• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.115-141
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• 2023

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup {exp tX} is a normal nilpotent subgroup commuting with {exp tX}, and X is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension 5 and those of dimension 7 whose Kähler reduction in the above sense is abelian.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.295-303
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• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.4
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• pp.1-8
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• 2004

A novol clock distribution scheme is proposed for high-speed and low-power digital system to minimize clock skew and reduce dynamic power consumption. This scheme has ideal zero-skew characteristic by using folded clock lines (FCL) and phase blending circuit. For analyzing suitable line structures to FCLs, microstrip line and coplanar line are placed with folded clock lines. Simulation results show that the maximum clock-skew between two receivers located 10mm apart is less than lops at 1㎓ and the maximum clock-skew between two receivers located 20mm apart is less than 60ps at 1㎓. Also the results show that the minimum skews of clock signals regardless of process, voltage, and temperature variation are invariant.

• East Asian mathematical journal
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• v.34 no.3
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• pp.305-316
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• 2018

Let R be a ring with identity. A right ideal ideal I of a ring R is called ref lexive (resp. completely ref lexive) if $aRb{\subseteq}I$ implies that $bRa{\subseteq}I$ (resp. if $ab{\subseteq}I$ implies that $ba{\subseteq}I$) for any $a,\;b{\in}R$. R is called ref lexive (resp. completely ref lexive) if the zero ideal of R is a reflexive ideal (resp. a completely reflexive ideal). Let K(R) (called the ref lexive radical of R) be the intersection of all reflexive ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an reflexive ideal of a ring are obtained; (2) reflexive (resp. completely reflexive) property is Morita invariant; (3) For any ring R, we have $K(M_n(R))=M_n(K(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a ring R, we have $K(R)[x]{\subseteq}K(R[x])$; in particular, if R is quasi-Armendaritz, then R is reflexive if and only if R[x] is reflexive.

• 전기의세계
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• v.26 no.2
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• pp.99-103
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• 1977

The object of this work is to study an optimal design problem of the proportional load-frequency controller for the single-control area power system. The selfservice power station is still a popular means as a power supplying source on ships or in a certain manufacturing area. The power system of this kind can be formulated as a single control-area system and it attracts a certain academic interest in controlling the system frequency under disturbances. In this paper, the single control-area system is mathematically formulated as a linear, time-invariant system in state-space under certain assumptions. The optimal proportional control law and the realization of the controller in closed loop-version is studied so that the final system designed can attain the system frequency to the nominal stationing value after the small load-disturbance. As in general cases of optimal design problems, the performance index is assumed to be quadratic in states and the control effort, and the infinite time control process is assumed in this work. The final control system realized depicts certain improvements in case study; in stability, transient responses and in steady-state frequency deviation, even though the steady state error did not attain the zero value.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.9
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• pp.431-437
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• 2001

Since the eddy current problem usually depends on the geometry of the moving conductive sheet and the shape of the pole projection area, there is no general method to find out its analytical solution. The analysis of the eddy current in a rotating disk is performed in the case of time-invariant field to find its analytical solution. As a method to solve the eddy current problem, the concept of the Coulomb charge and image method are proposed with the consideration of the boundary condition. Firstly, the line charge is obtained from the volume charge generated in the rotating disk and Coulomb's law is applied. Secondly, the finite disk radius is considered by introducing an imaginary eddy current to satisfy the boundary condition that the radial component of the eddy current is zero at the edge of the relating disk. Thirdly, the braking torque is calculated by applying Lorentz force law. Finally, the computed braking torque is compared with the measured one As a result, it can be said that the proposed model presents fairly accurate results in a low angular velocity range although a large error is observed as the angular velocity of the disk increases.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.211-223
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• 2009

Transient response analysis can be conducted either in the time domain, or via the frequency domain. Sometimes a frequency domain method (FDM) has advantages over a time domain method. A practical issue in the FDM is to find out an appropriate extended period, which may be affected by several factors, such as the excitation duration, the system damping, the artificial damping, the period of interest, etc. In this report, the extended period of the FDM based on the Duhamel's integral is investigated. This Duhamel's integral based FDM does not involve the unit impulse response function (UIRF) beyond the period of interest. Due to this fact, the ever-lasting UIRF can be simply set as zero beyond the period of interest to shorten the extended period. As a result, the preferred extended period is the summation of the period of interest and the excitation duration. This conclusion is validated by numerical examples. If the extended period is too short, then the front portion of the period of interest is more prone to errors than the rear portion, but the free vibration segment is free of the wraparound error.

• Journal of the Korean Chemical Society
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• v.39 no.8
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• pp.643-649
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• 1995

The Menschutkin type reactions of substituted(Z)-benzyl systems with substituted(Y)-pyridines and N,N-dimethyl aniline have been studied by the electro-conductometric method in acetonitrile at 35$^{\circ}C$ and 50$^{\circ}C$. On the plot of $k_{obs}$ versus concentrations of nucleophile under pseudo-first order conditions, 3,$4-(CH_3/O)_2$-benzyl bromide and $4-CH_3O$-benzyl bromide were a positive intercept at zero concentration of nucleophile. The $k_1$ value for each compound was invariant with the different nucleoephile. However, $4-CH_3-$ and other electron withdrawing substituents of benzyl bromides did not show the positive intercept. These results are suggested that the reactions have been proceeding simultaneously and independently for the activated benzyl bromides via direct bimolecular and intimate ion pair intermediate.

• Korean Journal of Cognitive Science
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• v.16 no.4
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• pp.323-331
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• 2005

This paper proposes an improved system for recognizing facial expressions in various internal states that is illumination-invariant and without detectable rue such as a neutral expression. As a preprocessing to extract the facial expression information, a whitening step was applied. The whitening step indicates that the mean of the images is set to zero and the variances are equalized as unit variances, which reduces murk of the variability due to lightening. After the whitening step, we used the facial expression information based on principal component analysis(PCA) representation excluded the first 1 principle component. Therefore, it is possible to extract the features in the lariat expression images without detectable cue of neutral expression from the experimental results, we ran also implement the various and natural facial expression recognition because we perform the facial expression recognition based on dimension model of internal states on the images selected randomly in the various facial expression images corresponding to 83 internal emotional states.