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Full-Text Articles in Physical Sciences and Mathematics
Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer
Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer
Mathematics Faculty Publications
In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫t0C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various Lp properties are studied under suitable conditions on the functions involved with this equation.
An Order Model For Infinite Classical States, Joe Mashburn
An Order Model For Infinite Classical States, Joe Mashburn
Mathematics Faculty Publications
In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …