We will show that if X is a tree-complete subspace of ∞ , which contains c 0 , then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming. 1. Introduction. It is known that ∞ has an equivalent strictly convex renorming [2]; however, by a result due to Lindenstrauss, it cannot be equivalently renormed in locally u...

Reverse-time migration (Baysal et al., 1984) has some potential advantages with respect to downward-continuation migration. It can migrate overturned and prismatic reflections even in the presence of strong lateral velocity variations (Biondi, 2002). It also models the amplitude of the transmitted wavefield more accurately than downward-continuation in the presence of sharp interfaces. However,...

Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.

The implicit midpoint rule (IMR) for nonexpansive mappings is established in Banach spaces. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a uniformly convex Banach space which either satisfies Opial’s property or has a Fréchet differentiable norm. Consequently, this algorithm applies in both `p and Lp for 1 < p < ∞.

where h >  is a stepsize. It is known that if f :RN →RN is Lipschitz continuous and sufficiently smooth, then the sequence {xn} generated by (.) converges to the exact solution of (.) as h→  uniformly over t ∈ [, t̄] for any fixed t̄ > . If we write the function f in the form f (t) = g(t) – t, then differential equation (.) becomes x′ = g(t)– t. Then the equilibrium problem associated w...

Remark 1 In this text, we always work between 0 and 1 with 1/2 playing the rôle of the midpoint. A simple rescaling allows to work between −1 and 1 with 0 playing the rôle of a midpoint. • A valued relation T is said to be reflexive if T (x, x) = 1, for all x ∈ X. A valued relation T on X such that T (x, y) ∈ {0, 1}, for all x, y ∈ X, is said to be crisp. As is usual, we write x T y instead of ...

To this end, we describe an area that arises from the midpoint of the navicular-calcaneal line (MPNCL), which contains both nerve divisions in the majority of cases. We called this area the danger zone. We identified the size and location of this danger zone by dissecting a total of 50 cadaveric feet. We measured the distance from the origin of each nerve division to both the navicular tuberosi...

We construct a linear interval system Ax = b with a 4 × 4 interval matrix whose all proper interval coefficients (there are also some noninterval ones) are of the form [−ε, ε]. It is proved that for each ε > 0, the interval hull [x, x] and interval hull of the midpoint preconditioned system [x, x] satisfy x1 = 0.6 and x1 = 1.2, hence midpoint preconditioning produces a 100% overestimation of x1...

This paper presents a detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises’ hardening material. A nonlinear scalar equation for determination of the plastic multiplier is derived. The solution of this equation for a hardening material, by the Newton-Raphson method, usually converges in threefour iteration...

This paper proposes a new technique to solve n-th order linear uncertain but bounded (interval) differential equations with interval initial conditions using the interval midpoint. First, the interval differential equation is solved in terms of the interval midpoint. This solution is then used to find the solution of the original interval differential equation. The method is discussed by consid...