• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1209-1219
• /
• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1891-1908
• /
• 2018

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{\(\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}\)^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

• Communications of the Korean Mathematical Society
• /
• v.25 no.1
• /
• pp.129-137
• /
• 2010

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.681-691
• /
• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.65-70
• /
• 1993

In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

• East Asian mathematical journal
• /
• v.37 no.1
• /
• pp.41-77
• /
• 2021

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (��, ξ, η, g) in a complex space form Mn+1(c), c ≠ 0. We denote by Rξ = R(·, ξ)ξ and A(i) be Jacobi operator with respect to the structure vector field ξ and be the second fundamental form in the direction of the unit normal C(i), respectively. Suppose that the third fundamental form t satisfies dt(X, Y ) = 2��g(��X, Y ) for certain scalar ��(≠ 2c)and any vector fields X and Y and at the same time Rξ is ��∇ξξ-parallel, then M is a Hopf hypersurface in Mn(c) provided that it satisfies RξA(1) = A(1)Rξ, RξA(2) = A(2)Rξ and ${\bar{r}}-2(n-1)c{\leq}0$, where ${\bar{r}}$ denotes the scalar curvature of M.

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.195-212
• /
• 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.

• Honam Mathematical Journal
• /
• v.27 no.3
• /
• pp.431-443
• /
• 2005

We investigate the equation Ax = y, where the vectors x and y are given and the operator A is normal and required to lie in CSL-algebra $AlG{\mathcal{L}}$. We desire a necessary and sufficient condition for the existence of a solution A.

• Journal of Institute of Control, Robotics and Systems
• /
• v.13 no.7
• /
• pp.631-636
• /
• 2007

An efficient obstacle avoidance algorithm is proposed in this paper to avoid dynamic obstacles using a collision vector while a tele-operated mobile robot is moving. For the verification of the algorithm, an operator watches through a monitor and controls the mobile robot with a force-reflection joystick. The force-reflection joystick transmits a virtual force to the operator through the Inter-net, which is generated by an adaptive impedance algorithm. To keep the mobile robot safe from collisions in an uncertain environment, the adaptive impedance algorithm generates the virtual force which changes the command of the operator by pushing the operator's hand to a direction to avoid the obstacle. In the conventional virtual force algorithm, the avoidance of moving obstacles was not solved since the operator cannot recognize the environment realistically by the limited communication bandwidth and the narrow view-angle of the camera. To achieve the dynamic obstacle avoidance, the adaptive virtual force algorithm is proposed based on the collision vector that is a normal vector from the obstacle to the mobile robot. To verify the effectiveness of the proposed algorithm, mobile robot navigation experiments with multiple moving obstacles have been performed, and the results are demonstrated.

• Nuclear Engineering and Technology
• /
• v.44 no.4
• /
• pp.379-386
• /
• 2012

A symptom-based procedure with a critical safety function monitoring system has been established to reduce the operator's diagnosis and cognitive burden since the Three-Mile Island (TMI) accident. However, it has been reported that a symptom-based procedure also requires an operator's cognitive efforts to cope with off-normal events. This can be caused by mismatches between a static model, an emergency operating procedure (EOP), and a dynamic process, the nature of an ongoing situation. The purpose of this study is to share the evidence of mismatches that may result in an excessive cognitive burden in conducting EOPs. For this purpose, we analyzed simulated emergency operation records and observed some operator behaviors during the EOP operation: continuous steps, improper description, parameter check at a fixed time, decision by information previously obtained, execution complexity, operation by the operator's knowledge, notes and cautions, and a foldout page. Since observations in this study are comparable to the results of an existing study, it is expected that the operational behaviors observed in this study are generic features of operators who have to cope with a dynamic situation using a static procedure.