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�)...

We revisit the evaluation of the pionic mechanism of the ū − d̄-asymmetry in the proton structure function. Our analysis is based on the unitarity relation between contributions of different mechanisms to the inclusive particle production and the total photoabsorption cross-section (i.e. the proton structure function). We reanalyze the role of isovector reggeons in inclusive production of nucleo...

We are concerned with viscous profiles (travelling waves and steady solutions) for mixed hyperbolic-parabolic systems in one space variable. For a class of systems including the compressible Navier Stokes equation, these profiles satisfy a singular ordinary differential equation in the form (0.1) dU dt = 1 ζ(U) F (U). Here U takes values in R and F : R → R is a regular function. The real valued...

After taking account of the scale dependence by means of the standard DGLAP evolution equation, the theoretical predictions of the chiral quark soliton model for the unpolarized and longitudinally polarized structure functions of the nucleon are compared with the recent high energy data. The theory is shown to explain all the qualitative features of the experiments, including the NMC data for F...

Traditional fractal image coding seeks to approximate an image function u as a union of spatially-contracted and greyscale-modified copies of itself, i.e., u ≈ Tu, where T is a contractive fractal transform operator on an appropriate space of functions. Consequently u is well approximated by ū, the unique fixed point of T , which can then be constructed by the discrete iteration procedure un+1 ...

We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance betwe...

We have constructed a state-of-the-art, high luminosity polarized proton and deuteron target and propose to measure the Sivers asymmetry for the ū and d̄ sea quarks in the nucleon for four different Bjorken xB bins in the range 0.1 < xB < 0.5, using the Drell-Yan process at SeaQuest. We will: i) perform the first measurement of the Sivers asymmetry in Drell-Yan scattering for sea quarks; ii) det...

Using the latest data pertaining to ū− d̄ asymmetry and the spin polarization functions, detailed implications of the possible values of the coupling strength of the singlet Goldstone boson η′ have been investigated in the χCQM with configuration mixing. Using ∆u, ∆3, ū− d̄ and ū/d̄, the possible ranges of the coupling parameters a, α2a, β2a and ζ2a, representing respectively the probabilities of ...