Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.

Mathematical model for computing precise local tie vectors for CMONOC co-located GNSS/VLBI/SLR stations

The seven co-located sites of the Crustal Movement Observation Network of China（CMONOC） in Shanghai, Wuhan, Kunming, Beijing, Xi＇an, Changchun, and Urumqi are equipped with Global Navigation Satellite System（GNSS）, very long baseline interferometry（VLBI）, and satellite laser ranging（SLR） equipment. Co-location surveying of these sites was performed in 2012 and the accuracies of the solved tie vectors are approximately 5 mm.This paper proposes a mathematical model that handles the least squares adjustment of the 3D control network and calculates the tie vectors in one step, using all the available constraints in the adjustment. Using the new mathematical model, local tie vectors can be more precisely determined and their covariance more reasonably estimated.

On Vector Quasi-Variational Inequality Problems in H-Space

The purpose to this paper is to study the existence problem of solutions to the vector quasivariational inequality for vector-valued functions inH-space.

Some New Results on Indices of Singular Points of a Polynomial Vector Field

Several new results on the indices of singular points in a polynomial vector field are proved in this paper(see Theorems 1-5).

ON DETECTION OF CHANGE POINTS USING MEAN VECTORS

In this paper,the authors consider the problem of change points within the framework of model selection and propose a procedure for estimating the locations of change points when the number of change points is known.The strong consistency of this procedure is also established. The problem of detecting change points is discussed within the framework of the simultaneous test procedure.The case where the number of change points is unknown will be discussed in another paper.