A fluid mixing valve construction having a housing provided with a pair of inlets respectively interconnected by a pair of valve seats to an outlet and with a valve member operated by a condition responsive unit for controlling the valve seats in accordance with the condition of fluid passing to the outlet and sensed by the condition responsive unit. A second condition responsive unit is operatively interconnected to the valve member to close one of the valve seats with the valve member if the first mentioned condition responsive unit does not close the one valve seat with the valve member even though the same is sensing a condition that would require the first mentioned condition responsive unit to close the one valve seat whereby the fluid mixing valve construction is substantially fail-safe.
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of the entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.