• Title, Summary, Keyword: difference operator

Search Result 242, Processing Time 0.029 seconds

Stability Criterion for Volterra Type Delay Difference Equations Including a Generalized Difference Operator

  • Gevgesoglu, Murat;Bolat, Yasar
    • Kyungpook Mathematical Journal
    • /
    • v.60 no.1
    • /
    • pp.163-175
    • /
    • 2020
  • The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

ON THE FINITE DIFFERENCE OPERATOR $l_{N^2}$(u, v)

  • Woo, Gyung-Soo;Lee, Mi-Na;Seo, Tae-Young
    • East Asian mathematical journal
    • /
    • v.16 no.1
    • /
    • pp.97-103
    • /
    • 2000
  • In this work, we consider a finite difference operator $L^2_N$ corresponding to $$Lu:=-(u_{xx}+u_{yy})\;in\;{\Omega},\;u=0\;on\;{\partial}{\Omega}$$, in $S_{h^2,1}$. We derive the relation between the absolute value of the bilinear form $l_{N^2}$(u, v) on $S_{h^2,1}{\times}S_{h^2,1}$ and Sobolev $H^1$ norms.

  • PDF

ON p, q-DIFFERENCE OPERATOR

  • Corcino, Roberto B.;Montero, Charles B.
    • Journal of the Korean Mathematical Society
    • /
    • v.49 no.3
    • /
    • pp.537-547
    • /
    • 2012
  • In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

STABILITY OF HAHN DIFFERENCE EQUATIONS IN BANACH ALGEBRAS

  • Abdelkhaliq, Marwa M.;Hamza, Alaa E.
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.4
    • /
    • pp.1141-1158
    • /
    • 2018
  • Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

CONVOLUTION PROPERTIES FOR ANALYTIC FUNCTIONS DEFINED BY q-DIFFERENCE OPERATOR

  • Cetinkaya, Asena;Sen, Arzu Yemisci;Polatoglu, Yasar
    • Honam Mathematical Journal
    • /
    • v.40 no.4
    • /
    • pp.681-689
    • /
    • 2018
  • In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.

Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

  • Nyamwala, Fredrick Oluoch;Ambogo, David Otieno;Ngala, Joyce Mukhwana
    • Kyungpook Mathematical Journal
    • /
    • v.60 no.2
    • /
    • pp.297-305
    • /
    • 2020
  • We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS

  • Lee, Dong-Won
    • Journal of the Korean Mathematical Society
    • /
    • v.44 no.6
    • /
    • pp.1429-1440
    • /
    • 2007
  • Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.

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

  • Kim, Seong-Hak;Seo, Jeong-Weon
    • Journal of Korean Society of Rural Planning
    • /
    • v.19 no.2
    • /
    • 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.

A COMPARISON THEOREM OF THE EIGENVALUE GAP FOR ONE-DIMENSIONAL BARRIER POTENTIALS

  • Hyun, Jung-Soon
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.2
    • /
    • pp.353-360
    • /
    • 2000
  • The fundamental gap between the lowest two Dirich-let eigenvalues for a Schr dinger operator HR={{{{ { { d}^{2 } } over { { dx}^{2 } } }}}}+V(x) on L({{{{ LEFT | -R,R RIGHT | }}}}) is compared with the gap for a same operator Hs with a different domain {{{{ LEFT [ -S,S RIGHT ] }}}} and the difference is exponentially small when the potential has a large barrier.

  • PDF