where α1 and α2 are positive regularization parameters. The main advantage of using the new data fitting term ∑n2 i=1 ( [z]i + [g]iei ) is that its second derivative with respect to [z]i is equal to [g]i e−[z]i , therefore it implies that the new data fitting term is strictly convex for all z. Here we add a fitting term ||z −w||2 in the new minimization method. We can interpret the total variat...

The first section of this paper defines and studies a graded ring K . F associated to any field F. By definition, K~F is the target group of the universal n-linear function from F ~ x ... • F ~ to an additive group, satisfying the condition that al • " ' x a, should map to zero whenever a i -q-a i + ~ = 1. Here F ~ denotes the multiplicative group F 0 . Section 2 constructs a homomorphism ~: K,...

Mahler’s measure is generalized to create the class of multiplicative distance functions. These functions measure the complexity of polynomials based on the location of their zeros in the complex plane. Several examples of multiplicative distance functions are given including those formed from equilibrium potentials of compact connected subsets of C. To each multiplicative distance function we ...

The global superstability of a dynamical system is allowed when all bounded orbits of this system are superstable, .i.e. There exist a minus infinity Lyapunouv exponent. In this paper it is shown that any globally superstable 2-D quadratic map is conjugate to the 1D quadratic map. This result allow us to determine some forms of superstable 1-D quadratic maps.

The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The rst, main, result is that, under reasonable restrictions on the form of the deenition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained c...

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose th...