• The Pure and Applied Mathematics
• /
• v.6 no.2
• /
• pp.121-127
• /
• 1999

We can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.

• East Asian mathematical journal
• /
• v.40 no.2
• /
• pp.209-229
• /
• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.325-344
• /
• 2015

Experimental tests on cellular beams with sinusoidal openings showed two main failure modes around the openings. They concern the formation of four plastic hinges and the local instability of the sinusoidal part of the opening. In parallel, numerical analysis of the sinusoidal part of the opening revealed the existence of an elastic rotational restraint between the intermediate web-post and the adjacent opening panel. The aim of the present study is to present an approach to quantify this rotational restraint. Through the response surface method, a mathematical model is proposed. It shows a great ability to predict the rotational restraint value as a function of the geometrical parameters of the opening. This model can be used to perform an extensive study with various geometrical configurations of beams with the aim to develop a reliable and realistic analytical model predicting the resistance of the sinusoidal openings.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.3
• /
• pp.59-70
• /
• 1993

This paper presents the results of experiments which compare the software complexity between programming languages, i.e, FORTRAN IV and FORTRAN 77, PASCAL and C language, respectively. Each experiment is performed to compare the complexity between programs of same problems using Halstead's method based on operator, and McCabe's based on data flow. As the results of 25 test programs experiments, FORTRAN 77 languages shows superiority to FORTRAN IV languages, and C than that of PASCAL languages, in the aspect of the global software complexity.

• Communications of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.867-877
• /
• 2020

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk 𝕌.

• Journal of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.479-491
• /
• 2008

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.

• Kyungpook Mathematical Journal
• /
• v.48 no.2
• /
• pp.331-335
• /
• 2008

In this paper, we investigate the number of ones in rows of Pascal's Rectangle. Using these results, we determine the existence of regular bipartite Steinhaus graphs. Also, we give an upper bound for the minimum degree of bipartite Steinhaus graphs.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.413-427
• /
• 2020

In this work we study 0-commuting matrix C(0) under relationships with the Pascal matrix C(1). Like kth power C(1)k is an arithmetic matrix of (kx+y)n with yx = xy (k ≥ 1), we express C(0)k as an arithmetic matrix of certain polynomial with yx = 0.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.989-993
• /
• 2022

In this paper, we prove Pascal's hexagon theorem by elementary tools only. We follow the well-known route to prove the theorem by Bezóut's theorem, explaining all the details in elementary argument. In particular, we prove a toy version of Study's lemma.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.16 no.10
• /
• pp.1009-1018
• /
• 1991

In this paper, we present a design and inplementation of the Hangul pascal programming language corresponding to Turbo pascal. The instructions of Hangul pascal were easily seledted to be understood of elementary middle, high school syudents, and Dos commands and error messages were translated into Hangul. Hangul-pascal were implemented into C-language under IBM PC XT / AT, MS-DOS.