We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Zs and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud–Sturmfels theory of binomial ideals over algebraically closed fields. We ...

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson’s theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson’s theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current dist...

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

The main result of this paper is a generalization the theorem Chevalley-Shephard-Todd to rings invariants pseudoreflection groups over Dedekind domains. In special case principal ideal domain in which group order invertible it proved that ring isomorphic polynomial ring. An intermediate every finitely generated regular graded algebra tensor product blowup algebras.