Displaying similar documents to “Extensions of linear operators from hyperplanes of l ( n )

Determinants of matrices associated with incidence functions on posets

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

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Let S = { x 1 , , x n } be a finite subset of a partially ordered set P . Let f be an incidence function of P . Let [ f ( x i x j ) ] denote the n × n matrix having f evaluated at the meet x i x j of x i and x j as its i , j -entry and [ f ( x i x j ) ] denote the n × n matrix having f evaluated at the join x i x j of x i and x j as its i , j -entry. The set S is said to be meet-closed if x i x j S for all 1 i , j n . In this paper we get explicit combinatorial formulas for the determinants of matrices [ f ( x i x j ) ] and [ f ( x i x j ) ] on any meet-closed set S . We also obtain necessary and sufficient conditions for...

M -estimation in nonlinear regression for longitudinal data

Martina Orsáková (2007)

Kybernetika

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The longitudinal regression model Z i j = m ( θ 0 , 𝕏 i ( T i j ) ) + ε i j , where Z i j is the j th measurement of the i th subject at random time T i j , m is the regression function, 𝕏 i ( T i j ) is a predictable covariate process observed at time T i j and ε i j is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth M -estimator of unknown parameter θ 0 .

On the divisibility of power LCM matrices by power GCD matrices

Jian Rong Zhao, Shaofang Hong, Qunying Liao, Kar-Ping Shum (2007)

Czechoslovak Mathematical Journal

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Let S = { x 1 , , x n } be a set of n distinct positive integers and e 1 an integer. Denote the n × n power GCD (resp. power LCM) matrix on S having the e -th power of the greatest common divisor ( x i , x j ) (resp. the e -th power of the least common multiple [ x i , x j ] ) as the ( i , j ) -entry of the matrix by ( ( x i , x j ) e ) (resp. ( [ x i , x j ] e ) ) . We call the set S an odd gcd closed (resp. odd lcm closed) set if every element in S is an odd number and ( x i , x j ) S (resp. [ x i , x j ] S ) for all 1 i , j n . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in...