1. A multivariate continuous model In this section, we provide the following concrete example that satisfies all the assumptions of Theorems 3 and 5 in our manuscript. Let yik be the response at time k for the i th subject from N(μik = β0 + xikβ1, 1), k = 1, . . . , T = 3, i = 1, . . . , n = 50. Let yi = (yi1, · · · , yiT ) . The true value of (β0, β1) is (1, -1). Covariates xik’s are iid rando...

The same relationship holds for the interfacial tension o-i at the consolute critical point (the critical point for phase separation) of a binary fluid mixture. Up to now no rigorous theory links the interfacial tension to properties of the bulk system. However, a phenomenological approach which should be valid in the vicinity of the critical point has been developed by Fisk and Widom. 2 Accord...

In Hard Disk Drives (HDD), it is necessary to decrease the Flying Height (FH) between the head and the disk (currently, FH is around 3-5 nm) so as to increase recording densities. Retaining the solid lubricant has become a difficult proposition owing to intermittent contact between the surfaces. ZTMD and Z are used as solid lubricant to lubricate these interfaces. In this paper, the behavior of...

A method for determination of the volume fraction in binary liquid mixtures by measurement of the equalization wavelength of intermodal interference of modes LP(01) and LP(11) in a liquid core optical fiber is presented in this paper. This method was studied using a liquid core optical fiber with fused silica cladding and a core made up of a binary silicon oil/chloroform liquid mixture with dif...

This paper presents the experimental investigations conducted on a vertical closed loop pulsating heat pipe (VCLPHP) to evaluate the thermal performance. The values of thermal resistance and heat transfer coefficient obtained in the experimentation is used as evaluation parameters. The VCLPHP used has capillary tubes having an inner diameter of 2mm and outside diameter 3mm and bent into 5 turns...

Let < be a complete and transitive binary relation on the set of all lotteries on finite sets of prizes. Then < is mixture continuous if and only if it satisfies the Archimedean axiom and a condition called local mixture dominance.

The objective of the present study was to develop a physiologically based pharmacokinetic (PBPK) model for a ternary mixture of alkyl benzenes [toluene (TOL), m-xylene (XYL), and ethylbenzene (EBZ)] in rats and humans. The approach involved the development of the mixture PBPK model in the rat and extrapolation to humans by substituting rat physiological parameters and blood:air partition coeffi...

A new approach to calculate the axially symmetric binary gas flow is proposed Dalton’s law for partial pressures contributed by each species of a binary gas mixture (argon and helium) is incorporated into numerical simulation of rarefied axially symmetric flow inside a rotating cylinder using the time relaxed Monte-Carlo (TRMC) scheme and the direct simulation Monte-Carlo (DSMC) method. The res...

In Hard Disk Drives (HDD), it is necessary to decrease the Flying Height (FH) between the head and the disk (currently, FH is around 3-5 nm) so as to increase recording densities. Retaining the solid lubricant has become a difficult proposition owing to intermittent contact between the surfaces. ZTMD and Z are used as solid lubricant to lubricate these interfaces. In this paper, the behavior of...