Displaying similar documents to “The continuous solutions of a generalized Dhombres functional equation”

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 .

The Henstock-Kurzweil approach to Young integrals with integrators in BV φ

Boonpogkrong Varayu, Tuan-Seng Chew (2006)

Mathematica Bohemica

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In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral ∫ a b f d g exists if f ∈ B V φ [ a , b ] , g ∈ B V ψ [ a , b ] and ∑ n = 1 ∞ φ - 1 ( 1 / n ) ψ - 1 ( 1 / n ) < ∞ . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.