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The classical linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, we show that the optimal plan follows an unstable separatrix which is present in the associated Hamiltonian system.
We consider free massive matter fields in static scalar, electric and gravitational backgrounds. Tuning these backgrounds to the brink of vacuum decay, we identify a term in their effective action that is singular. This singular term is universal, be
An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared integration. Explic
In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $Nge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equatio
We present a proof of convergence of the Hamiltonian Monte Carlo algorithm in terms of Functional Analysis. We represent the algorithm as an operator on the density functions, and prove the convergence of iterations of this operator in $L^p$, for $1<
In this paper the effect of the search for a primitive on the theory of integration is discussed.