• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1061-1074
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• 2003

We first show the analyticity of Stokes operator in Besov spaces $B_{p,q}$$^{a}$ ( $R_{＋}$$^{n}$). Then, we estimate the asymptotic behavior of the Stokes solutions. We also show the Hodge decomposition.n.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.151-156
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• 2010

The object of the present paper is to introduce ${\Lambda}$-dual and the concept of sectional analyticity (Abschinitts-anatytique or AA property) of an FK-space.The motivation for AA-property is that a sequence space having AK-property possess AA-property.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1071-1084
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• 2000

We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂$^2$(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

• International journal of advanced smart convergence
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• v.9 no.1
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• pp.1-9
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• 2020

This study was conducted to investigate the effects of computer attitudes such as anxiety, confidence, preference, usefulness, and computer literacy on their critical thinking ability, targeting college students at unspecified university universities. The period of data collection was from January 10, 2020 to January 17, 2020. A total of 213 people participated in the study. For data analysis, SPSS 18.0 was used for frequency analysis, Pearson correlation, x2 square, and simple regression analysis. As a result of the analysis, the difference of interests under the statistical significance level among general characteristics was Gender (x²=55.7^***, p<0.001), Age (x²=407.5^***, p<0.001), Resident (x²=127.5^***, p<0.001) Family (x²=289.4^***, p<0.001). In the simple regression analysis, computer liking (t=2.102, p<0.05) and computer use ability affected Truth seeking (t=-6.319, p<0.01), computer use ability was affecting analyticity (t=-5.630, p<0.01), computer use ability was affecting systematicity (t=-2.545, p<0.05), computer use ability was affecting maturity under statistical significance (t=-2.583, p<0.05). In conclusion, this study suggests that computer liking and computer use ability affect the sub-factor components of critical thinking disposition, truth seeking, analyticity, systematicity, and maturity, therefore the emphasis of this study is to emphasize that it is desirable to use the computer as a medium of learning based on computer literacy rather than worrying about excessive computer use.

• Asia Pacific Journal of Corpus Research
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• v.4 no.1
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• pp.1-23
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• 2023

The Japanese language, as a typical agglutinating language, permits large noun phrases (NP) containing ten or more morphemes. In this paper, we argue that the nature of the NP in Japanese is changing. Our data are drawn from the Balanced Corpus of Contemporary Written Japanese. We conduct a series of apparent-time studies of ongoing changes in complex NPs. We first examine the length of compound nouns, followed by the usage of bound suffixes. We then examine ongoing changes in complex NPs that contain genitive case markers. Finally, we examine noun incorporation. All of our studies show a trend towards shorter, less complex NPs. Furthermore, our results suggest that the usage rate of phrases that modify the noun inside the NP (compound nouns, bound nouns, NPs containing genitive case, noun incorporation) appears to be decreasing over time. On the other hand, the usage rate of modifying material outside of the NP (positional phrases, relative clauses) appears to be increasing over time. We conclude by suggesting that our results reflect a diachronic change of decreasing synthetic morphology and increasing analytic morphology. We end by pointing out the implications of this work on our understanding syntheticity and analyticity.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1223-1240
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• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1223-1256
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• 2013

We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.

• Journal of Korean Academy of Nursing Administration
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• v.16 no.4
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• pp.389-398
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• 2010

Purpose: This study was done to identify the relationship between critical thinking disposition and problem solving ability in nursing students, thereby providing basic data for nursing education. Method: A convenience sample was drawn from 161 nursing students. Data were collected from June 2008 to October 2008. Instruments used in the study were the California Critical Thinking Disposition Inventory (CCTDI) developed by Facione & Facione (1992) and the Problem Solving Inventory (PSI) developed by Heppner & Petersen (1982). The collected data were analyzed using t-test, ANOVA, Scheffe' test, Pearson correlation coefficients and multiple regression with SPSS 12.0. Results: The total mean score for CCTDI was 278.41 and PSI was 119.23. For general characteristics, there were statistically significant differences in CCTDI according to satisfaction with nursing majors (F=6.29, p=.00) and PSI according to academic achievement (F=3.45, p=.02) and marital status (t=2.43, p=.02). A statistically significant negative correlation was found between CCTDI and PSI. Critical thinking self-confidence, Analyticity and Inquisitiveness were significant predictors of PSI. Conclusion: The findings of this study indicate that critical thinking disposition influences problem solving ability. Therefore, the findings provide significant basic data for nursing education and nursing practice.