On the norm of GCD and related matrices.
On the maximum row and column sum norm of GCD and related matrices.
On the non-quadraticity of values of the q-exponential function and related q-series
Orders with a normal basis
Orthogonal designs II.
Periodicity of β-expansions for certain Pisot units*
Given β > 1, let TβThe iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β.In [17], K. Schmidt analyzed the set of periodic points of Tβ, where β is a Pisot number. In an attempt to generalize some of his results, we study, for certain Pisot units, a different expansion that we call linear expansionwhere each ei...
Počátky teorie matic v Českých zemích a jejich ohlasy [Book]
Powers of a matrix and combinatorial identities.
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Singular differences of powers of -matrices
The Bernoullian of a Matrix. (A Generalization of the Bernoulli Numbers)
Si associano ad una matrice infinita di un certo tipo altre due matrici dello stesso tipo, dette rispettivamente bernoulliana e antibernoulliana di A. Si studiano alcune proprietà di queste matrici. Si ottiene in tal via una generalizzazione dei classici numeri di Bernoulli.
The factorization of an integral matrix into a product of two integral symmetric matrices I
The Hankel transform and some of its properties.
The inverse of the Pascal lower triangular matrix modulo .
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The reciprocal super Catalan matrix
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
Theorie der Körper von Matrizen.
Time delay in chemical exchange during an NMR pulse
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all...