This dissertation considers a suite of search problems in which agents are trying to find goals in minimum expected time. Unlike search in data structures in which time is measured by a number operations, search in metric spaces measures time by units of distance and has received much less attention. In particular, search strategies that attempt to minimize expected search time are only availab...

By Doob’s theorem, supermartingales indexed by the natural numbers decompose into the difference of a uniformly integrable martingale and an increasing process. The relative ease of working with increasing processes rather than supermartingales explains the prominent role of this result in stochastic analysis and in the theory of stochastic integration. Meyer [19] then proved that, under the us...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the RieszThorin interpolation theorem we get the corresponding results in Lp(R+), 1 ≤ p ≤ 2 for the Kontorovich-Lebedev, Mehler-Fock and Olevskii index transforms. An inversion theorem is proved for general index transformat...

Many results involving expected utility theory call upon the notions of absolute risk aversion, prudence and/or temperance. The present paper exploits a representation of the FriedmanSavage utility premium to give a general foundation for such coefficients and for their higherorder extensions.

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

The general distance matrix D was modified to distinguish cis/trans isomers of cycloalkanes. A new topological index, VDI (±1) , was derived from the modified distance matrix (D mod) according to the calculation of VDI proposed in a previous paper. This new structural descriptor discriminates all compounds studied in this paper. The regression analysis against the boiling temperatures (t b) for...