Let q be a power of a prime p. Matrices over Fq in which every subset of basis size of the columns are independent, are of interest in coding theory, matroid theory, and projective geometry. For any positive integer m ≤ p and bijection σ : N≤q−1 ∪ {0} → Fq, we show that the m× (q + 1) matrix Hq,m, with {Uq}i,j = 

AIM To evaluate the outcome of laser iridotomy using 532-nm Nd: YAG laser (PASCAL) with short pulse duration and Nd: YAG laser compared to conventional combined laser iridotomy. METHODS Retrospective, nonrandomized, comparative case series. Forty-five eyes of 34 patients underwent laser iridotomy. Twenty-two eyes underwent iridotomy using short duration PASCAL and Nd: YAG laser, and 23 eyes u...

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319—320], we prove that if a slowly decreasing sequence of real numbers is Abel summable, then it is convergent in the ordinary sense. Subjclass [2010] : 40A05; 40E05; 40G10.

Assume ∅ < log−1 (|N |). Every student is aware that N → B′′. We show that F̃ ∈ M̃. In contrast, a central problem in tropical PDE is the derivation of points. Now it would be interesting to apply the techniques of [20] to semi-admissible functors.

In this paper, we address the problem of the eeciency of the main phase of most data mining applications: The frequent pattern extraction. This problem is mainly related to the number of operations required for counting pattern supports in the database, and we propose a new method, called pattern counting inference, that allows to perform as few support counts as possible. Using this method, th...

Our GRB theory, previously developed using GRB 991216 as a prototype, is here applied to GRB 980425. We fit the luminosity observed in the 40–700 keV, 2–26 keV and 2–10 keV bands by the BeppoSAX satellite. In addition the supernova SN1998bw is the outcome of an " induced gravitational collapse " triggered by GRB 980425, in agreement with the GRB-Supernova Time Sequence (GSTS) paradigm (Ruffini ...

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence ai,j = ai−1,j + ai,j−1, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 14 (2002), to appear].