• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.561-568
• /
• 2016

In this paper, the effect of absolute values on the behavior of functions f in the spaces $\mathcal{Q}_K$ is investigated. It is clear that $g{\in}\mathcal{Q}_K({\partial}{\mathbb{D}}){\Rightarrow}{\mid}g{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$, but the converse is not always true. For f in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that the condition together with ${\mid}f{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$ is equivalent to $f{\in}\mathcal{Q}_K$. As an application, a new criterion for inner-outer factorisation of $\mathcal{Q}_K$ spaces is given. These results are also new for $Q_p$ spaces.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.3
• /
• pp.311-315
• /
• 2008

We introduce nonnegative interval-valued set functions and nonnegative measurable interval-valued Junctions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [17]. We also obtained absolutely continuity of them in [9]. In this paper, we investigate some characterizations of the monotone interval-valued set function defined by the interval-valued Choquet integral, and such as subadditivity, superadditivity, null-additivity, converse-null-additivity.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.503-515
• /
• 2011

Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) which has symmetric Ricci tensor $Ric^D$ is projectively flat, then the connection D is Einstein-Weyl; but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure ($D,\;g,\;{\omega}$) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.559-568
• /
• 2019

In this paper we introduce and study the concept of of (${\varphi}$, ${\psi}$)-am-enability of a locally compact group G, where ${\varphi}$ is a continuous homomorphism on G and ${\psi}:G{\rightarrow}{\mathbb{C}}$ multiplicative linear function. We prove that if the group algebra $L^1$ (G) is (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-amenable then G is (${\varphi}$, ${\psi}$)-amenable, where ${\tilde{\varphi}}$ is the extension of ${\varphi}$ to M(G). In the case where ${\varphi}$ is an isomorphism on G it is shown that the converse is also valid.

• Journal of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.105-127
• /
• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Journal of Hospice and Palliative Care
• /
• v.24 no.4
• /
• pp.199-203
• /
• 2021

This paper provides practical suggestions for how palliative care clinicians can address the expressions of spiritual struggle voiced by patients and their loved ones. In addition to practical tips for listening and responding, ethical guidance and opportunities for self-reflection related to spiritual care are briefly discussed. Principles to guide practice when the clinician is listening and responding to a patient expressing spiritual struggle include being non-directive, honoring (vs. judging) the patient's spiritual or religious experience, keeping the conversation patient-centered, focusing on the core theme of what the patient is expressing presently, using the patient's terminology and framing, and responding "heart to heart" or "head to head" to align with the patient. Ultimately, the goal of a healing response from a spiritual care generalist is to allow the patient to "hear" or "see" themselves, to gain self-awareness. To converse with patients about spirituality in an ethical manner, the clinician must first assess the patient's spiritual needs and preferences and then honor these.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1327-1337
• /
• 2022

Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽_p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽_pⁿ. Eventually, we use these results to construct some optimal constant composition codes.

• Computers and Concrete
• /
• v.31 no.1
• /
• pp.1-7
• /
• 2023

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clamped-clamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.

• Bulletin of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.17-22
• /
• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• 중국학논총
• /
• no.64
• /
• pp.53-73
• /
• 2019

In the teaching of Chinese characters, making full use of the phonetic function of phonetic symbols can help learners improve their learning efficiency. The research on the characteristics of phonetic symbols and the rules of their construction is the premise of teaching Chinese characters with phonetic symbols. The phonetic symbols that can accurately prompt the pronunciation of the whole word and the homophone characters that they constitute provide the applicable materials for the teaching of Chinese characters. The split method simply and intuitively reflects the internal relationship among shape, sound and meaning in pictophonetic characters. "The analogy method of homophonic character group" and "the converse method of homophonic character group" are the combination of the function of the sound prompt and the characteristics of the analogy and induction of homophonic character, which can not only help students save the time of memorizing the sound, but also effectively increase the amount of literacy. The quantitative analysis of phonetic symbols and homophone symbols is of great significance to the classification of Chinese characters and the improvement of textbook editing.