• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.809-822
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• 2007

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.

• Computational Structural Engineering
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• v.11 no.1
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• pp.261-274
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• 1998

In this paper, local and global error estimates for the element-free Galerkin (EFG) method are proposed. The essence of proposed error estimates is to use the difference between the values of the projected stress and these given directly by the EFG solution. The stress projection can be obtained simply by taking product of shape function based on a different domain of influence with the stresses at nodes. In this study, it was found that the effectivity index is optimized if the domain of influence in stress projection procedure is the smallest that retains regularity of the matrices in EFG. Numerical tests are shown for various 1D and 2D examples illustrating the good effectiveness of the proposed error estimator in the global energy norm and in the local error estimates.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.3
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• The Journal of Asian Finance, Economics and Business
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• v.5 no.3
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• pp.157-167
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• 2018

This research aims to generalize the conceptual basis of precariousness of employment, study the factors and scale of unsustainable of employment in the countries of the Eurasian Economic Union (EAEU). The concept of precariousness of employment is formed in social and economic studies about 40 years ago, but objective and subjective conditions and forms of unsustainable employment existed before. This study proposes a classification of forms of precariousness of employment on 16 criteria: the duration and timing of agreements, contract terms, the nature of income; the degree of labor autonomy; the level of formality; the level of openness; the level of vulnerability; the conditions of growth of qualification; the level of flexibility; the level of stability; regularity; the severity of the danger of work; in relation to the workplace; the quality of employment, the level of social security. In this research highlighted factors (globalization, demography, migration, structure factors, shadow and informal economy, social development and living standards, unemployment), and systematized certain trends of precariousness of employment, channels and means, forms of manifestation. The empirical analysis identified of the labor potential of the Eurasian countries and new quantitative estimates of the levels of unsustainable employment in the Eurasian Economic Space.