• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제37권6호
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• pp.464-469
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• 2011

Introduction: As dental implant surgery is becoming increasingly popular, it has become one of the causes for the hypesthesia of the inferior alveolar nerve, along with other surgical procedures, such as a third molar extraction. In addition, it tends to cause legal problems between the operator and patient. Therefore, there must be a proper method that is reliable, objective and economical to assess the nerve impairment. For this reason, an attempt was made to use an Electric Pulp Tester to assess inferior alveolar nerve block anesthesia. Materials and Methods: Thirty patients were tested. Electric pulp testing of the lower jaw skin was performed at the three different times, before anesthesia, at the onset of sensory changes and after 15 minutes waiting from the onset, and on the 10 points of the chin, which produced 10 sections on the skin area. Results: Twenty seven patients (90%) could feel the electric stimulus on the chin at all 10 points before local anesthesia and the scores represent the statistical differences between the right and left points except R4 and L4. After anesthesia, the difference between the right and left points (L3-R3, L4-R4, L5-R5) increased significantly with time but two points (L2, R2) showed no significant difference. The scores on the left chin (L3, L4, L5) increased, whereas the other points (R1-R5, L1, L2) showed no significant differences. Conclusion: This study highlights the potential clinical use of an electric pulp tester for an assessment of inferior alveolar nerve impairment.

• 대한수학회논문집
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• 제31권1호
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• pp.147-161
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• 2016

In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.

• 대한수학회지
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• 제35권3호
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.

• 대한수학회보
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• 제26권2호
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• pp.185-190
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• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• 대한수학회보
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• 제54권2호
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• pp.705-714
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• 2017

Let $A^2_{{\alpha},{\beta}}(\mathbb{B}_n)$ denote the space of holomorphic functions that are $L^2$ with respect to a weight of form ${\omega}_{{\alpha},{\beta}}(z)=(1-{\mid}z{\mid}^{\alpha}e^{-{\frac{\beta}{1-{\mid}z{\mid}}}}$, where ${\alpha}{\in}\mathbb{R}$ and ${\beta}$ > 0 on the unit ball $\mathbb{B}_n$. We obtain some results for the boundedness and compactness of $Ces{\grave{a}}ro$ operator on $A^2_{{\alpha},{\beta}(\mathbb{B}_n)$.

• 대한수학회보
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• 제55권2호
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• pp.533-543
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• 2018

Under the symbol ${\Omega}$ is a combination of ${\phi}_i$ ($i=1,2,3,{\ldots},n$) which has a suitable growth condition, for dimension n = 2 and $n{\geq}3$, when the initial data f belongs to homogeneous Sobolev space, we obtain the global $L^q$ estimate for maximal operators generated by operators family $\{S_{t,{\Omega}}\}_{t{\in}{\mathbb{R}}}$ associated with solution to dispersive equations, which extend some results in [27].

• 호남수학학술지
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• 제36권4호
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• pp.805-812
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• 2014

For unit tangent sphere bundles $T_1M$ with the standard contact metric structure (${\eta},\bar{g},{\phi},{\xi}$), we have two fundamental operators that is, $h=\frac{1}{2}{\pounds}_{\xi}{\phi}$ and ${\ell}=\bar{R}({\cdot},{\xi}){\xi}$, where ${\pounds}_{\xi}$ denotes Lie differentiation for the Reeb vector field ${\xi}$ and $\bar{R}$ denotes the Riemmannian curvature tensor of $T_1M$. In this paper, we study the Reeb ow invariancy of the corresponding (0, 2)-tensor fields H and L of h and ${\ell}$, respectively.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.307-310
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• 1995

In the conventional systems, a human must have knowledge of machines and of their special language in communicating with machines. In one side, it is desirable for a human but in another side, it is true that achieving it is very elaborate and is also a significant cause of human error. To reduce this sort of human load, an intelligent man-machine interface is desirable to exist between a human operator and machines to be operated. In the ordinary human communication, not only linguistic information but also visual information is effective, compensating for each others defect. From this viewpoint, problem of translating verbal expressions to some visual image is discussed here in this paper. The location relation between any two objects in a visual scene is a key in translating verbal information to visual information, as is the case in Fig.l. The present translation system advances in knowledge with experience. It consists of Japanese Language processing, image processing, and Japanese-scene translation functions.

• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.