The time-harmonic eddy current problem with either voltage or current intensity excitation is considered. We propose and analyze a new finite element approximation of the problem, based on a weak formulation where the main unknowns are the electric field in the conductor, a scalar magnetic potential in the insulator and, for the voltage excitation problem, the current intensity. The finite elem...

We rederive and discuss the result of the previous paper that in the standard model θ-term related to W-boson field can not be induced by weak instantons. This follows from the existence of the fermion zero mode in the instanton field even when Yukawa couplings are switched on and there are no massless particles. We consider the new index theorem connecting the topological charge of the weak ga...

After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ. In a delightful argument, Laver [L78] proved that any supercompact cardinal κ can be made indestructible by <κ-directed closed forcing. This indestructibility, however, is evidently not itself indestructible, for it is always ruined by small forcing: in [H96] the first author recen...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

Abstract Topological measures and deficient topological are defined on open closed subsets of a space, generalize regular Borel measures, correspond to (nonlinear in general) functionals that linear singly generated subalgebras or cones functions. They lack subadditivity, many standard techniques measure theory functional analysis do not apply them. Nevertheless, we show classical results proba...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

High-order topological phases host robust boundary states at the of boundary, which can be interpreted from their topology. In this work, considering interplay between superconductors and magnetic fields to gap surface three-dimensional weak insulators, we show that second-order (TSCs) featuring helical or chiral Majorana hinge modes third-order TSC corner realized. Remarkably, higher-order TSC...

In this paper, we describe some topological properties of dualistic partial metric spaces and establish some fixed point theorems for weak contraction mappings of rational type defined on dual partial metric spaces. These results are generalizations of some existing results in the literature. Moreover, we present examples to illustrate our result.