Some preliminary remarks on the relevance of topological essentiality in general equilibrium theory and game theory

We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement.fixed point theory, game theory, equilibrium theory, stability of Nash equilibrium, multiplicity of equilibria

Impossibility of Stable and Non-damaging bossy Matching Mechanism

In this paper we prove the impossibility of stability rules that satisfy a concept weaker than nonbossiness. Stability and nonbossiness are essential to matching theory. However, Kojima Fuhito(2010) shows that a matching mechanism that is both stable and nonbossy dose not exist. We define a new concept that is weaker than nonbossiness and consider whether or not stability and the new concept are compatible. Unfortunately, we show that these properties are incompatible.matching, stability, non-damaging bossy, impossibility theorem.

A Cellular Automata Model with Probability Infection and Spatial Dispersion

In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and spatiotemporal approach are shown by using cellular automata theory. It is interesting to note that both size of the endemic equilibrium and density of the individual increase with the increasing of the neighborhood size and infection rate, but the infections decrease with the increasing of the recovery rate. The stability of the system around the positive interior equilibrium have been shown by using suitable Lyapunov function. Finally experimental data simulation for SARS disease in China and a brief discussion conclude the paper

A Point's Point of View of Stringy Geometry

The notion of a "point" is essential to describe the topology of spacetime. Despite this, a point probably does not play a particularly distinguished role in any intrinsic formulation of string theory. We discuss one way to try to determine the notion of a point from a worldsheet point of view. The derived category description of D-branes is the key tool. The case of a flop is analyzed and Pi-stability in this context is tied in to some ideas of Bridgeland. Monodromy associated to the flop is also computed via Pi-stability and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref adde

The stability of macroeconomic systems with Bayesian learners

We study abstract macroeconomic systems in which expectations play an important role. Consistent with the recent literature on recursive learning and expectations, we replace the agents in the economy with econometricians. Unlike the recursive learning literature, however, the econometricians in the analysis here are Bayesian learners. We are interested in the extent to which expectational stability remains the key concept in the Bayesian environment. We isolate conditions under which versions of expectational stability conditions govern the stability of these systems just as in the standard case of recursive learning. We conclude that the more sophisticated Bayesian learning schemes do not alter the essential expectational stability findings in the literature.Rational expectations (Economic theory)

Stability Tests for a Class of 2D Continuous-Discrete Linear Systems with Dynamic Boundary Conditions

Repetitive processes are a distinct class of 2D systems of both practical and theoretical interest. Their essential characteristic is repeated sweeps, termed passes, through a set of dynamics defined over a finite duration with explicit interaction between the outputs, or pass profiles, produced as the system evolves. Experience has shown that these processes cannot be studied/controlled by direct application of existing theory (in all but a few very restrictive special cases). This fact, and the growing list of applications areas, has prompted an on-going research programme into the development of a 'mature' systems theory for these processes for onward translation into reliable generally applicable controller design algorithms. This paper develops stability tests for a sub-class of so-called differential linear repetitive processes in the presence of a general set of initial conditions, where it is known that the structure of these conditions is critical to their stability properties

Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.Comment: 7 pages, 2 figures; first of a two-part serie