• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.175-192
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• 2004

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's unique-ness theorem.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.549-558
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• 2012

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.623-632
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• 2010

A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.

• Bulletin of the Korean Chemical Society
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• v.17 no.2
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• pp.188-192
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• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• Investigative Magnetic Resonance Imaging
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• v.3 no.1
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• pp.13-19
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• 1999

MRI imaging provides many benefits such as noninvasive, 3-dimensional imaging capabilities. But it has relatively serious drawback that is the long data collection time, compared with other imaging modality. Many studies have been performed for fast MR imaging. But EPI and SEPI (4-6) are required to expensive hardware. In this paper, we introduce to Burst imaging technique. It can reduce imaging time by use of a mulitple RF excitation technique. Further it is easily implemented to the normal MRI system. But a pixel profile in the conventional burst sequence is so poor that excited area by burst sequence is a small portion of a pixel. This causes poor signal to noise ratio in burst image. therefore frequency sweeping of RF pulse for burst imaging sequence is proposed to improve pixel profile. A burst pulse train is shaped by liner or nonlinear frequency sweeping function so that all the spins within a pixel are excited, thereby improving the signal to noise ratio. It also shows that the pixel profiles are dependent on how frequency sweep is made. Computer simulations with Bloch equation and experimental results obtained using a 1.0 T NMR imaging system are presented.

• Journal of Magnetics
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• v.22 no.1
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• pp.1-6
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• 2017

Magnetic properties of CoPt nanoparticles (average size = 2.1 nm) encapsulated in synthesized protein shell have been investigated with SQUID (Superconducting Quantum Interference Device) magnetometer and analyzed by the recently developed non-equilibrium magnetization calculation by our group [T. H. Lee et al., Phys. Rev. B 90, 184411 (2014)]. Field dependence of magnetization measured at 2 K was successfully analyzed with modified Langevin function. In addition, small hysteresis loops having the coercive field of 890 Oe were observed at 2 K. Temperature dependence of magnetization has been measured with zero field cooled (ZFC) and field cooled (FC) protocol with slightly modified sequence in accordance with non-equilibrium magnetization calculation. The analysis on the M vs. T data revealed that the anisotropy energy barrier distribution is found to be very different from the log-normal distribution found in a size distribution. Zero temperature coercive field and Bloch coefficient have also been extracted from the analysis and the validity of those values is checked.

• Journal of the Optical Society of Korea
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• v.16 no.3
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• pp.196-202
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• 2012

We observe that the transmission and reflection efficiencies of a one-dimensional metallic grating under transverse-magnetic illumination calculated using the Fourier modal method (FMM) with the Fourier factorization rules have peculiar fluctuations, albeit small in magnitude, as the number of field harmonics increases. It is shown that when the number of Fourier terms for the electromagnetic field is increased from that in the conventional FMM, the fluctuations due to non-convergent highly evanescent eigenmodes can be eliminated. Our examination reveals that the fluctuations originate from the Gibbs phenomenon inherent in the Fourier-series representation of a permittivity function with discontinuities, and from non-convergence of highly evanescent internal Bloch eigenmodes.

• ETRI Journal
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• v.21 no.1
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• pp.1-27
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• 1999

We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

• Investigative Magnetic Resonance Imaging
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• v.20 no.1
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• pp.27-35
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• 2016

Purpose: Among RF pulses, a sinc pulse is typically used for slice selection due to its frequency-selective feature. When a sinc pulse is implemented in practice, it needs to be apodized to avoid truncation artifacts at the expense of broadening the transition region of the excited-band profile. Here a sinc pulse tailored by a new apodization function is proposed that produces a sharper transition region with well suppression of truncation artifacts in comparison with conventional tailored sinc pulses. A multiband pulse designed using this newly apodized sinc pulse is also suggested inheriting the better performance of the newly apodized sinc pulse. Materials and Methods: A new apodization function is introduced to taper a sinc pulse, playing a role to slightly shift the first zero-crossing of a tailored sinc pulse from the peak of the main lobe and thereby producing a narrower bandwidth as well as a sharper pass-band in the excitation profile. The newly apodized sinc pulse was also utilized to design a multiband pulse which inherits the performance of its constituent. Performances of the proposed sinc pulse and the multiband pulse generated with it were demonstrated by Bloch simulation and phantom imaging. Results: In both simulations and experiments, the newly apodized sinc pulse yielded a narrower bandwidth and a sharper transition of the pass-band profile with a desirable degree of side-lobe suppression than the commonly used Hanning-windowed sinc pulse. The multiband pulse designed using the newly apodized sinc pulse also showed the better performance in multi-slice excitation than the one designed with the Hanning-windowed sinc pulse. Conclusion: The new tailored sinc pulse proposed here provides a better performance in slice (or slab) selection than conventional tailored sinc pulses. Thanks to the availability of analytical expression, it can also be utilized for multiband pulse design with great flexibility and readiness in implementation, transferring its better performance.