• 대한수학회지
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• 제60권1호
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• pp.195-212
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• 2023

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜_ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜_ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.467-474
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• 2022

In this article, we consider the integral operator 𝓒^b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒^b,c operators on Bloch spaces.

• 대한수학회보
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• 제60권6호
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• pp.1555-1566
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• 2023

A Hilbert space operator A ∈ B(H) is a generalised n-projection, denoted A ∈ (G-n-P), if A^*n = A. (G-n-P)-operators A are normal operators with finitely countable spectra σ(A), subsets of the set $\{0\}\,{\cup}\,\{\sqrt[n+1]{1}\}.$ The Aluthge transform à of A ∈ B(H) may be (G - n - P) without A being (G - n - P). For doubly commuting operators A, B ∈ B(H) such that σ(AB) = σ(A)σ(B) and ${\parallel}A{\parallel}\,{\parallel}B{\parallel}\;{\leq}\;{\parallel}{\tilde{AB}}{\parallel},$ ${\tilde{AB}}\;{\in}\;(G\,-\,n\,-\,P)$ if and only if $A\;=\;{\parallel}{\tilde{A}}{\parallel}\,(A_{00}\,{\oplus}\,(A_0\,{\oplus}\,A_u))$ and $B\;=\;{\parallel}{\tilde{B}}{\parallel}\,(B_0\,{\oplus}\,B_u),$ where A₀₀ and B₀, and A₀ ⊕ A_u and B_u, doubly commute, A₀₀B₀ and A₀ are 2 nilpotent, A_u and B_u are unitaries, A^*n_u = A_u and B^*n_u = B_u. Furthermore, a necessary and sufficient condition for the operators αA, βB, αà and ${\beta}{\tilde{B}},\;{\alpha}\,=\,\frac{1}{{\parallel}{\tilde{A}}{\parallel}}$ and ${\beta}\,=\,\frac{1}{{\parallel}{\tilde{B}}{\parallel}},$ to be (G - n - P) is that A and B are spectrally normaloid at 0.

• 대한수학회지
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• 제17권1호
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• pp.81-90
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• 1980

• 대한수학회지
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• 제14권2호
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• pp.185-196
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• 1978

• 한국CDE학회논문집
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• 제13권6호
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• pp.429-439
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• 2008

With a remote operated manipulator system, the situation at a remote site can be rendered through remote visualized image to the operator. Then the operator can quickly realize situations and control the slave manipulator by operating a master input device based on the information of the virtual image. In this study, the remote operator visual support system (ROVSS) was developed for viewing support of a remote operator to perform the remote task effectively. A visual support model based on virtual environment was also inserted and used to fulfill the need of this study. The framework for the system was created by Windows API based on PC and the library of 3D graphic simulation tool such as ENVISION. To realize this system, an operation test environment for a limited operating site was constructed by using experimental robot operation. A 3D virtual environment was designed to provide accurate information about the rotation of robot manipulator, the location and distance of operation tool through the real time synchronization. In order to show the efficiency of the visual support, we conducted the experiments by four methods such as the direct view, the camera view, the virtual view and camera view plus virtual view. The experimental results show that the method of camera view plus virtual view has about 30% more efficiency than the method of camera view.

• BMB Reports
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• 제42권5호
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• pp.293-298
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• 2009

Temperate mycobacteriophage L1 encodes an unusual repressor (CI) for regulating its lytic-lysogenic switching and, in contrast to the repressors of most temperate phages, it binds to multiple asymmetric operator DNAs. Here, ions like $Na^+$, $Cl^-$, and $acetate^-$ ions were demonstrated to facilitate the optimal binding of CI to cognate operator DNA, whereas $K^+$, $Li^+$, ${NH_4}^+$, $Mg^{2+}$, $carbonate^{2-}$, and $citrate^{3-}$ ions significantly affected its operator binding activity. Of these ions, $Mg^{2+}$ unfolded CI most severely at room temperature and, compared to $Mg^{2+}$, $Na^+$ provided improved thermal stability to CI. Furthermore, the intrinsic tryptophan fluorescence of CI was changed notably upon replacing $Na^+$ with $Mg^{2+}$ and these opposing effects of $Mg^{2+}$ and $Na^+$ were also noticed in their actions on the C-terminal fragment (CTD) of CI. Taken together, $Na^+$ appeared to be more appropriate than $Mg^{2+}$ for maintaining the biologically active conformation of CI needed for its optimal binding to operator DNA.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.27-30
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• 1998

Let A and B be $m{\times}n$ matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A+B) = rank(A)+rank(B) implies that rank(T(A) + T(B)) = rankT(A) + rankT(B). We characterize the set of all linear operators which preserve the set of pairs of $n{\times}n$ matrices on which the rank is additive.

• Journal of Magnetics
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• 제16권2호
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• pp.108-113
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• 2011

The electron spin resonance lineshape (ESRLS) function for the electron spin resonance linewidth (ESRLW) of $Cr^{3+}$ (S = 3/2) in ferroelectric lithium niobate single crystals doped with 0.05 wt% of Cr, is obtained by using the projection operator technique (POT), developed by Argyres and Sigel. The ESRLS function is calculated to be axially symmetric about the c - axis and analyzed by using the spin Hamiltonian $H_{SP}={\mu}_B(B{\cdot}{^\leftrightarrow_{g}}{\cdot}S)+S{\cdot}{^\leftrightarrow_{D}}{\cdot}S$ with the parameters g = 1.972 and D = $0.395\;cm^{-1}$. In the ca plane, the linewidths show a strong angular dependence, whereas in the ab plane, they are independent of the angle. This result implies that the resonance center has an axial symmetry along the c - axis. Further, from the temperature dependence of the linewidths that is shown, it can be seen that the linewidths increase as the temperature increases, at a frequency of v = 9.27GHz. This result implies that the scattering effect increases with increasing temperature. Thus, the POT is considered to be more convenient to explain the scattering mechanism as in the case of other optical resonant systems.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.183-194
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• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.