An explicit formula for the Skorokhod map Γ0,a on [0, a] for a > 0 is provided and related to similar formulas in the literature. Specifically, it is shown that on the space D[0,∞) of right-continuous functions with left limits taking values in R, Γ0,a(ψ)(t) = ψ(t) − [( ψ(0) − a )+ ∧ inf u∈[0,t] ψ(u) ] ∨ sup s∈[0,t] [ (ψ(s) − a) ∧ inf u∈[s,t] ψ(u) ] . is the unique function taking values in [0,...

The correlation between the pancreatic and external abdominal motion due to respiration was investigated on two patients. These studies utilized four dimensional computer tomography (4D CT), a four dimensional (4D) electromagnetic transponder system, and a gating belt system. One 4D CT study was performed during simulation to quantify the pancreatic motion using computer tomography images at ei...

We introduce a low-order stabilized discretization of the primitive equations of the ocean with highly reduced computational complexity. We prove stability through a specific inf–sup condition, and weak convergence to a weak solution. We also perform some numerical tests for relevant flows. © 2012 Elsevier Ltd. All rights reserved.

This paper considers the problem of homogenization of a class of convex HamiltonJacobi equations in spatio-temporal stationary ergodic environments. Special attention is placed on the interplay between the use of the Subadditive Ergodic Theorem and continuity estimates for the solutions that are independent of the oscillations in the equation. Moreover, an inf-sup formula for the effective Hami...

We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf-sup condition is satisfied for this pair. Two numerical experiments are presented to support the theoretical results.

We present a method for solving the Stokes problem in unbounded domains. It relies on the coupling of the transparent boundary operator and a spectral method in spherical coordinates. It is done explicitly by the use of vector-valued spherical harmonics. A uniform inf-sup condition is proved, which provides an optimal error estimate.

In this paper we investigate the System of fuzzy relation equations with inf → composition. We base on the knowledge of he system of fuzzy relation equations with sup−∗-composition. First, the general notions are explained and then are shown the smallest and maximal solutions. Finally is investigated a simple criterion of solvability for a special case of fuzzy sets.

A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec-Klee property; and it has the fixed point property if there exists ε > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ (−A) fails to be (2 − ε)-separated. In particular, E-convex Banach spaces, a cla...

Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual recursive formulation is contractive. JEL codes: C61, C73, D82, E61.

This article studies a least-squares finite element method for the numerical approximation of compressible Stokes equations. Optimal order error estimates for the velocity and pressure in theH are established. The choice of finite element spaces for the velocity and pressure is not subject to the inf-sup condition. c © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 62–70...