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Characterizations of Lie higher and Lie triple derivations on triangular algebras
Jiankui Li,Qihua Shen 대한수학회 2012 대한수학회지 Vol.49 No.2
In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.
METRIC FOLIATIONS ON HYPERBOLIC SPACES
이경배,이승훈 대한수학회 2011 대한수학회지 Vol.48 No.1
On the hyperbolic space D^n, codimension-one totally geodesic foliations of class C^k are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0,π] → S^(n−1)of class C^(k−1) with z(0) = e1 = z(π) satisfying
NONDIFFERENTIABLE SECOND-ORDER MINIMAX MIXED INTEGER SYMMETRIC DUALITY
Tilak Raj Gulati,Shiv Kumar Gupta 대한수학회 2011 대한수학회지 Vol.48 No.1
In this paper, a pair of Wolfe type nondifferentiable second order symmetric minimax mixed integer dual problems is formulated. Symmetric and self-duality theorems are established under η1/η2-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.
Algebras with pseudo-Riemannian bilinear forms
Zhiqi Chen,Ke Liang,Fuhai Zhu 대한수학회 2011 대한수학회지 Vol.48 No.1
The purpose of this paper is to study pseudo-Riemannian al-gebras, which are algebras with pseudo-Riemannian non-degenerate sym-metric bilinear forms. We find that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposi-tion of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automor-phism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.
On irreducibility of induced modules and an adaptation of the Wigner--Mackey method of little groups
Geetha Venkataraman 대한수학회 2013 대한수학회지 Vol.50 No.6
This paper deals with sufficiency conditions for irreducibilityof certain induced modules. We also construct irreducible representationsfor a group G over a field K where the group G is a semidirect product ofa normal abelian subgroup N and a subgroup H. The main results areproved with the assumption that char K does not divide |G| but there isno assumption made of K being algebraically closed.
Quasi m-Cayley strongly regular graphs
Klavdija Kutnar,Luis Martinez,Aleksander Malnic,Dragan Marusic 대한수학회 2013 대한수학회지 Vol.50 No.6
We introduce a new class of graphs, called quasi m-Cayleygraphs, having good symmetry properties, in the sense that they admita group of automorphisms G that fixes a vertex of the graph and actssemiregularly on the other vertices. We determine when these graphs arestrongly regular, and this leads us to define a new algebro-combinatorialstructure, called quasi-partial difference family, or QPDF for short. Wegive several infinite families and sporadic examples of QPDFs. We alsostudy several properties of QPDFs and determine, under several condi-tions, the form of the parameters of QPDFs when the group G is cyclic.
조철현,홍한솔,신형석 대한수학회 2013 대한수학회지 Vol.50 No.6
The concept of "orbifold embedding" is introduced. This is more general than sub-orbifolds. Some properties of orbifold embeddings are studied, and in the case of translation groupoids, orbifold embedding is shown to be equivalent to a strong equivariant immersion.
Semiprime submodules of graded multiplication modules
이상철,Rezvan Varmazyar 대한수학회 2012 대한수학회지 Vol.49 No.2
Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever InK ⊆ Q,where I ⊆ h(R), n is a positive integer, and K h(M), then IK⊆Q. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad(Q) ∩ h(M) = Q ∩ h(M). Furthermore if M is finitely generated,then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q) ∩ h(M))n(grad(0M) ∩ h(M))= (Q ∩ h(M))n(grad(0M) ∩ Q ∩ h(M)):Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K ̸= M and Q ∩ K Mg for all g 2 G, then we prove that Q + K is almost semiprime in M.
PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER Φ-MIXING ASSUMPTION
Jie Li 대한수학회 2012 대한수학회지 Vol.49 No.2
In the paper by Liu and Lin (Statist. Probab. Lett. 76(2006), no. 16, 1787{1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under ϕ-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.