• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.5 no.4
• /
• pp.322-326
• /
• 2005

We investigate the properties of A-transformations, P-transformations and L-transformations in metric spaces, t-norms and T-fuzzy equivalence relations.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.725-731
• /
• 2023

Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in [4], in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.

• Bulletin of the Korean Chemical Society
• /
• v.25 no.2
• /
• pp.285-288
• /
• 2004

A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.3
• /
• pp.194-206
• /
• 2023

We present families of nonlinear transformations useful for numerical evaluation of weakly singular integrals. First, for end-point singular integrals, we define a prototype function with some appropriate features and then suggest a family of transformations. In addition, for interior-point singular integrals, we develop a family of nonlinear transformations based on the aforementioned prototype function. We take some examples to explore the efficiency of the proposed nonlinear transformations in using the Gauss-Legendre quadrature rule. From the numerical results, we can find the superiority of the proposed transformations compared to some existing transformations, especially for the integrals with high singularity strength.

• Korean Journal of Mathematics
• /
• v.31 no.4
• /
• pp.495-504
• /
• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.

• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.627-635
• /
• 2018

In this paper, we use the notion of characters of transformations provided in [8] by Purisang and Rakbud to define a notion of weak regularity of transformations on an arbitrarily fixed set X. The regularity of a semigroup of weakly regular transformations on a set X is also investigated.

• Communications of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.643-645
• /
• 2024

In this note, we aim to correct some of the results presented in [1]. Namely, the statements of Proposition 2.1, Corollary 2.2, Corollary 2.3, Theorem 2.4 and Theorem 2.6, concerning only the monoids 𝓞𝓟_n and 𝓟𝓞𝓟_n, have to exclude transformations of rank two. All other results of [1], as well as those mentioned above but for the monoids 𝓞𝓡_n and 𝓟𝓞𝓡_n, do not require correction.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.573-584
• /
• 2016

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on ${\mathbb{Z}}_{2^n}$ which generates an n-bit word sequence without consecutive elements of period $2^n$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.133-146
• /
• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• East Asian mathematical journal
• /
• v.22 no.1
• /
• pp.71-77
• /
• 2006

By applying various known summation theorems to a general transformation formula based upon Bailey's transformation theorem due to Slater, Exton has obtained numerous and new quadratic transformations involving hypergeometric functions of order greater than two(some of which have typographical errors). We aim at first deriving a general quadratic transformation formula due to Exton and next providing a list of quadratic formulas(including the corrected forms of Exton's results) and some more results.