• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.127-133
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• 2018

We look at Toeplitz arrays on ${\mathbb{Z}}^d$ and study a characterizing property for pure discrete spectrum in terms of the periodic structures of the Toeplitz arrays.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.363-368
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• 2008

In this paper, we find some properties of multiplication modules and give an alternative proof of a Theorem of P.F. Smith.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.125-131
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• 2021

In the paper, we investigate the representation of the numerical range W(An) for the 2 × 2 complex matrix A, in terms of the numerical range W(A) of the matrix A, and the elements of A or the eigenvalue of A.

• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.95-111
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• 2006

In [6], we have recently proved that an additive inverse semiring S is a Clifford semifield if and only if S is a subdirect product of a field and a distributive lattice. In this paper, we study the matrix semiring over a Clifford semifield.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.109-119
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• 2023

As for the practical purpose of mathematics education, the extrinsic purpose is emphasized. As an alternative to this, a discussion on mathematics education as a character education is urgently requested. It can be said that the main purpose of learning mathematics is to have a form of life that values the form and structure of mathematics. The epistemological basis of such an idea can be seen as based on Kant's philosophy. Kant's epistemology can provide one answer to the question of the intrinsic purpose of mathematics education.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.109-143
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• 2011

Augustus De Morgan became to be deeply interested in the education of pure mathematics since he came to teach in UCL because of the specific nature of natural philosophy lectures, the academical knowledge and reasoning powers of the students, and the negative attitudes of London society on mathematics. During his long tenure, he really tried his best to make his students understand the important concepts and the principles of pure mathematics, and logically explain the processes of inducing and proving the laws of pure mathematics. When he could not stay as a mere researcher, he had to concern himself with and pay attention to the problems of educating students. And then his teaching style was constructed in a specific way by the various attitudes about mathematics, the boundary relationship between the adjacent academical branches, and the social and systematic nature of UCL.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.253-265
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• 2018

In this paper, we introduce the concept of Fibonacci sequences on MV-algebras and study them accurately. Also, by introducing the concepts of periodic sequences and power-associative MV-algebras, other properties are also obtained. The relation between MV-algebras and Fibonacci sequences is investigated.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.225-234
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• 2023

In this paper, we use the use the linear operator ʒ^x_τ,σ(u, v, y)𝔣(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.801-810
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• 2023

The aim of this paper, investigated of weighted space which contained the unbounded functions which is to be approximated by linear operators in terms some Well-known approximation tools such as the modulus of smoothness and K-functional. The characteristics of the identical theorem between modulus of smoothness and K-functional are consider. In addition to the establish the direct, converse and identical theorem by using some linear operators in terms modulus Ditzian-Totik.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.589-596
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• 2007

In this paper we prove that the extension of pure injective module is pure injective if and only if the cotorsion envelope and the pure injective envelope of any R-module M are isomorphic over M. And we prove that if the product of pure injective envelopes of flat modules is a pure injective envelope and the product of flat covers is a flat cover, then the product of cotorsion envelopes is a cotorsion envelope.