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.

PURPOSE To examine the effects of panretinal photocoagulation (PRP) using a pattern scanning laser (PASCAL) system on the retinal nerve fiber layer (RNFL) thickness in patients with diabetic retinopathy. METHODS This retrospective study included 105 eyes with diabetic retinopathy, which consisted of three groups: the PASCAL group that underwent PRP with the PASCAL method (33 eyes), the conven...

In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 ...

1 Clermont Université, Université Blaise Pascal, LMGE, F-63000 Clermont-Ferrand, France 2 CNRS, UMR 6023, Laboratoire Microorganismes: Génome et Environnement, BP 80026, F63171 Aubière Cedex, France Clermont Université, Université Blaise Pascal, ICCF, F-63000 Clermont-Ferrand, France CNRS, UMR 6504, Institut de Chimie de Clermont-Ferrand, BP 80026, F-63171 Aubière Cedex, France * magalie.stauff...

It is well-known that Pascal and Brianchon theorems characterize conics in a Pappian projective plane. But, using these theorems and their modifications we shall show that the notion of a conic (or better a Pascal-Brianchon set) can be defined without any use of theory of projectivities or of polarities as usually.

The present paper shows that any sequence of integers laying along a finite ray in any Pascal-pyramid is log-concave, consequently unimodal. Further, we describe an algorithm which provides the plateaus of the diagonal sequences locating on layer n of the regular Pascal pyramid.

Interactive program development tools are being increasingly recognized as helpful in the construction of programs. This paper describes an integrated incremental program development system for Pascal called Pathcal. Pathcal contains facilities for creation, editing, debugging and testing of procedures and programs. The system facilities are all Pascal procedures or variables and because of thi...

PURPOSE The aim of this study was to evaluate the changes in thickness of each macular retinal layer, the peripapillary retinal nerve fiber layer (RNFL), and central macular thickness (CMT) after 577-nm pattern scanning laser (PASCAL) photocoagulation in patients with diabetic retinopathy. METHODS This retrospective study included 33 eyes with diabetic retinopathy that underwent 577-nm PASCAL...

The main paper demonstrated how the object proposal evaluation protocol is ‘gameable’ and performed some experiments to detect this ‘gameability’. In this supplement, we present additional details and results which support the arguments presented in the main paper. In section 1, we list and briefly describe the different object proposal algorithms which we used for our experiments. Following th...