# Vietnam Journal of Mathematics

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 17-23

*R*be an associative ring with identity, and let

*S*(

*R*) be the nonempty set of all the proper ideals of

*R*generated by central idempotents. Recall that if

*P*is a maximal element of the set

*S*(

*R*), then the factor ring

*R*/

*P*is called a Pierce stalk of

*R*. Let . In this article, we first point out that is a compact space with Zariski topology, and then we give a characterization of the Grothendieck...

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 43-49

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 115-120

*X*

_{0},

*X*

_{1}),(

*Y*

_{0},

*Y*

_{1}) and a linear operator

*T*on

*X*

_{0}+

*X*

_{1}to

*Y*

_{0}+

*Y*

_{1}such that either

*T*:

*X*

_{0}→

*Y*

_{0}is compact or

*T*:

*X*

_{1}→

*Y*

_{1}is compact, the operators

*T*:

*X*

_{ j }→

*Y*

_{ j }being bounded, it holds that the interpolation operator

*T*:[

*X*

_{0},

*X*

_{1}]

_{ θ }→[

*Y*

_{0},

*Y*

_{1}]

_{ θ }is compact.

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 59-80

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 11-16

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 1-10

*q*-subharmonic functions in . We prove that maximality of

*q*-subharmonic functions is a local notion and give a condition to check the maximality of

*C*

^{2}

*q*-subharmonic functions.

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 25-42

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 81-96

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 51-58

Vietnam Journal of Mathematics > 2013 > 41 > 1 > 97-113

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 149-160

*L*

^{∞}(

*L*

^{2})-error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by parabolic integro-differential equations. The state and the costate are discretized by the order

*k*Raviart–Thomas mixed finite element spaces, and the control is approximated by piecewise polynomials of order

*k*≥0. We derive error estimates for...

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 121-134

*GCR*-lightlike submanifolds of indefinite Cosymplectic manifolds and give an example. We also study the existence of this class in indefinite Cosymplectic space form. Then we prove that there does not exist a totally contact umbilical

*GCR*-lightlike submanifold of an indefinite Cosymplectic manifold other than totally contact geodesic

*GCR*-lightlike submanifold and moreover it is a totally...

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 233-244

*ϕ*-implicit relation are proved, generalizing the results from Abbas et al. (Filomat, 25:1–17, 2011, Theorems 2.4 and 2.11).

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 167-179

*n*+3 hyperplanes.

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 217-232

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 161-166

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 135-148

*T*

^{∗}-extensions. As a consequence, an isometrically isomorphic classification of two-step nilpotent quadratic Lie algebras can be obtained from the classification of 3-vectors. Next, we apply the study of two-step nilpotent quadratic Lie algebras to the classification of non-commutative symmetric Novikov...

Vietnam Journal of Mathematics > 2013 > 41 > 2 > 181-215

*y*=(

*y*

_{ j })

_{ j≥1}of possibly countably many parameters, normalized such that |

*y*

_{ j }|≤1. Under suitable analyticity assumptions on the ODEs,...

Vietnam Journal of Mathematics > 2013 > 41 > 3 > 303-312

*M*is called

*δ*-supplemented if, for every submodule of

*N*of

*M*, there exists

*L*≤

*N*such that

*M*=

*N*+

*L*and

*N*∩

*L*≪

_{ δ }

*L*. A module

*M*is called

*δ*-lifting if, for any

*N*≤

*M*, there exists a decomposition

*M*=

*A*⊕

*B*such that

*A*≤

*N*and

*N*∩

*B*≪

_{ δ }

*M*. In this paper, we study

*e*-supplemented modules and

*e*-lifting modules which are generalized

*δ*-supplemented modules and...

Vietnam Journal of Mathematics > 2013 > 41 > 3 > 341-352

*σ*-complete metric-like space and prove some common fixed point theorems in such spaces. Our results unify and generalize several well-known results in the literature and the recent result of Amini-Harandi [Fixed Point Theory Appl. 2012:204, 2012]. Some examples are included which show that the generalization is proper.