• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1075-1090
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• 2023

In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)^*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operator which are the generalization of (m, n)-paranormal and (m, n)^*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)^*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operators. Moreover, these classes of composition operators on L² spaces are characterized.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1345-1356
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• 2013

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

• BMB Reports
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• v.42 no.5
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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.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2486-2488
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• 2003

This paper describes a remote monitoring system of temperature controller for cold-storage, of farm produce. In the cold-storage, it is important that farm produces are fresh. Unfortunately, when an operator goes out from the cold-storage temperature change could be occurred due to the various reasons, for an example, a valve of cooler is broken. The temperature change results in a serious problem of the quality of farm produce. To prevent the problem, the operator has to look to the current state of the temperature of the cold-storage, even he is in long away. Thus, the monitoring system to show the temperature should be required to the operator who can move away. Therefore, this paper propose of the remote monitoring system of the temperature. The proposed system is expected to help the operator's facilities, and the management of farm produce.

• East Asian mathematical journal
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• v.24 no.1
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• pp.67-79
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• 2008

In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.417-424
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• 2015

In this paper the following is proved: Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. If XE = EX for each E ${\in}$ L, then there exists an operator A in AlgL such that AX = Y if and only if sup $\left{\frac{\parallel{XEf}\parallel}{\parallel{YEf}\parallel}\;:\;f{\in}H,\;E{\in}L\right}$ = K < $\infty$ and YE=EYE. Let x and y be non-zero vectors in H. Let P_x be the orthogonal pro-jection on sp(x). If EP_x = P_xE for each E $\in$ L, then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y. (2) < f, Ey > y =< f, Ey > Ey for each E ${\in}$ L and f ${\in}$ H.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.73-76
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• 1998

It is proved that the partial differential operator $D_x + ix^q D^2_y$ is not locally solvable in any open set which intersects the line x = 0, when $q = - \frac{2l-1}{2k-1}$ is not an integer.