
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Cited by 79 (8 self)
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High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries, digital search trees, quadtrees, and distributed leader election.
The curious history of Faà di Bruno’s formula
 Amer. Math. Monthly
, 2002
"... the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t)) ..."
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Cited by 47 (0 self)
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the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t))
Convoluted generalized white noise, Schwinger functions and their continuation to Wightman functions
, 2008
"... We construct Euclidean random fields X over IR d, by convoluting generalized white noise F with some integral kernels G, as X = G ∗ F. We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Sc ..."
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Cited by 17 (12 self)
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We construct Euclidean random fields X over IR d, by convoluting generalized white noise F with some integral kernels G, as X = G ∗ F. We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields. We present a partial negative result on the reflection positivity of convoluted generalized white noise. Furthermore, by representing the kernels Gα of the pseudo–differential operators (− ∆ + m 2 0) −α for α ∈ (0,1) and m0> 0 as Laplace transforms we perform the analytic continuation of the (truncated) Schwinger functions of X = Gα ∗ F, obtaining the corresponding (truncated) Wightman distributions on Minkowski space which satisfy the relativistic postulates on invariance, spectral property, locality and cluster property.
On the distribution of the sum of n nonidentically distributed uniform random variables
 Annals of the Institute of Statistical Mathematics
"... integrals. Abstract. The distribution of the sum of independent identically distributed uniform random variables is wellknown. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit ..."
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Cited by 11 (1 self)
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integrals. Abstract. The distribution of the sum of independent identically distributed uniform random variables is wellknown. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulæ for the distribution of the sum of n nonidentically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulæ some special cases which have appeared in the literature.
The 2adic valuation of the coefficients of a polynomial
 Scientia, Series A
"... Abstract. In this paper we compute the 2adic valuations of some polynomials associated with the definite integral ∫ ∞ dx 0 (x4 + 2ax2. + 1) m+1 1. ..."
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Cited by 7 (3 self)
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Abstract. In this paper we compute the 2adic valuations of some polynomials associated with the definite integral ∫ ∞ dx 0 (x4 + 2ax2. + 1) m+1 1.
Lattice Paths between Diagonal Boundaries
 Electronic J. Combinatorics
, 1998
"... A bivariate symmetric backwards recursion is of the form d[m, n]=w 0 (d[m1, n]+d[m, n1])+# 1 (d[mr 1 ,ns 1 ]+d[ms 1 ,nr 1 ])++# k (d[mr k ,ns k ] +d[ms k ,nr k ]) where # 0 ,...# k are weights, r 1 ,...r k and s 1 ,...s k are positive integers. We prove three theorems about solving symmetri ..."
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Cited by 7 (0 self)
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A bivariate symmetric backwards recursion is of the form d[m, n]=w 0 (d[m1, n]+d[m, n1])+# 1 (d[mr 1 ,ns 1 ]+d[ms 1 ,nr 1 ])++# k (d[mr k ,ns k ] +d[ms k ,nr k ]) where # 0 ,...# k are weights, r 1 ,...r k and s 1 ,...s k are positive integers. We prove three theorems about solving symmetric backwards recursions restricted to the diagonal band x + u<y<xl. With a solution we mean a formula that expresses d[m, n] as a sum of di#erences of recursions without the band restriction. Depending on the application, the boundary conditions can take di#erent forms. The three theorems solve the following cases: d[x+u, x] = 0 for all x # 0, and d[x l, x] = 0 for all x # l (applies to the exact distribution of the KolmogorovSmirnov twosample statistic), d[x + u, x]=0 for all x # 0, and d[x  l +1,x]=d[xl+1,x1] for x # l (ordinary lattice paths with weighted left turns), and d[y, y  u +1]=d[y1,yu+1]for all y # u and d[x  l +1,x]=d[xl+1,x1] for x # l. The first theorem is a gene...
A Finite Difference Approach To Degenerate Bernoulli And Stirling Polynomials
 DISCRETE MATH
, 1992
"... Starting with divided differences of binomial coefficients, a class of multivalued polynomials (three parameters), which includes Bernoulli and Stirling polynomials and various generalizations, is developed. These carry a natural and convenient combinatorial interpretation. Some particular calculati ..."
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Cited by 7 (5 self)
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Starting with divided differences of binomial coefficients, a class of multivalued polynomials (three parameters), which includes Bernoulli and Stirling polynomials and various generalizations, is developed. These carry a natural and convenient combinatorial interpretation. Some particular calculations are done and several factorization results are proven and conjectured.