• 제목/요약/키워드: nullity

검색결과 39건 처리시간 0.019초

ON LOCALLY 𝜙-CONFORMALLY SYMMETRIC ALMOST KENMOTSU MANIFOLDS WITH NULLITY DISTRIBUTIONS

  • De, Uday Chand;Mandal, Krishanu
    • 대한수학회논문집
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    • 제32권2호
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    • pp.401-416
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    • 2017
  • The aim of this paper is to investigate locally ${\phi}-conformally$ symmetric almost Kenmotsu manifolds with its characteristic vector field ${\xi}$ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ${\xi}$ belongs to the $(k,\;{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$.

SOME RESULTS ON ALMOST KENMOTSU MANIFOLDS WITH GENERALIZED (k, µ)'-NULLITY DISTRIBUTION

  • De, Uday Chand;Ghosh, Gopal
    • 대한수학회논문집
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    • 제34권4호
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    • pp.1289-1301
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    • 2019
  • In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.

신용장거래에 있어서 제3자 사기에 관한 해석 (Interpretation of 3rd Party's Fraud Exception Rule Under Law of Letters of Credit)

  • 한기문
    • 무역상무연구
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    • 제36권
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    • pp.29-46
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    • 2007
  • The fraud exception rule allows for the issuing bank to dishonor the claim if it the documents and transactions bear fraud though the documents presented are complied with the terms and conditions of the letter of credit. A question arises whether the fraud exception rule can apply to innocent beneficiary when fraud is made by 3rd party. United City Merchants v. Royal Bank of Canada showed a good example how to handle in case of innocent beneficiary. At this case House of Lord found that innocent beneficiary deserves payment applying nullity exception rule. I believe that the nullity exception rule is employed for the benefit of innocent beneficiary as far as the issuer and applicant get no actual damage by the 3rd party's fraudulent action which is shown on documents.

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On a Classification of Almost Kenmotsu Manifolds with Generalized (k, µ)'-nullity Distribution

  • Ghosh, Gopal;Majhi, Pradip;Chand De, Uday
    • Kyungpook Mathematical Journal
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    • 제58권1호
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    • pp.137-148
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    • 2018
  • In the present paper we prove that in an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}-nullity$ distribution the three conditions: (i) the Ricci tensor of $M^{2n+1}$ is of Codazzi type, (ii) the manifold $M^{2n+1}$ satisfies div C = 0, (iii) the manifold $M^{2n+1}$ is locally isometric to $H^{n+1}(-4){\times}R^n$, are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to $H^{n+1}(-4){\times}\mathbb{R}^n$.

NULLITY OF THE LEVI-FORM AND THE ASSOCIATED SUBVARIETIES FOR PSEUDO-CONVEX CR STRUCTURES OF HYPERSURFACE TYPE

  • Chung, Kuerak;Han, Chong-Kyu
    • 대한수학회보
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    • 제56권1호
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    • pp.169-178
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    • 2019
  • Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

AN ITERATIVE METHOD FOR ORTHOGONAL PROJECTIONS OF GENERALIZED INVERSES

  • Srivastava, Shwetabh;Gupta, D.K.
    • Journal of applied mathematics & informatics
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    • 제32권1_2호
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    • pp.61-74
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    • 2014
  • This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.