Hypoellipticity in Gevrey classesG is characterized for a simple family of sums of squares of vector fields satisfying the bracket hypothesis, with analytic coefficients. It is shown that hypoellipticity holds if and only if s is greater than or equal to an optimal exponent that may take on any rational value.

Min et al. (2009) presented two complementary techniques that use the diffusion approximation to allow efficient Monte-Carlo radiation transfer in very optically thick regions: a modified random walk and a partial diffusion approximation. In this note, I show that the calculations required for the modified random walk method can be significantly simplified. In particular, the diffusion coeffici...

Due to the assumption that the best practice methods refer to each input separately instead of the whole set of inputs used by a firm, the benchmark technology as defined in the stochastic varying coefficient frontier model may be infeasible and theoretically improper whenever the maximum response coefficients are not coming from the same production unit. To overcome this problem we suggest an ...

an experimental study has been conducted on the hydrodynamics of a stage mixer-settler to obtain an appropriate design. in this paper several tests was performed to investigate full factorial design of experiments. since each test was repeated seven times, the repeatability of the test was confirmed (p=1 bar and t=25 °c). sauter diameter was determined by photographing both the mixer and settle...

MOTIVATION Modern functional genomics generates high-dimensional datasets. It is often convenient to have a single simple number characterizing the relationship between pairs of such high-dimensional datasets in a comprehensive way. Matrix correlations are such numbers and are appealing since they can be interpreted in the same way as Pearson's correlations familiar to biologists. The high-dime...

A new modified diffusi on coefficient (MDC) technique for solv ing conve ction diffusion equation is proposed. The Galerkin finite-element discretization process is applied on the modified equation rather than the original one. For a class of one-dimensional convec-tion–diffusion equations, we derive the modi fied diffusion coefficient analytically as a function of the equation coefficients and...

a simple and sensitive, solid-phase extraction method for the removal of citalopram drug from waste water has been developed by using magnetic nanoparticles modified with surfactant sodium dodecyl sulfate. these magnetic nanoparticles have shown great adsorptive tendency towards citalopram drug. the effect of different parameters influencing the extraction efficiency of this drug were investiga...

introduction: in the developed world, particularly in developing countries, livestock is the most important agricultural sub-sector.livestock of primary and secondary industries has an especial place in the national economybecause of their greatvalue of products, creating job opportunities, providing health products for consumers, increasing export income of the economy throughaccessing global ...