The theoretical fundamentals of software stability were elaborated on the basis of software dynamic theory. The concepts of internal and external equilibrium have been introduced and the condition of reliability has been proved. The law of defect flow equilibrium has been formulated. The existence of unknown before mutual dependences among the defect flows in software has been revealed.

A logistic matrix model for age-structured population dynamics is constructed. This model discretizes a continuous, density-dependent model with age structure, i.e. it is an extension of the logistic model to the case of age-dependence. We prove the existence and uniqueness of its equilibrium and give a necessary and sufficient condition for the local stability of the equilibrium.

This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasi-concavity of functions and convexity or compactness of choice sets. A new condition, called “local dominatedness property”, is shown to be necessary and further, under some mild continuity condition, sufficient for the existence of equilibrium. We then apply the basic result obtained ...

The paper covers the 1924–1949 debate on the conjectural variations approach to duopoly theory and focuses on the evolution of economists’ views about the imposition of a consistency condition on the firms’ conjectures. The main point is that, although the consistency condition entailed a notion of interactive equilibrium that resembled the modern correct conjectures equilibrium, most neoclassi...

In this paper, we consider a delayed diffusive Leslie–Gower predator–prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexist...

expansive soils can be found in many parts of the world particularly in arid and semi-arid regions. these soilspose a significant hazard to civil engineering structures due to its high swelling and shrinkage potential. this paperpresents the results of an experimental program developed to investigate the effect of cyclic drying and wetting on theswelling potential of expansive soils with variou...

This paper studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homo...

In lecture 8 we have formulated the condition of static equilibrium of bodies and structures by studying a small change (variation) of the total potential energy. The system was said to be in equilibrium if the first variation of the total potential energy vanishes. The analysis did not say anything about the stability of equilibrium. The present lecture will give an answer to that question by ...

We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, th...