In infrared-stable fixed-point field theories, the interaction energy of a test particle is proportional to the non-relativistic (heavy source) coordinate-space potential derived from the field strength produced by that source. This is no longer true in ultraviolet-stable fixed-point field theories (UVSFPFT) as they may not have a finite infrared fixed point. This leads to the possibility that ...

The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation Tx = x does not possess a solution, it is contemplated to resolve a problem of finding an element x such that x is in proximity to Tx in some sense. Best proximity p...

Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f, g), is introduce...

An important element in a model of non-singular string cosmology is a phase in which classical corrections saturate the growth of curvature in a deSitter-like phase with a linearly growing dilaton (an ‘algebraic fixed point’). As the form of the classical corrections is not well known, here we look for evidence, based on a suggested symmetry of the action, scale factor duality and on conformal ...

Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the principle of equivalence for (system of) gauge fields is formulated. Bozhidar Z. Iliev: Normal frames, connections, gauge fields 1

We define a fixed point topological charge for the two–dimensional O(3) lattice σ–model which is free of topological defects. We use this operator in combination with the fixed point action to measure the topological susceptibility for a wide range of correlation lengths. The results strongly suggest that it is not a physical quantity in this model. The procedure, however, can be applied to oth...

Models of supersymmetricD-term inflation require a new mass scale near 10 GeV in order to match the density perturbation spectrum observed by COBE. Attempts to obtain such a scale from the anomalous U(1) of string theories fail in most string models. However there is hope that models based on non-standard embeddings in M-theory can solve the discrepancy. We will show that such models still suff...

In this paper we show the homoclinic bifurcations which are involved in some contact bifurcations of basins of attraction in noninvertible two-dimensional map. That is, we are interested in the link between contact bifurcations of a chaotic area and homoclinic bifurcations of a saddle point or of an expanding fixed point located on the boundary of the basin of attraction of the chaotic area. We...

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

We investigate positive solutions of a prey-predator model with predator saturation and competition under homogeneous Dirichlet boundary conditions. First, the existence of positive solutions and some sufficient and necessary conditions is established by using the standard fixed point index theory in cones. Second, the changes of solution branches, multiplicity, uniqueness, and stability of pos...