The notion of a Γ-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group Γ replaces the group Z 2. The case Γ = Z k has also been studied, from the algebraic point of view by V.Kac [10] and from the point of view of the differential geometry by Ledger, Obata [12], Kowalski [11] or Wolf-Gray [18] in terms of k-symmetric spaces. In t...

The notion of a Γ-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group Γ replaces the group Z2. The case Γ = Z k has also been studied, from the algebraic point of view by V.Kac [14] and from the point of view of the differential geometry by Ledger, Obata [17], Kowalski [16] or Wolf-Gray [20] in terms of k-symmetric spaces. In th...

Ranked voting data arise when voters select and rank more than one candidate with an order of preference. Cook et al.[1] introduced data envelopment analysis (DEA) to analyze ranked voting data. Obata et al.[2] proposed a new method that did not use information obtained from inefficient candidates to discriminate efficient candidates. Liu et al.[3] ranked efficient DMUs on the DEA frontier with...

Various Liouville type theorems for conformally invariant equations have been obtained by Obata ([9]), Gidas, Ni and Nirenberg ([4]), Caffarelli, Gidas and Spruck ([1]), Viaclovsky ([10] and [11]), Chang, Gursky and Yang ([2] and [3]), and Li and Li ([5], [6] and [7]). See e. g. theorem 1.3 and remark 1.6 in [6] where these results (except for the one in [7]) are stated more precisely. In this ...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

In this paper, we define and study two operators $Phi^s$ and $Psi^s$ with grill. Characterization and basic properties of these operators are obtained. Also, we generalize a grill topological spaces via topology $tau^s$ induced from operators $Phi^s$ and $Psi^s$.