Recently Takahashi has introduced James type constant. In this paper, we will introduce some new properties of the constant such as monotonicity, uniform non-squareness characterized by James type constant, and so on. We also investigate some relations between James type constant and other constants. Our main results of the paper are three examples of the constant. These examples include lp (p ...

It is obvious that lp (/> 2:1) or any Hubert space satisfies (A). In §3 it is shown that Lp (p>l) does likewise. The method of proof is entirely different from that of Clarkson. In §4 it is shown that if X is any Banach space having the property that every function on a linear interval to X, which satisfies a Lipschitz condition, is differentiable almost everywhere, then also every function of ...

We show that the unit ball of lp(Γ) in its weak topology is a continuous image of σ1(Γ) and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when Γ is uncountable. For a set Γ and a real number 1 < p < ∞, the Banach space lp(Γ) is a reflexive space, hence its unit ball is compact in the weak topology and in fact, it ...

where 1 sp < co. This definition is far from being intrinsic. For an intrinsic definition of WrTp(Mm, N”) see [ 11. In this space, beside the standard topology induced by the norm (1. ]ll,p, we also have weak topology and weak convergence. Let fk, f E W’~p(Mm), where 1 < p < co. We say that fk converges to f in weak topology iff fk + f in Lp and the set (lIVfk[lp)k is bounded. Weak convergence ...

We give a necessary condition for a set in Lp(Ω) spaces (1 < p <∞) to be self-extremal that partially extends our previous results to the case of Lp spaces. Examples of self-extremal sets in Lp(Ω) (1 < p <∞) are also given. In [4, 5], we introduced the notion of (self-) extremal sets of a Banach space (X ,‖ · ‖). For a nonempty bounded subset A of X , we denote by d(A) its diameter and by r(A) ...

In [18] and [19] we have studied compact embeddings of weighted function spaces on Rn, id : Hs q (w(x),Rn) −→ Lp(R), s > 0, 1 < q ≤ p < ∞, s − n/q + n/p > 0, with, for example, w(x) = 〈x〉α, α > 0, or w(x) = logβ〈x〉, β > 0, and 〈x〉 = (2 + |x|2)1/2. We have determined the behaviour of their entropy numbers ek(id). Now we are interested in the limiting case 1/q = 1/p + s/n. Let w(x) = logβ〈x〉, β >...

We consider the problem of computing shortest paths in three-dimensions in the presence of a single-obstacle polyhedral terrain, and present a new algorithm that for any p ≥ 1, computes a (c + ε)approximation to the Lp-shortest path above a polyhedral terrain in O( ε log n log log n) time and O(n log n) space, where n is the number of vertices of the terrain, and c = 2(p−1)/p. This leads to a F...

In this paper we pose the problem of approximating an arbitrary belief function (b.f.) with a consonant one, in a geometric framework in which belief functions are represented by the vectors of their basic probabilities, or “mass space”. Given such a vector ~ mb, the consonant b.f. which minimizes an appropriate distance function from ~ mb can be sought. We consider here the classical L1, L2 an...

how to cite this article: derakhshanfar h, modanlookordi m, amini a, shahrami a. a comparative study of the sedative effect of oral midazolam and oral promethazine medication in lumbar puncture. iran j child neurol. 2013 spring;7(2):11-16.   objective lumbar puncture (lp) essentially is a painful and stressful procedure that indicated for diagnosis and therapeutic purposes. one way to reduce th...

We give regularity results for solutions of a parabolic equation in non-rectangular domains U = ∪t∈]0,1[{t} × It with It = {x : 0 < x < φ(t)}. The optimal regularity is obtained in the framework of the space Lp with p > 3/2 by considering the following cases: (1) When φ(t) = tα, α > 1/2 with a regular right-hand side belonging to a subspace of Lp(U) and under assumption p > 1 + α. We use Labbas...