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We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the Lq,p-cohomology of that manifold. The Lq,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L(M) modulo the exact forms which are exterior differentials of forms in L(M).

The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that

This paper presents LQ control problem based on numerical computation with guaranteed accuracy. By using the proposed methods, it is possible to guarantee numerical quality about design of control system. This paper also proposes a problem which finds the numerical optimal controller from a set of solutions solved by verified LQ control problem.

Three experiments were conducted to evaluate the effects of diet and monensin on performance, digestibility, and methane production in steers fed forage-based diets. In Exp. 1, 72 individually fed steers (300 ± 25 kg) were used in a randomized block design arranged as 2 separate 2 × 2 factorials with two common treatments, thus 6 diets were fed with 12 steers per treatment. Factors included hig...

BACKGROUND Epidemiologic studies have classified 18 genotypes of the human papillomavirus (HPV) as (probably) high-risk (HR) based on their association with cervical cancer, i.e., HPV 16, 18, 26, 31, 33, 35, 39, 45, 51, 52, 53, 56, 58, 59, 66, 68, 73, and 82. Given the fact that certain HR HPV types confer an increased risk of cervical (pre)cancer, type-specific identification might aid clinica...

In adaptive control problems one may drop the requirement of identifying the true system in order to simplify the problem of control. It will be shown that in the adaptive LQ control problem this does not at all lead to an easier problem. A MS Subject Classijication: 93C40. Kqvwords: Adaptive LQ control, Closed-loop identification, Certainty equivalence.

We study the Cauchy problem for the damped wave equation. In a previous paper [16] the author has shown the Lp-Lq estimates between the solutions of the damped wave equation and the solutions of the corresponding heat equation. In this paper, we show new Lp-Lq estimates for the damped wave equation with odd initial data.