• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.523-534
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• 2010

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.

• Journal of Korean Philosophical Society
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• v.145
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• pp.217-244
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• 2018

This paper reviews how $J{\ddot{u}}rgen$ Moltmann embraces and transforms the philosophy of Ernst Bloch. For what are the hopes of the two thinkers who presuppose opposing worldviews? This question will provide a good opportunity to look at how different religious types, based on different worldviews in modern philosophy of religion, can understand and communicate with one another. Ernst Bloch was a philosopher who originally interpreted Judeo-Christian thought through Marxism and Persian Dualism and helped to carry out the intrinsic criticism of the doctrine of Christian eschatology by developing atheism of Christianity into a philosophy of hope. Bloch and Moltmann deal with the concepts of future, humanity, nation, and hope in the eschatological horizon, but their worldviews are so different. For example, the connection between the Beginning and Ending, Disjunction or Continuation, the Core of Existence and Resurrection, Messianism and Marxism, Atheism and Theism, Persian Dualism and Judeo-Christian Monotheism. Therefore, a one-sided interpretation that ignores worldview differences in the hopes of these two thinkers should be avoided. Moltmann actively embraced the Messianism of the Jewish thinker, Bloch, by excluding Marxism, made the spectrum of broad-minded horizons diminished in the union of Messianism and Marxism. Moltmann replaced the utopian possibilities of matter in the Ontology of Not-Yet-Being, with the resurrection of Christ, who was crucified, and with the God of Creation and the God of Exodus. By overthrowing the position of atheism in Christianity, which was very important for Bloch, with the system of Trinitarian Monotheism, it resulted in the disconnection and conflict between the Old Testament and the New Testament, especially the ignorance of the tension between God the Lord and Jesus Christ.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.185-200
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• 2013

We study the bounded and the compact weighted composition operators from the Hardy space $H^{\infty}$ into BMOA and into VMOA, from BMOA into $H^{\infty}$, as well as from BMOA into the Bloch space. We also provide new boundedness and compactness criteria for the weighted composition operators on BMOA and on VMOA.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.85-103
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• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1711-1719
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• 2015

We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.307-317
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• 2004

In the setting of the half-plane of the complex plane, we show that for $r\geq0$, the dual space of the weighted bergman spaces B$^{1}{\gamma}$ is the Bloch space of the half-plane and we study some bounded linear operators induced by radial derivatives.

• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.77-82
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• 1973

A method of obtaining the partition function for a system of electrons is developed by defining a new density matrix, in which the Fermi statistics is explicitly incorporated. The corresponding Bloch equation is formulated and a practical method of solving the equation is obtained for weak potential. This theory is applied to structurally disordered ststems which might be reasonable models for liquid metals.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.581-594
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• 2019

In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

• Journal of Magnetics
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• v.11 no.2
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• pp.83-86
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• 2006

Controlling magnetic domains in soft underlayer (SUL) of perpendicular magnetic recording (PMR) is an important issue for the application of PMR in HDD. We studied the magnetic domain structures in SUL using the finite element based micromagnetic simulation (FEMM) for the SUL models with different thicknesses. The purpose is to simulate the magnetic domain wall noise when the SUL thickness and saturation magnetization are changed. The simulation results show that a 15 nm SUL forms simpler Neel wall domain wall pattern and 40 nm SUL forms complex Bloch wall. To visualize the effect of these domain walls stray field at a read sensor position, the magnetic stray field of the domain walls at air bearing surface (ABS) which is 50 nm above the SUL was simulated and the results imply that Bloch walls have stronger stray field with more complicated field patterns than Neel walls and this becomes a significant noise source. Therefore, the thickness of the SUL should be controlled to avoid the formation of Bloch walls.