• 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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.781-794
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• 2021

Let Ω be a smoothly bounded pseudoconvex domain in ℂⁿ and assume that the (n - 2)-eigenvalues of the Levi-form are comparable in a neighborhood of z₀ ∈ bΩ. Also, assume that there is a smooth 1-dimensional analytic variety V whose order of contact with bΩ at z₀ is equal to 𝜂 and 𝚫_n-2(z₀) < ∞. We show that the maximal gain in Hölder regularity for solutions of the ${\bar{\partial}}$-equation is at most ${\frac{1}{\eta}}$.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1193-1206
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• 2009

C. Guenther studied the stability of DeTurck flows by using maximal regularity theory and center manifolds, but these arguments can not solve the stability of Ricci flows because the Ricci flow equation is not strictly parabolic. Recognizing this deficiency, the present paper considers and obtains the stability of Ricci flows, and of quasi-Ricci flows in view of some Killing conditions.

• Korean Journal of Applied Biomechanics
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• v.32 no.4
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• pp.121-127
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• 2022

Objective: The purpose of this study was to investigate potential effects of transcranial direct current stimulation (tDCS) on bimanual force control capabilities in healthy young adults. Method: Eighteen right-handed healthy young adults (10 females and 8 males; age: 23.55 ± 3.56 yrs) participated in this crossover design study. All participants were randomly allocated to both active-tDCS and sham-tDCS conditions, respectively. While receiving 20 min of active- or sham-tDCS interventions, all participants performed bimanual isometric force control tasks at four submaximal targeted force levels (i.e., 5%, 10%, 15, and 20% of maximal voluntary contraction: MVC). To compare bimanual force control capabilities including force accuracy, variability, and regularity between active-tDCS and sham-tDCS conditions, we conducted two-way repeated measures ANOVAs (2 × 4; tDCS condition × Force levels). Results: We found no significant difference in baseline MVC between active-tDCS and sham-tDCS conditions. Moreover, our findings revealed that providing bilateral tDCS including anodal tDCS on left primary motor cortex (M1) and cathodal on right M1 while conducting bimanual force control trials significantly decreased force variability and regularity at 5%MVC. Conclusion: These findings suggest that providing bilateral tDCS on M1 areas may improve bimanual force control capabilities at a relatively low targeted force level.

• Language and Information
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• v.8 no.2
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• pp.73-91
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• 2004

The nominative and accusative postpositions in Korean may intervene between the negative auxiliary verb ANH and its complement verb phrase. As Korean is an OV language, this means that 'verb + {nom, acc} + ANH' as well as the simpler concatenation 'verb + ANH' is possible. This fact, together with an overwhelming regularity of these postpositions' optionality in virtually all constructions, poses a problem for formal approaches to the syntax of the language. Working in a constraint-based grammatical framework shaped by such works as Sag and Wasow (1999) and Copestake (2002), we put forth type hierarchies for major_class, which represents verb inflection, and for pos, which has two immediate subtypes, i.e., htrp_pos and ord_pos. What we call the 'half transparency' of the case postpositions separates them from all the other lexical items in the language. The type htrp_pos is used to constrain one of the two newly proposed head_comp_rules, where a newly proposed feature HEAD2 of a phrase inherits its value from the HEAD feature of the head word. The COMPS list of the negative auxiliary ANH is seen as containing a single phrase whose HEAD is a kind of nominal clause and whose HEAD2 is something that is one of the three maximal types: acc, nom, and null.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.9
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• pp.514-526
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• 2004

Microarray is a new technique for gene expression experiment, which has gained biologist's attention for recent years. This technology enables us to obtain hundreds and thousands of expression of gene or genotype at once using microarray Since it requires manual work to analyze patterns of gene expression, we want to develop an effective and automated tools to analyze microarray image. However it is difficult to analyze DNA chip images automatically due to several problems such as the variation of spot position, the irregularity of spot shape and size, and sample contamination. Especially, one of the most difficult problems in microarray analysis is the block and spot addressing, which is performed by manual or semi automated work in all the commercial tools. In this paper we propose a new algorithm to address the position of spot and block using a new concept of regular structure grid searching. In our algorithm, first we construct maximal I-regular sequences from the set of input points. Secondly we calculate the rotational angle and unit distance. Finally, we construct I-regularity graph by allowing pseudo points and then we compute the spot/block address using this graph. Experiment results showed that our algorithm is highly robust and reliable. Supplement information is available on http://jade.cs.pusan.ac.kr/~autogrid.