• 제목/요약/키워드: Positive operator

검색결과 209건 처리시간 0.033초

A NEW PROOF TO CONSTRUCT MULTIVARIABLE GEOMETRIC MEANS BY SYMMETRIZATION

  • KIM, SEJONG;PETZ, DENES
    • Journal of applied mathematics & informatics
    • /
    • 제33권3_4호
    • /
    • pp.379-386
    • /
    • 2015
  • The original geometric mean of two positive definite operators A and B is given by A#B = A1/2(A-1/2BA-1/2)1/2A1/2. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.

EXISTENCE AND ITERATION OF POSITIVE SOLUTION FOR A THREE-POINT BOUNDARY VALUE PROBLEM WITH A p-LAPLACIAN OPERATOR

  • Ma, De-Xiang
    • Journal of applied mathematics & informatics
    • /
    • 제25권1_2호
    • /
    • pp.329-337
    • /
    • 2007
  • In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

A NOTE ON A GENERAL MAXIMAL OPERATOR

  • Kim, Kyung-Hwa
    • 대한수학회논문집
    • /
    • 제10권1호
    • /
    • pp.155-162
    • /
    • 1995
  • Let $\mu$ be a positive Borel measure on $R^n$ which is positive on cubes. For any cube $Q \subset R^n$, a Borel measurable nonnegative function $\varphi_Q$, supported and positive a.e. with respect to $\mu$ in Q, is given. We consider a maximal function $$ M_{\mu}f(x) = sup \int \varphi Q$\mid$f$\mid$d_{\mu} $$ where the supremum is taken over all $\varphi Q$ such that $x \in Q$.

  • PDF

ON A LOTKA-VOLTERRA TYPE SIMPLE FOOD-CHAIN MODEL

  • Ko, Wonlyul;Ryu, Kimun
    • 충청수학회지
    • /
    • 제20권3호
    • /
    • pp.231-243
    • /
    • 2007
  • In this paper, we study a Lotka-Volterra type simple food chain model. We investigate the positive coexistence of the steady states to the model and give some results for the extinction of species under certain assumptions which can be interpreted as Domino effect and Biological control. The methods of a decoupling operator and the fixed point index theory on a positive cone are used as well as the comparison argument. Numerical evidences for our results also are provided.

  • PDF

EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH A SINGULAR WEIGHT

  • Jeongmi Jeong;Yong-Hoon Lee
    • East Asian mathematical journal
    • /
    • 제40권1호
    • /
    • pp.51-61
    • /
    • 2024
  • In this work, we study the existence of a positive solution for nonlinear fractional differential equation with a singular weight. For the proof, we introduce newly defined solution operator and use well-known Krasnoselski's fixed point theorem. We also give an example with a singular weight which may not be integrable.

산촌생태마을 운영매니저의 역할에 대한 인식 특성 분석 - 역량강화교육 개선을 중심으로 - (Analysis of Cognition Characteristic for Operators' Roles in Mountain Eco Villages - focused on an improvement of empowerment training -)

  • 김성학;서정원
    • 농촌계획
    • /
    • 제19권2호
    • /
    • pp.173-181
    • /
    • 2013
  • The importance of human resources empowerment for operation and management is increasing for sustainable effects and improvement in mountain eco village development projects. This study aimed to understand the cognition characteristics of operator who works for mountain eco villages as part of the mountain village development and to suggest improvement methods in empowerment training aspects. The survey contained operator's empowerment and operator systems in mountain eco villages and the results were analyzed for the study. Operators who joined the mountain eco village operator training course by Korea Forest Service were conducted the survey on March 12th~13th in 2012 and March 13th~15th in 2013. 69 and 58 of questionnaires were collected respectively and analyzed for the study. T-test was applied to Intergroup cognition difference and regression analysis was used for influential factors in necessity of operator's role. Collected data was analyzed by statistical package programme SPSS 18.0 version. According to the comparison of empowerment cognition with contingent upon training experience, 'harmony with residents' showed significantly difference at p<0.05 level. In the recognition comparison for prospect of future mountain eco village development, 'various training experiences' was significantly difference at p<0.01 level between positive and negative prospect group. Regression analysis revealed that 'communication with village leader', 'harmony with residents', and 'idea related to the project' have an effect on necessity of operator's empowerment significantly. Based on the results, the study suggests improved directions for operator's empowerment training as a horizontal leader who conduces a mountain village.

An Approximated Reasoning with Compensation

  • Kim, Chang-Suk;Kim, Dae-Su
    • 한국지능시스템학회논문지
    • /
    • 제11권6호
    • /
    • pp.558-562
    • /
    • 2001
  • In this paper, a fuzzy hyperresolution principle called CFHR. Compensatory Fuzzy Hyperresolution, with positive compensation facility is proposed. Usually hyperresolution has several terms of conditon parts. Theser terms have to be connected by the an connective. If the main/max operator to be used the and operation, there is some dependency problem of the min/max operator. So , we propose a compensatory operator EGM and applied it to the CFHR, We show the CFHR does more meaningful reasoning than existing method. We also prove the completeness of CFHR.

  • PDF

ON THE SEMI-HYPONORMAL OPERATORS ON A HILBERT SPACE

  • Cha, Hyung-Koo
    • 대한수학회논문집
    • /
    • 제12권3호
    • /
    • pp.597-602
    • /
    • 1997
  • Let H be a separable complex Hilbert space and L(H) be the *-algebra of all bounded linear operators on H. For $T \in L(H)$, we construct a pair of semi-positive definite operators $$ $\mid$T$\mid$_r = (T^*T)^{\frac{1}{2}} and $\mid$T$\mid$_l = (TT^*)^{\frac{1}{2}}. $$ An operator T is called a semi-hyponormal operator if $$ Q_T = $\mid$T$\mid$_r - $\mid$T$\mid$_l \geq 0. $$ In this paper, by using a technique introduced by Berberian [1], we show that the approximate point spectrum $\sigma_{ap}(T)$ of a semi-hyponomal operator T is empty.

  • PDF

THE UNIT TANGENT SPHERE BUNDLE WHOSE CHARACTERISTIC JACOBI OPERATOR IS PSEUDO-PARALLEL

  • Cho, Jong Taek;Chun, Sun Hyang
    • 대한수학회보
    • /
    • 제53권6호
    • /
    • pp.1715-1723
    • /
    • 2016
  • We study the characteristic Jacobi operator ${\ell}={\bar{R}({\cdot},{\xi}){\xi}$ (along the Reeb flow ${\xi}$) on the unit tangent sphere bundle $T_1M$ over a Riemannian manifold ($M^n$, g). We prove that if ${\ell}$ is pseudo-parallel, i.e., ${\bar{R}{\cdot}{\ell}=L{\mathcal{Q}}({\bar{g}},{\ell})$, by a non-positive function L, then M is locally flat. Moreover, when L is a constant and $n{\neq}16$, M is of constant curvature 0 or 1.

CERTAIN MAXIMAL OPERATOR AND ITS WEAK TYPE $L^1$($R^n$)-ESTIMATE

  • Kim, Yong-Cheol
    • 대한수학회논문집
    • /
    • 제16권4호
    • /
    • pp.621-626
    • /
    • 2001
  • Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

  • PDF