• Kyungpook Mathematical Journal
• /
• v.48 no.3
• /
• pp.359-366
• /
• 2008

Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.715-722
• /
• 2006

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

• Nuclear Engineering and Technology
• /
• v.54 no.10
• /
• pp.3620-3630
• /
• 2022

The diagnosis of abnormalities in a nuclear power plant is essential to maintain power plant safety. When an abnormal event occurs, the operator diagnoses the event and selects the appropriate abnormal operating procedures and sub-procedures to implement the necessary measures. To support this, abnormality diagnosis systems using data-driven methods such as artificial neural networks and convolutional neural networks have been developed. However, data-driven models cannot always guarantee an accurate diagnosis because they cannot simulate all possible abnormal events. Therefore, abnormality diagnosis systems should be able to detect their own potential misdiagnosis. This paper proposes a rulebased diagnostic validation algorithm using a previously developed two-stage diagnosis model in abnormal situations. We analyzed the diagnostic results of the sub-procedure stage when the first diagnostic results were inaccurate and derived a rule to filter the inconsistent sub-procedure diagnostic results, which may be inaccurate diagnoses. In a case study, two abnormality diagnosis models were built using gated recurrent units and long short-term memory cells, and consistency checks on the diagnostic results from both models were performed to detect any inconsistencies. Based on this, a re-diagnosis was performed to select the label of the second-best value in the first diagnosis, after which the diagnosis accuracy increased. That is, the model proposed in this study made it possible to detect diagnostic failures by the developed consistency check of the sub-procedure diagnostic results. The consistency check process has the advantage that the operator can review the results and increase the diagnosis success rate by performing additional re-diagnoses. The developed model is expected to have increased applicability as an operator support system in terms of selecting the appropriate AOPs and sub-procedures with re-diagnosis, thereby further increasing abnormal event diagnostic accuracy.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.525-536
• /
• 2013

In this paper we give a non-existence theorem for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2({\mathbb{C}}^{m+2})$ with re-current normal Jacobi operator ${\bar{R}}_N$.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.889-899
• /
• 2018

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove $${\parallel}f(A)Xg(B){\pm}g(B)Xf(A){\parallel}_2{\leq}{\Large{\parallel}}{\frac{(I+{\mid}A{\mid})X(I+{\mid}B{\mid})+(I+{\mid}B{\mid})X(I+{\mid}A{\mid})}{^dA^dB}}{\Large{\parallel}}_2$$, where A, B, $X{\in}{\mathbb{M}}_n$ such that A, B are Hermitian with ${\sigma}(A){\cup}{\sigma}(B){\subset}{\mathbb{D}}$ and f, g are analytic on the complex unit disk ${\mathbb{D}}$, g(0) = f(0) = 1, Re(f) > 0 and Re(g) > 0.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.139-145
• /
• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.779-789
• /
• 2012

In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit the eigenvalue problem of the Liouville operator and re-examine the method previously reported [Chem. Phys. 1977, 20, 93]. Then we apply the notion and concept of the eigenfunctions of the Liouville operator and knowledge acquired in the study of the eigenfunctions to cast collision bracket integrals into more convenient and suitable forms for numerical simulations. One of the alternative forms is given in the form of time correlation function. This form, on a further manipulation, assumes a form reminiscent of the Chapman- Enskog collision bracket integrals, but for dense gases and liquids as well as solids. In the dilute gas limit it would give rise precisely to the Chapman-Enskog collision bracket integrals for two-particle collision. The alternative forms obtained are more readily amenable to numerical simulation methods than the collision bracket integrals expressed in terms of a classical collision operator, which requires solution of classical Lippmann-Schwinger integral equations. This way, the aforementioned kinetic theory of dense fluids is made fully accessible by numerical computation/simulation methods, and the transport coefficients thereof are made computationally as accessible as those in the linear response theory.

• Journal of Intelligence and Information Systems
• /
• v.3 no.2
• /
• pp.1-9
• /
• 1997

These papers propose an evolutionary algorithm for re-using output of waste fuel of light water reactor system in nuclear power plants. Evolutionary algorithm is useful for optimization of the large space problem. The wastes contain several re-useable elements, and they should be carefully selected and blended to satisfy requirements as input material to the heavy water nuclear reactor system. This problem belongs to a NP-hard like the 0/1 Knapsack problem. Two evolutionary strategies are used as a, pp.oximation algorithms in the highly constrained combinatorial optimization problem. One is the traditional strategy, using random operator with evaluation function, and the other is heuristic based search that uses the vector operator reducing between goal and current status. We also show the method, which performs the feasible teat and solution evaluation by using the vectorized data in problem. Finally, We compare the simulation results of using random operator and vector operator for such combinatorial optimization problems.

• International journal of advanced smart convergence
• /
• v.4 no.2
• /
• pp.103-108
• /
• 2015

The electric utility has the responsibility of reducing the impact of peaks on electricity demand and related costs. Therefore, they have introduced Direct Load Control System (DLCS) to automate the external control of shedding customer load that it controls. Since the number of customer load participating in the DLC program are keep increasing, DLCS operators a re facing difficulty in monitoring and controlling customer load. The existing DLCS needs constant operator intervention, e.g., whenever the load is about to exceed a predefined amount, it needs operator's intervention to control the on/off status of the load. Therefore, DLCS operators need the state-of-the-art DLCS, which can control automatically the on/off status of the customer load without intervention as much as possible. This paper presents an intelligent DLCS using the active database. The proposed DLCS is applying the active database to DLCS which can avoid operator's intervention as much as possible. To demonstrate the validity of the proposed system, variable production rules and intelligent demand controller are presented.

• Bulletin of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.23-26
• /
• 1987

The aim of this note is to study some properties of Schrodinger operators, the magnetic case, $H_{0}$ (a)=1/2(-i.del.-a)$^{2}$; H(a)= $H_{0}$ (a)+V, where a=( $a_{1}$,.., $a_{n}$ ).mem. $L^{2}$$_{loc}$ and V is a potential energy. Also, we are interested in solutions, .psi., of H(a).psi.=E.psi. in the sense that (.psi., $e^{-tH}$(a).PSI.)= $e^{-tE}$(.psi.,.PSI.) for all .PSI..mem. $C_{0}$ $^{\infty}$( $R^{n}$ ) (see B. Simon [1]). In section 2, under some conditions, we find that a semibounded quadratic form of H9a) exists and that the Schrodinger operator H(a) with Re V.geq.0 is accretive on a form domain Q( $H_{0}$ (a)). But, it is well-known that the Schrodinger operator H=1/2.DELTA.+V with Re V.geq.0 is accretive on $C_{0}$ $^{\infty}$( $R^{n}$ ) in N Okazawa [4]. In section 3, we want to discuss $L^{p}$ estimates of Schrodinger semigroups.ups.