The main result of this paper is a convexity theorem for momentum mappings J :M → g∗ of certain hamiltonian actions of noncompact semisimple Lie groups. The image of J is required to fall within a certain open subset D of g∗ which corresponds roughly via the orbit method to the discrete series of representations of the group G. In addition, J is required to be proper as a map from M to D. A rel...

The main result of this paper is a convexity theorem for momentum mappings J :M → g∗ of certain hamiltonian actions of noncompact semisimple Lie groups. The image of J is required to fall within a certain open subset D of g∗ which corresponds roughly via the orbit method to the discrete series of representations of the group G. In addition, J is required to be proper as a map from M to D. A rel...

Abstract. We prove that rank-(n−1) convexity does not imply S-quasiconvexity (i.e., quasiconvexity with respect to divergence free fields) in M for m > n, by adapting the well-known Šverák’s counterexample [5] to the solenoidal setting. On the other hand, we also remark that rank-(n − 1) convexity and Squasiconvexity turn out to be equivalent in the space of n×n diagonal matrices. This follows ...

We prove that rank-.n 1/ convexity does not imply quasiconvexity with respect to divergence free fields (so-called S-quasiconvexity) in M n for m > n, by adapting the well-known Šverák’s counterexample to the solenoidal setting. On the other hand, we also remark that rank-.n 1/ convexity and S-quasiconvexity turn out to be equivalent in the space of n n diagonal matrices.

A multivariate polynomial p(x) = p(x1, . . . , xn) is sos-convex if its Hessian H(x) can befactored as H(x) = M (x)M(x) with a possibly nonsquare polynomial matrix M(x). It iseasy to see that sos-convexity is a sufficient condition for convexity of p(x). Moreover, theproblem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefiniteprogram, wh...

The notion of sos-convexity has recently been proposed as a tractable sufficient condition for convexity of polynomials based on sum of squares decomposition. A multivariate polynomial p(x) = p(x1, . . . , xn) is said to be sos-convex if its Hessian H(x) can be factored as H(x) = M (x) M (x) with a possibly nonsquare polynomial matrix M(x). It turns out that one can reduce the problem of decidi...

There are many symmetries in intuitionistic fuzzifying topology. In the present paper, notion of topology as an extension and a preliminary research on bi-intuitionistic fuzzy is introduced. A theory with semantic method logic established.

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...