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Full-Text Articles in Physical Sciences and Mathematics
Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding
Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding
Branko Ćurgus
Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first n - 1 derivatives.
An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett
An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett
Branko Ćurgus
Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.