• Title/Summary/Keyword: n-norm

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WEAKTYPE $L^1(R^n)$-ESTIMATE FOR CRETAIN MAXIMAL OPERATORS

  • Kim, Yong-Cheol
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1029-1036
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    • 1997
  • Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

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The Effects of Smoking Cessation School Program on Smoking Behavior in Adolescent Smokers (금연학교 교육프로그램이 청소년 흡연자의 흡연행위에 미치는 효과)

  • Song, Mi-Ra;Kim, Soon-Lae
    • Research in Community and Public Health Nursing
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    • v.12 no.1
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    • pp.115-124
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    • 2001
  • This study was designed to investigate the effects of a smoking cessation school program on attitudes towards smoking cessation, the subjective norm, perceived behavioral controls, the intent to cease smoking and smoking behavior. Also included was the goals of the program itself. Study subjects were 80 adolescent smokers who at least attended the smoking cessation school program without absence. had smoked one cigarette at the time of the first study before the program and attended the first. second. and third studies (The study was conducted from September 26. to December 21. 1999. a period of 59 days). Data collection was performed using the TPB questionnaire which was developed by Jee Yon-Ock(1994). The survey included questions covering the intended areas of study mentioned above. The first data was collected during the first day of the five day program. The second survey was conducted immediately after the last day of the program and the last survey was four weeks later. Data was analyzed with a SAS/PC program including N. %. a paired t-test. The results were as follows; 1. After the program. the scores representing attitude towards smoking cessation (before program: 14.5. after program: 16.8) and perceived behavioral control (before program: 1.2. after program: 2.1) rose significantly, but the scores for attitudes towards the subjective norm and the intent to cease smoking were not notably different. 2. After the program. the frequency of daily smoking fell significantly (before program: 5.7 cigarettes. after program: 3.2 cigarettes). In conclusion, the five day smoking cessation school program increased attitude. perceived behavioral control and decreased smoking behavior but did not influence subjective norm, smoking cessation intention. Thus, further study is required to better evaluate the effects of the program and to improve any shortcomings.

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A Study on Standardization of K-WPPSI-IV: Analyses of Reliability and Validity (한국 Wechsler 유아지능검사 4판(K-WPPSI-IV)의 표준화연구: 신뢰도와 타당도분석)

  • Park, Hyewon;Lee, KyungOk;Lee, Sang-Hee;Park, Minjung
    • Korean Journal of Childcare and Education
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    • v.12 no.4
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    • pp.111-130
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    • 2016
  • This study examined the reliability and validity evidence of the Korean version of Wechsler Primary & Preschool Scale for Intelligence(K-WPPSI-IV), which was standardized recently. Following the stratified sampling for Korean population in terms of region and maternal education level, 1,700 children aged 2.6~7.7 years were recruited for Korean norm development. The split-half reliability (N=1,700) was high(Fisher's z(.75-.89)) and test-retest reliability(N=100) was satisfactory ranging from .95 to .68. The inter-rater reliability(N=110) was very high(.96-1.0). Discriminant and convergent validities were revealed by correlational patterns among subtests and indices. Future studies are needed to extend both reliability and validity of K-WPPSI-IV by collecting data with a various sample group and a variety of instruments.

CONVERGENCE RATE OF CONVOLUTION TYPE DELTA SEQUENCE IN HIGHER DIMENSION

  • SHIM HONG TAE;PARK CHIN HONG
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.701-707
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    • 2005
  • Delta sequences play an important role in convergence and approximation theory. Much of classical approximation theory is based on delta sequence. The rate of convergence of certain types of these sequences in Sobolev spaces has recently been studied. Here we estimate convergence rate of convolution type delta sequence in higher dimension.

ON THE FUZZY STABILITY OF CUBIC MAPPINGS USING FIXED POINT METHOD

  • Koh, Heejeong
    • The Pure and Applied Mathematics
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    • v.19 no.4
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    • pp.397-407
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    • 2012
  • Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

ON THE BEHAVIOR OF L2 HARMONIC FORMS ON COMPLETE MANIFOLDS AT INFINITY AND ITS APPLICATIONS

  • Yun, Gabjin
    • Korean Journal of Mathematics
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    • v.6 no.2
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    • pp.205-212
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    • 1998
  • We investigate the behavior of $L^2$ harmonic one forms on complete manifolds and as an application, we show the space of $L^2$harmonic one forms on a complete Riemannian manifold of nonnegative Ricci curvature outside a compact set with bounded $n/2$-norm of Ricci curvature satisfying the Sobolev inequality is finite dimensional.

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WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Koo, HYUNGWOON;NAM, KYESOOK;YI, HEUNGSU
    • Journal of the Korean Mathematical Society
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    • v.42 no.5
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    • pp.975-1002
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    • 2005
  • On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

SOME ASPECTS OF ELLIPTIC VARIATIONAL INEQUALITIES

  • Butt, Rizwan
    • Journal of applied mathematics & informatics
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    • v.4 no.2
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    • pp.433-446
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    • 1997
  • In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.

NONCONFORMING SPECTRAL ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS

  • Kumar, N. Kishore
    • Journal of applied mathematics & informatics
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    • v.32 no.5_6
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    • pp.761-781
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    • 2014
  • An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

2차원 요소분할과 오차해석에 대한 연구

  • 최남구;유형선
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.10a
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    • pp.226-232
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    • 2001
  • 본 논문에서는 자동 요소분할에 따른 공간상의 오차에 대해 연구하였다. 즉, 분할되어진 각 요소에서 산출된 응력과 변형률의 오차 norm들에 기초한 오차평가방법을 사용하였는데, 이는 각 요소들의 오차를 직접적으로 계산해 내는 매우 정밀한 방법이다. 위의 일련과정들을 몇 개의 구조물에 적용해 보았으며, 동일한 구조물에 대해서, AUTOCAD 3D-Mesh 기능을 사용하여 유사한 수의 요소로 분할, 수동으로 좌표 값과 요소 배열 값을 입력하여 구조물의 요소당 오차 값을 비교해 보았다.