Gauge theories commonly employ complex vector-valued fields to reduce symmetry groups through the Higgs mechanism of spontaneous symmetry breaking. The geometry of the internal space V is tacitly assumed to be the metric geometry of some static, nondynamical hermitian metric k. In this paper, we consider G-principal bundle gauge theories, where G is a subgroup of U(V ,k) (the unitary transforma...

and Applied Analysis 3 Proposition 2.5. Let X,G be a G-metric space. Then the following statements are equivalent. 1 The sequence {xn} is G-Cauchy. 2 For every ε > 0, there is k ∈ N such that G xn, xm, xm < ε, for all n,m ≥ k. Definition 2.6. A G-metric space X,G is called G-complete if every G-Cauchy sequence in X,G is G-convergent in X,G . Proposition 2.7. Let X,G be a G-metric space. Then, f...

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

A resistance network is a connected graph (G, c). The conductance function cxy weights the edges, which are then interpreted as conductors of possibly varying strengths. The Dirichlet energy form E produces a Hilbert space structure (which we call the energy space HE) on the space of functions of finite energy. We use the reproducing kernel {vx} constructed in [JP09b] to analyze the effective r...

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

In [], Choudhury proved that if X is a complete metric space, then every weak C-contraction has a unique fixed point; see [, Theorem .]. This result was generalized to a complete, partially ordered metric space in []; see [, Theorems ., . and .]. There were some generalizations of a metric such as a -metric, aD-metric, aG-metric, a conemetric, and a complex-valuedmetric. The notion...