Some curvature estimates are derived from geometrical data concerning quasi-conformality properties of some commuting linearly independent vector fields on a compact Riemannian manifold.

Abstract: In this work, a nonsmooth multiobjective optimization problem involving generalized invexity with cone constraints and Applications (for short, (MOP)) is considered. The Kuhn-Tucker necessary and sufficient conditions for (MOP) are established by using a generalized alternative theorem of Craven and Yang. The relationship between weakly efficient solutions of (MOP) and vector valued s...

Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limitedmemory BFGS method. Moreover, one ...

In this paper, we give several existence theorems for solutions of the generalized quasi–variational inequalities under new conditions. Even in topological vector spaces, our results are new.

In this paper, using the maximal element theorem, we prove some existence theorem for vector quasi-variational-like inequalities without monotonicity and without compactness.

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space W , we study what we call quasi compatible subsets of Hom(W,W ((x))) and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncom...

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of generalized vector and scalar Hartmann potentials. This is done provided the vector and scalar potentials hold some relation. Namely, one must be equals to or minus the other. Finally the case of some quasi-exactly solvable potentials are briefly commented.

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators in non-compact settings in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators in non-compact settings, we shall use the concept of e...