Acta Mathematica Vietnamica最新文献

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided.

In this paper, we present the complete convergence for weighted sums of coordinatewise pairwise negative quadrant dependent random variables taking values in Hilbert spaces. As an application of the results, the complete convergence of degenerate von Mises statistics is investigated.

We obtain some weighted (L^{p})-Sobolev estimates with gain on p and the weight for solutions of the (overline{partial })-equation in linearly convex domains of finite type in (mathbb {C}^{n}) and apply them to obtain weighted (L^{p})-Sobolev estimates for weighted Bergman projections of convex domains of finite type for quite general weights equivalent to a power of the distance to the boundary.

We study the problem of reconstructing an unknown source term in parabolic equations from integral observations. It is reformulated into a variational problem in combination with Tikhonov regularization and then a formula for the gradient of the objective functional to be minimized is computed via a solution of an adjoint problem. The variational problem is discretized by the splitting method based on finite difference schemes and solved by the conjugate gradient method. A numerical scheme for numerically estimating singular values of the solution operator in the inverse problem is suggested. Some numerical examples are presented to show the efficiency of the method.

We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with Real connection on manifolds with involution.

In this paper, using Nevanlinna theory and linear algebra, we characterize transcendental meromorphic solutions of nonlinear differential equation of the form

where (lge 2), (nge l+2) are integers, f(z) is a meromorphic function, (Q_d(z,f)) is a differential polynomial in f(z) of degree (dle n-(l+1)) with rational functions as its coefficients, (p_{1}(z)), (p_{2}(z)), (dots ), (p_{l}(z)) are non-vanishing rational functions and (alpha _{1}(z)), (alpha _{2}(z)), (dots ), (alpha _{l}(z)) are nonconstant polynomials such that (alpha _{1}^prime (z)), (alpha _{2}^prime (z)), (dots ), (alpha _{l}^prime (z)) are distinct. Further, we give the necessary conditions for the existence of meromorphic solutions of the above equation, and supply the example to demonstrate the sharpness of the condition of the obtained theorem.

In this note, a condition (open persistence) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme X can be extended to a (pre)closure operation on sheaves of submodules of a coherent (mathcal {O}_X)-module (resp. sheaves of ideals in (mathcal {O}_X)). A second condition (glueability) is given for such an operation to behave nicely. It is shown that for an operation that satisfies both conditions, the question of whether the operation commutes with localization at single elements is equivalent to the question of whether the new operation preserves quasi-coherence. It is shown that both conditions hold for tight closure and some of its important variants, thus yielding a geometric reframing of the open question of whether tight closure localizes at single elements. A new singularity type (semi F-regularity) arises, which sits between F-regularity and weak F-regularity. The paper ends with (1) a case where semi F-regularity and weak F-regularity coincide, and (2) a case where they cannot coincide without implying a solution to a major conjecture.

In connection with [Theorem 4.6, Linear Algebra Appl. 646, 119–131, (2022)], we show that each matrix in the commutator subgroup of the general linear group over a centrally-finite division ring D, in which each element in the commutator subgroup of D is a product of at most s commutators, can be written as a product of at most (3+3leftlceil frac{s}{lfloor n/2 rfloor } rightrceil ) commutators of involutions if (mathrm {char,}Dne 2), where ({displaystyle lceil x rceil }), ({displaystyle lfloor x rfloor }) denote the ceiling and floor functions of x, respectively. Moreover, we also present the special case when (D= mathbb {H}), the division ring of quaternions, and an application in real group algebras.