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A Borsuk--Ulam type theorem over iterated suspensions of real projective spaces
Ryuichi Tanaka 대한수학회 2012 대한수학회지 Vol.49 No.2
A CW complex B is said to be I-trivial if there does not exist a Z2-map from Si-1 to S() for any vector bundle over B and any integer i with i > dim . In this paper, we consider the question of determining whether kRPn is I-trivial or not, and to this question we give complete answers when k ̸= 1, 3, 8 and partial answers when k = 1, 3, 8. A CW complex B is I-trivial if it is "W-trivial", that is, if for every vector bundle over B, all the Stiefel{Whitney classes vanish. We nd, as a result, that kRPn is a counterexample to the converse of this statement when k = 2, 4 or 8 and n ≥ 2k.
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.
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.
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.
Rolling Stones with nonconvex sides I: regularity theory
이기암,Eunjai Rhee 대한수학회 2012 대한수학회지 Vol.49 No.2
In this paper, we consider the regularity theory and the exis-tence of smooth solution of a degenerate fully nonlinear equation describ-ing the evolution of the rolling stones with nonconvex sides:{M(h) = ht - F(t, z, zhzz) in f 0 < z ≤ 1}× [0,T]ht(z, t) = H(hz(z, t), h) on f z = 0 g:We establish the Schauder theory for C2,α-regularity of h.
The chiral superstring Siegel form in degree two is a lift
Cris Poor,David S. Yuen 대한수학회 2012 대한수학회지 Vol.49 No.2
We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t=2 over the theta group Γ1(1, 2) to Siegel modular cusp forms over certain subgroups Γpara(t, 1, 2) of paramodular groups. The theta group lift given here is a modication of the Gritsenko lift.