* Correspondence: lijueyou@163. com Department of Mathematics, Chongqing Normal University, Chongqing, 400047, PR China Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems...

*Correspondence: [email protected] Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia Abstract In the present paper, we are concerned with second-order duality for nondifferentiable minimax fractional programming under the second-order generalized convexity type assumptions. The weak, strong and converse duality theorems are proved. Results obtained in this paper ext...

Universal source codes achieve the optimal performance without apriori knowledge of the source statistics. The problem of universal lossy source coding for general non-stationary processes is considered here. Fixed rate and fixed distortion lossy source codes derived from the Lempel-Ziv scheme are shown to be universal for non-stationary processes with abstract alphabets. We define the rate dis...

*Correspondence: [email protected] Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550, Japan Abstract We introduce a new nonlinear mapping similar to the nonspreading mapping which is defined by Kohsaka and Takahashi (Arch. Math. 91:166-177, 2008). We prove fixed point theorems for such a mapping without the convexity of the domain. We also prove...

Abstract We give topological criteria for the convexity and the concavity of a current or a voltage in a resistive circuit, as a function of a source voltage or current, when the nonlinear resistor characteristics are all either convex or concave. When the criteria are satisfied, all circuits with the same structure will have a convex, or all will have a concave transfer characteristic. The app...

Abstract. This paper addresses the synchronized region problem, which is reduced to a matrix stability problem, for complex dynamical networks. For any natural number n, the existence of a network which has n disconnected synchronized regions is theoretically demonstrated. This shows the complexity in network synchronization. Convexity characteristic of stability for matrix pencils is further d...

*Correspondence: [email protected] Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, P.R. China Abstract This paper is concerned with fractional differential inclusions with three-point fractional integral boundary conditions. We consider the fractional differential inclusions under both convexity and nonconvexity conditions on the multivalued term. Some new existenc...

Abstract We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary...

Abstract The conditional quantile function m(X) of response variable Y given the value of covariate X is modeled through a single-index model, i.e. m(X) = m(θ 0 X) for some unknown parameter vector θ0. An iterated algorithm is proposed to estimate θ0. To establish the root-n consistency of the estimator, we prove a convexity lemma for almost sure convergence, parallel to the results by Pollard ...

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two-dimensional metric continuum with a continuous median operator, for which there is no median-preserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negat...