1 I n t r o d u c t i o n This is a fol low-up o f our paper [3], where we establish that l i~(l _ s) f~ fn lf(x) f(Y)lPd~ d p ~ yld-77;~p y ~ IIVSIIL~(.), for any p E [1, oo), where f~ is a smooth bounded domain in lRd,d > 1. On the other hand, if 0 < s < 1, p > 1 and sp < d, the Sobolev inequality for fractional Sobolev spaces (see, e.g., [1], Theorem 7.57 or [6], Sect ion 3.3) asserts that (...

nuclear cross sections that determine core multiplication strongly depend on core temperature (e.g., the doppler, moderator density effects etc). on the other hand, since this heat is generated by the neutron flux in the reactor core, the temperature distribution in the core will depend heavily on its neutronic behavior. fuel centerline temperature could be the limiting constraint on reactor po...

The problem of inference for the proportion of successes in a finite populations is given much less attention in both inference and application courses than the related infinite population problem. However, the finite population problem is both interesting and useful in its own right while also providing insight into various approaches for the infinite population case. This article explores exa...

Subdifferentials of convex functions and some regular functions f are expressed in terms of limiting gradients at points in a given dense subset of dorn Vf.

XML promises to provide a powerful interoperable general framework for the development of music representation systems. Unfortunately current XML encoding systems for music focus almost exclusively on Western music from the 17 century onwards, and on the Western notation system, Common Music Notation (CMN). This is regrettably limiting, with cultural, theoretical, and practical consequences for...

A spinning disc reactor was investigated as a process intensification technology for photocatalysis and compared with a conventional annular reactor. It was found that the average photonic efficiency achieved in the SDR was three times larger than the maximum photonic efficiency achieved in the annular reactor, 0.19±0.08% versus 0.062 ± 0.009%, indicating that the SDR is significantly more effi...

A next-generation neutrino oscillation experiment using reactor neutrinos could give important information on the size of mixing angle θ 13. The motivation and goals for a new reactor measurement are discussed in the context of other measurements using off-axis accelerator neutrino beams. The reactor measurements give a clean measure of the mixing angle without ambiguities associated with the s...

Hydrolysis is the rate limiting step for particulate/solid substrates under anaerobic digestion. The first order kinetic model is commonly applied to describe this step and it can be determined by anaerobic batch test. In this paper we assess three issues with respect to defining the hydrolysis rate constant; source of inoculum, influence of substrate to inoculum ratio and the pre-incubation ti...