• 호남수학학술지
• /
• 제41권3호
• /
• pp.515-530
• /
• 2019

The concept of fuzzy sets in UP-algebras was first introduced by Somjanta et al. [Fuzzy sets in UP-algebras; 2016]. In this paper, we introduce and study fuzzy proper UP-filters of UP-algebras and prove their generalizations and characteristic fuzzy sets of proper UP-filters. Moreover, we discuss the relations between fuzzy proper UP-filters and their level subsets.

• 대한수학회논문집
• /
• 제10권3호
• /
• pp.653-659
• /
• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제30권3_4호
• /
• pp.202-211
• /
• 2003

객체지향 방법론에서 정적 및 동적 모델에 관한 구문(Syntax)과 의미론(Semantics)의 형식적 정의는 잘 이루어 졌으나 객체 상호작용의 행위에 대한 형식론은 아직까지 제시되지 않았다. 본 논문에서는 객체 상호작용을 묘사하는 UML의 순서(Sequence) 다이어그램을 토대로 프로세스 대수를 사용하여 객체 상호작용을 정의하고 객체 상호작용의 특성을 정규화 시킨다. 이러한 결과는 M. Snoeck과 G. Dedene[9]가 제시한 종속존재 관계의 개념을 상호작용 관계의 개념으로 대체하여 형식론을 전개할 수 있음을 보여준다.

• 대한수학회지
• /
• 제57권4호
• /
• pp.1005-1018
• /
• 2020

A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹ⁿ(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

• Journal of electromagnetic engineering and science
• /
• 제4권1호
• /
• pp.17-22
• /
• 2004

In this paper, we implement an efficient MLC/PDL system for AWGN channels. In terms of the tradeoff between the hardware implementation and system performance, proposed algebra LDPC codes are optimized by the Gaussian approximation(GA) according to the rate of each level assigned by the capacity rule and chosen as the component code. System performance with Ungerboeck Partitioning(UP), Miked Partitioning(MP) and Gray Mapping(GM) of 8PSK are evaluated, respectively. Many results are presented in this paper; they can indicate that the proposed MLC/PDL system using optimized algebra LDPC codes with different code rate, capacity rule and Gray mapping(GM) can achieve the best performance.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.371-399
• /
• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• 대한수학회지
• /
• 제48권1호
• /
• pp.1-12
• /
• 2011

The purpose of this paper is to study pseudo-Riemannian algebras, which are algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We nd that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposition of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automorphism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.1077-1108
• /
• 2019

The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper t-(strong) level subsets and lower t-(strong) level subsets in UP-algebras.

• Journal of applied mathematics & informatics
• /
• 제41권3호
• /
• pp.657-685
• /
• 2023

This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss t-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.

• 대한수학회보
• /
• 제20권1호
• /
• pp.31-36
• /
• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).