This paper introduces three new types of combinatorial designs, which we call external difference families (EDF), external BIBDs (EBIBD) and splitting BIBDs. An EDF is a special type of EBIBD, so existence of an EDF implies existence of an EBIBD. We construct optimal splitting A-codes by using EDF. Then we give a new bound on the number of shares required in robust secret sharing schemes (i.e.,...

Let G be the graph of a triangulated surface Σ of genus g ≥ 2. A cycle of G is splitting if it cuts Σ into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding components have genera k and g− k. It was conjectured that G contains a splitting cycle (Barnette ’1982). We confirm this conjecture for an infinite family of triangulations by com...

One possible type of the matrix splitting is introduced. Using this matrix splitting, we introduce a few properties and representations of generalized inverses as well as iterative methods for computing various solutions of singular linear systems. This matrix splitting is a generalization of the known index splitting from [13] and a proper splitting from [4]. Using a generalization of the cond...

Let M1 and M2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of ∂M1 to some component of ∂M2 by a homeomorphism φ. We show that when φ is “sufficiently complicated” then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of Mi is an unstabilized splitting of M , (2) every low genus, unstabilized Heegaard splitti...

The Beltrami flow is an efficient non-linear filter, that was shown to be effective for color image processing. The corresponding anisotropic diffusion operator strongly couples the spectral components. Usually, this flow is implemented by explicit schemes, that are stable only for small time steps and therefore require many iterations. In this paper we introduce a semi-implicit scheme based on...

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [6] in order to remove mixed Poisson-Gaussian (MPG) noise. existing splitting algorithm TV-IC, an inner loop by Newton method had be adopted one nonlinear optimization subproblem, which increased computation cost per outer loop. By introducing a bilinear constraint a...

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

* Correspondence: fuquanxia@sina. com Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China Full list of author information is available at the end of the article Abstract In this paper, a projective splitting method for solving a class of generalized mixed variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm...

We rst analyse a semi-discrete operator splitting method for nonlinear, possibly strongly degenerate, convection-diiusion equations. Due to strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data. Hence weak solutions satisfying an entropy condition are sought. We then propose and analyse a fully discrete splitting method which employs a front ...

Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...