• Title/Summary/Keyword: $R_f$

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ON A SYMMETRIC FUNCTIONAL EQUATION

  • Chung, Jae-Young
    • Honam Mathematical Journal
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    • v.34 no.3
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    • pp.375-379
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    • 2012
  • We find a general solution $f:G{\rightarrow}G$ of the symmetric functional equation $$x+f(y+f(x))=y+f(x+f(y)),\;f(0)=0$$ where G is a 2-divisible abelian group. We also prove that there exists no measurable solution $f:\mathbb{R}{\rightarrow}\mathbb{R}$ of the equation. We also find the continuous solutions $f:\mathbb{C}{\rightarrow}\mathbb{C}$ of the equation.

STATIC AND RELATED CRITICAL SPACES WITH HARMONIC CURVATURE AND THREE RICCI EIGENVALUES

  • Kim, Jongsu
    • Journal of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1435-1449
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    • 2020
  • In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

BOUNDEDNESS AND INVERSION PROPERTIES OF CERTAIN CONVOLUTION TRANSFORMS

  • Yakubovich, Semyon-B.
    • Journal of the Korean Mathematical Society
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    • v.40 no.6
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    • pp.999-1014
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    • 2003
  • For a fixed function h we deal with a class of convolution transforms $f\;{\rightarrow}\;f\;*\;h$, where $(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}$ as integral operators $L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.

Analysis of Small-Subunit rDNA Sequences Obtained from Korean Peridinium bipes f. occultatum (Dinophyceae) (한국산 와편모조류 Peridinium bipes f. occultatum의 Small-Subunit Ribosomal DNA(SSU rDNA) 염기서열 분석)

  • Ki, Jang-Seu;Cho, Soo-Yeon;Han, Myung-Soo
    • ALGAE
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    • v.20 no.1
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    • pp.25-30
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    • 2005
  • To clarify some confusions concerning identification of the Korean Peridinium species, genotypic analysis was performed with their SSU rDNA sequences. PCR was used to amplify the partial SSU rDNA of Peridinium isolates collected from three different Korean waters (Juam, Sang-sa and Togyo Reservoirs). The PCR products were allowed directly to sequence, which revealed each 942 bp of rDNA sequence. Analyses of the rDNA sequences showed that all the Korean isolates had the same genotype (100% sequence homology), and they were nearly identical to a Japanese strain of P. bipes f. occultatum (NIES 364; 99.8% sequence similarity). The sequence-based comparisons could clearly resolve P. bipes f. occultatum isolated from three different Korean waters.

ON A GENERALIZED DIFFERENCE SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION AND STATISTICAL CONVERGENCE

  • Bataineh Ahmad H.A.
    • Communications of the Korean Mathematical Society
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    • v.21 no.2
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    • pp.261-272
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    • 2006
  • In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

A NOTE ON GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS

  • RAZA, MOHD ARIF;REHMAN, NADEEM UR;GOTMARE, A.R.
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.73-81
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    • 2021
  • Let R be a prime ring, Qr be the right Martindale quotient ring and C be the extended centroid of R. If �� be a nonzero generalized skew derivation of R and f(x1, x2, ⋯, xn) be a multilinear polynomial over C such that (��(f(x1, x2, ⋯, xn)) - f(x1, x2, ⋯, xn)) ∈ C for all x1, x2, ⋯, xn ∈ R, then either f(x1, x2, ⋯, xn) is central valued on R or R satisfies the standard identity s4(x1, x2, x3, x4).

Fabrication and Characterization of ${LiMn_2}{O_4}$ Cathode for Lithium Rechargeable Battery by R.F.Magnetron Sputtering (R.F. Magnetron Sputtering을 이용한 리튬이차전지 정극용 ${LiMn_2}{O_4}$의 제조 및 특성)

  • 우태욱;손영국
    • Journal of the Korean Ceramic Society
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    • v.37 no.6
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    • pp.552-558
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    • 2000
  • LiMn2O4 thin fiolm cathodes for Li-ion secondary battery were fabricated by r.f. magnetron sputtering technique. As-deposited films were amorphous. A spinel structure could not be obtained LiMn2O4 films by in-situ thermal annealing. After post thermal annealing over $700^{\circ}C$ in oxygen atmosphere, LiMn2O4 films prepared above 100 W r.f. power could be crystallized into a spinel structure. The electrochemical property of the LiMn2O4 film cathodes was tested in a Li/1 M LiClO4 in PC/LiMn2O4 cell. From cyclic voltammetry at scan rate of 2mV/sec of 2.5~4.5V, LiMn2O4 electrode prepared by post annealing at 75$0^{\circ}C$ showed good initial capacity. LiMn2O4 electrode prepared by post annealing at 80$0^{\circ}C$ showed the best crycling performance.

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TOEPLITZ TYPE OPERATOR IN ℂn

  • Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.697-705
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    • 2014
  • For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.