The mortality response of lightbrown apple moth, Epiphyas postvittana (Walker), to a controlled atmosphere (CA) cold storage treatment for apricots was investigated. The mean estimated times for 99% mortality (LT99) of 1st and 5th instar larvae inoculated onto apricots and exposed to 1.5% O2, 3% CO2 (CA) at 0°C, were 19.9 ± 0.13 and 22.4 ± 0.24 d, respectively. The treatment time for 50% mortal...

We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some generalizations Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions calculus. Our results proved by using two-dimensional Jensen’s and Fubini’s theorem scales. When α=1, then obtain well-known time-scale due to Hardy. As special cases...

This note deals with the inequality (∫ b a |u(x)|w0(x)dx )1/q ≤ C (∫ b a |u(x)|wk(x)dx )1/p , (1) more precisely, with conditions on the parameters p > 1, q > 0 and on the weight functions w0, wk (measurable and positive almost everywhere) which ensure that (1) holds for all functions u from a certain class K with a constant C > 0 independent of u. Here −∞ ≤ a < b ≤ ∞ and k ∈ N and we will cons...

for every u∈W1,p(Rn). It is easy to see that the proposition fails when s > 1, where s = q/p. In this paper we are trying to find out what happens if s > 1. We show that it does not only become true but obtains better estimates. The described result is stated and proved in Section 3. The method invoked is different from that by Cazenave in [2]; it relies on some Littlewood-Paley theory and Beso...

We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. 0. Introduction Suppose Ω ⊂ R is a bounded domain and let d(x) = dist(x, ∂Ω). We consider integral Hardy inequalities (0.1) ∀u ∈ ...

Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...

We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...

Abstract We study weighted inequalities of Hardy and Hardy–Poincaré type find necessary sufficient conditions on the weights so that considered hold. Examples with optimal constants are shown. Such then used to quantify convergence rate solutions doubly nonlinear fast diffusion equation towards Barenblatt profile.