Survival after freezing was measured for seeds and germinants of four seedlots each of interior spruce (Picea glauca x engelmannii complex), lodgepole pine (Pinus contorta Dougl. ex Loud.), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) and western red cedar (Thuja plicata Donn ex D. Donn). Effects of eight seed treatments on post-freezing survival of seeds and germinants were tested: dry, ...

Let P be a linear, elliptic second order symmetric operator, with an associated quadratic form q, and let W be a potential such that the Hardy inequality λ0 ∫ Ω Wu 2 ≤ q(u) holds with (non-negative) best constant λ0. We give sufficient conditions so that the spectrum of the operator 1 W P is [λ0,∞). In particular, we apply this to several well-known Hardy inequalities: (improved) Hardy inequali...

The main purpose of this paper is to briefly review the earlier works of multiparameter Hardy space theory and boundedness of singular integral operators on such spaces defined on product of Euclidean spaces, and to describe some recent developments in this direction. These recent works include discrete multiparameter Calderón reproducing formulas and Littlewood-Paley theory in the framework of...

* Correspondence: [email protected] Department of Engineering Sciences and Mathematics, LuleåUniversity of Technology SE 971 87 Luleå, Sweden Full list of author information is available at the end of the article Abstract First we present and discuss an important proof of Hardy’s inequality via Jensen’s inequality which Hardy and his collaborators did not discover during the 10 years of research ...

Franklin BM, Xiang L, Collett JA, Rhoads MK, Osborn JL. Open problem-based instruction impacts understanding of physiological concepts differently in undergraduate students. Adv Physiol Educ 39: 327–334, 2015; doi:10.1152/advan.00082.2015.—Student populations are diverse such that different types of learners struggle with traditional didactic instruction. Problem-based learning has existed for ...

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...