‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

The dinuclear dialkoxo-bridged complexes [(TiCl)(2)(mu-O(2)L)(mu-{(eta(5)-C(5)Me(4)SiMeO)(2)(mu-O)})] (O(2)L = 1,2-O(2)C(2)H(4), 1,2-O(2)C(6)H(4), 1,2-(OCH(2))(2)C(6)H(4), O(2)SiPh(2)) were obtained by reaction of [(TiCl(2))(2)(mu-{(eta(5)-C(5)Me(4)SiMeO)(2)(mu-O)})] () with the corresponding dilithium salt () or diol (, , ). Alkylation of and with ClRMg afforded [(TiR)(2)(mu-O(2)L)(mu-{(eta(5)...

In this work, overshoot and undershoot effects associated with step-and-shoot IMRT (SSIMRT) delivery on a Varian Clinac 21iX are investigated, and their impact on patient-specific QA point dose measurements and treatment plan delivery are evaluated. Pinnacle3 SSIMRT plans consisting of 5, 10, and 15 identical 5 × 5 cm2 MLC defined segments and MU/segment values of 5 MU, 10 MU, and 20 MU were ut...

We consider a standard Hodgkin-Huxley model neuron with a Gaussian white noise input current with drift parameter mu and variance parameter sigma(2). Partial differential equations of second order are obtained for the first two moments of the time taken to spike from (any) initial state, as functions of the initial values. The analytical theory for a 2-component (V,m) approximation is also cons...

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...