In this paper, we consider rods whose thickness vary linearly between and . Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the displacement fields of the form u = Ue + ū, where Ue stands for the translation-rotations of the cross-sections and ū is related to their deformations. We establish a priori estimates...

In this work, we study the following Generalized Variational Inequality Problem (for short, GVIP): Given a closed convex set K in a reflexive Banach space E with the dual E, a multifunction T : K → 2E∗ , and a vector b ∈ E, find x̄ ∈ K such that there exists ū ∈ T(x̄) satisfying 〈ū− b, y− x̄〉 ≥ 0, for all y ∈ K. By using generalized projection and the well-known Fan–KKM Theorem, we prove existence...

Flavor asymmetry in light antiquark distributions is discussed. In particular, recent progress on the ū/d̄ asymmetry is explained. Then, we discuss possible future experimental studies.

Here, we assume that Ω is a bounded domain in R, 1 ≤ n ≤ 3, with a Lipschitz boundary Γ, Q = Ω × (0, T ), Σ = Γ × (0, T ), and y0 ∈ L∞(Ω). BV (0, T ) denotes the space of bounded variation functions defined in (0, T ), with 0 < T < ∞ given. The controllers in (P) are supposed to be separable functions with respect to fixed spatial shape functions gj and free temporal amplitudes uj . The specifi...

The gray filled circle represents the coupling of the virtual photon to the target, taking the target from an initial state X to some final state Y , which we incorporate into a scattering amplitude factor ˆ ν (q), where M q = p − p� = k� − k. The full matrix element for the process is: M = (−ie)ū(p�)γμu(p) −igμν ˆ ν (q) (1) q2 M Parts a) and b) of the problem analyze the structure of the ū(p�)...