We show that the Dirac operator on a spin manifold does not admit L eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if the manifold is complete and carries a non-complete vector field which outside a compact set is gradient conformal and non-vanishing.

Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first-order terms of the metric, the calculations are performed with an accuracy of second order. It is shown that such quantum corrections give rise to modified gravity.

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used...

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian 4-manifolds. Compared with the more widely ...

This paper proposes an improved Object Oriented metrics, which may be used for the high-level design quality assessment of Object Oriented software. An integrated approach has been adopted to get a single class based metrics that may be used for cumulative measure of all aspects of object oriented design (encapsulation, inheritance and polymorphism), and hence an indication of quality of class ...

Let C(X) be the hyperspace of all subcontinua of a metric continuum X. Alejandro Illanes has proved that C(X) is a finitedimensional Cartesian product if and only if X is an arc or a circle. In this paper we shall prove, using the inverse systems and limits, that if X is a non-metric rim-metrizable continuum and C(X) is a finitedimensional Cartesian product, then X is a generalized arc or a gen...

Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W . The smallest cardinality of a strong resolving set for G is called the strong metric dime...

A number of spacetime fields in string theory—notably the metric, dilaton, bulk (bosonic and type 0) closed string tachyon, and bosonic open string tachyon—have the property that, whenever the spacetime field configuration factorizes in an appropriate sense, the matter sector of the world-sheet theory factorizes into a tensor product of two decoupled theories. Since the beta functions for such ...

The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems in the product spaces of complete quasi-ordered metric spaces. The fixed point theorems in the product spaces will be the special case of coincidence point theorems in the product spaces. We also show that the concept of fixed point theorems in the product spaces extends the concept o...

We first introduce two functions on finitely additive probability spaces that behave well under products: discrepancy, which measures how close one space comes to extending another, and bi-discrepancy, which is a pseudo-metric on the collection of all spaces on a given set, and a metric on the collection of complete spaces. We then apply these to show that the Loeb space of the internal product...