The following inequality is a generalization of Minkowski's inequality C12.4 to double integrals. In some sense it is also a theorem on the change of the order of iterated integrals, but equality is only obtained if p = 1. 13.14 Theorem (Minkowski's inequality for integrals) Let XX and YY be-finite measure spaces and u u X × Y → ¯ be ⊗-measurable. Then X Y uuxx yy dyy p dxx 1/p Y X uuxx yy p dx...

bstract. We propose novel matrix-form representations of the onventional forward three-dimensional (3-D) discrete cosine transorm (DCT) and the inverse 3-D DCT. The pair of the computationlly efficient 3-D DCTs causes the formulation to be more concise ith a systematic structure, which has a high potential for the develpment of other applications via the 3-D DCT pair. Applications for nlargemen...

The E-algorithm is the most general sequence transformation actually known, since it contains as particular cases almost all the sequence transformations discovered so far : Richardson polynomial extrapolation , Shanks' transformation , summation processes , Germain-Bonne transformation , Levin's generalized transformations , the process p and rational extrapolation. In 10] some results concern...

Cristian C. Rusa, Min Wei, Todd A. Bullions, Xintao Shuai, Tamer Uyar and Alan E. Tonelli* Fiber & Polymer Science Program, North Carolina State University, Campus Box 8301, Raleigh, NC 27695-8301, USA Center For High Performance Manufacturing, ESM, Mail Code: 0219, 219 Norris Hall, Virginia Tech, Blacksburg, VA 24061-0219, USA Department of Biomedical Engineering, Case Western Reserve Universi...

satisfies the du Bois-Reymond form of the Euler equations. The principal purpose of the present note is to give an alternate proof of these results of McShane and Tonelli. In addition to being simpler in detail than the previous proofs, the differentiability theorems of §§2 and 3 involve weaker hypotheses than the corresponding theorems of McShane and Tonelli, both in regard to conditions on th...

P. F. Lovibond and D. R. Shanks (2002) suggested that expectancy of the unconditional stimulus and emotional ratings are valid indexes of awareness in Pavlovian conditioning and that participants are aware if they can discriminate the conditional stimuli. However, research suggests that processes that are irrelevant to awareness affect these measures. Further, as awareness refers to conscious e...

Barrett, A. M., Crowther, A F Dunlop, D., Shanks, R. G., and Smith, L. H. (1968). Naunyn-ScImiedeberg's Arch. exp. Path. Pharmak. In press. Braunwald, E., Sarnoff, S. J., and Stainsby, W. N. (1958). Circulat. Res., 6, 319. Brick, I., Hutchison, K. J., Roddie, I. C., and Shanks, R. G. (1968). Arch. Pharmacol. exp. Path. In press. Burkart, F., Barold, S., and Sowton, E. (1967). Amer. 7. Cardiol.,...

abstract soil compaction is a main factor that reduces the cane yield in sugarcane fields, in southwest of iran, especially in ratoon cropping system. therefore, sub-soiling practices could alleviate adverse effects of compaction and increased yield. in according to this aim, a study was to evaluate the effect of  ratooning practice systems consisting of control (no subsoiler), two and four sha...

Given a Tonelli Hamiltonian H : T ∗M → R of class C, with k ≥ 4, we prove the following results: (1) Assume there is a critical viscosity subsolution which is of class C in an open neighborhood of a positive orbit of a recurrent point of the projected Aubry set. Then, there exists a potential V : M → R of class Ck−1, small in C topology, for which the Aubry set of the new Hamiltonian H + V is e...