Let an count the number of 2-dimensional rook paths Rn,n from (0, 0) to (2n, 0). Rook pathsRm,n are the lattice paths from (0, 0) to (m+n,m−n) with allowed steps (x, x) and (y,−y) where x, y ∈ N+. In answer to the open question proposed by M. Erickson et al. (2010), we shall present a combinatorial proof for the recurrence of an, i.e., (n + 1)an+1 + 9(n − 1)an−1 = 2(5n + 2)an with initial condi...

Abstract: I discuss the initial conditions for a parton cascade.

A few months ago, a graduate student in another country called me (Vaughan) to ask for the source code of one of my multi-robot simulation experiments. The student had an idea for a modification that she thought would improve the system’s performance. By the standards of scientific practice this was a perfectly reasonable request and I felt obliged to give it to her. With our original code, the...

We investigate the Q evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalontype) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in excellent agreement with deep inelastic scattering experimental data from HERA. Key-words: Quantum Chromodynamics, ...

This paper is concerned with the following retarded Liénard equation x(t) + f1(x(t))(x (t)) + f2(x(t))x (t) + g1(x(t)) + g2(x(t− τ(t))) = e(t). We prove a new theorem which ensures that all solutions of the above Liénard equation satisfying given initial conditions are bounded. As one will see, our results improve some earlier results even in the case of f1(x) ≡ 0.

[1] Radioisotope evaluation of a cold-core, anticyclonic eddy surveyed in September 2004 on the Chukchi Sea continental slope was used to determine its age since formation over the shelf environment. Because the eddy can be shown to have been generated near the shelf break, initial conditions for several age-dependent tracers could be relatively well constrained. A combination of Ra/Ra, excess ...

How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and distribution of matter in the universe, the initial spectrum of density fluctuations, and the formation and evolution of galaxies, clusters of galaxies, and la...

We aim to study rolling tachyon cosmological solutions in de Sitter gravity. The solutions are taken to be flat FRW type and these are not time-reversal symmetric. We find that cosmological constant of our universe has to be fine-tuned at the level of the action itself, as in KKLT string compactification. The rolling tachyon can give rise to required inflation with suitable choice of the initia...

This paper considers a new combined dissociative and kick-out diffusion model subject to boundary and initial conditions that model out-diffusion. Both asymptotic and numerical solutions are presented, and the transition from dissociative to kickout behaviour is studied. Noteworthy components of the asymptotically reduced problems include a number of novel non-local diffusion equations. A relat...

We present results from axisymmetric, time-dependent magnetohydrodynamic (MHD) simulations of the collapsar model for gamma-ray bursts. Our main conclusion is that, within the collapsar model, MHD effects alone are able to launch, accelerate and sustain a strong polar outflow. We also find that the outflow is Poynting flux-dominated, and note that this provides favorable initial conditions for ...