This paper presents the first numerical solution to the non-linear evolution equation for diffractive dissociation processes in deep inelastic scattering. It is shown that the solution depends on one scaling variable τ = Q2/QD 2 s (x, x0), where Q D s (x, x0) is the saturation scale for the diffraction processes. The dependence of the saturation scale Qs (x, x0) on both x and x0 is investigated...

Lu = aij(x)Diju for u ∈ C(Ω). Suppose u ∈ C(Ω) is a supersolution in Ω, i.e. Lu ≤ 0. Then if φ ∈ C(Ω) satisfies Lφ > 0, we get L(u− φ) < 0 in Ω, hence by the maximum principle, u− φ does not have interior local minima in Ω. Put differently, if φ ∈ C(Ω) is such that u− φ has a local minimum at x0 ∈ Ω, then necessarily Lφ(x0) ≤ 0. Geometrically, u− φ having a local minimum at x0 means that the gr...

We develop a method to compute synthetic kilonova light curves that combines numerical relativity simulations of neutron star mergers and the $\texttt{SNEC}$ radiation-hydrodynamics code. describe our implementation initial boundary conditions, r-process heating, opacities for simulations. validate approach by carefully checking energy conservation is satisfied comparing results with those two ...

Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, a proper condition which makes Newton’s method converge, and an exact estimate for the radius of the ball of the inverse function theorem are given in a Banach space. Also, the relevant results on premises of Kantorovich and Smale types are improved in this paper. We continue to discuss the problem of conv...

We observe the differential equation dG(z) / dz = (x0 z + x1 (1- z))G(z) in space of power series noncommutative indeterminates x0, , where coefficients G(z) are holomorphic functions on simply connected domain ℂ \ [(-∞,0)∪(1,+∞)].Researches this some conditions turn out different solutions which admit Drinfel'd associator as a bridge. In paper, we review representations these by generating spe...

and Applied Analysis 3 Besides, if for any x, y ∈ M, there exists z ∈ M which is comparable to x and y, 2.4 then f has a unique fixed point. Proof. We first show that f has a fixed point. Since x0 f x0 and f is an increasing function, we obtain by induction that x0 f x0 f2 x0 f3 x0 · · · f x0 · · · . 2.5 Put xn 1 f x0 , n 1, 2, . . . For each integer n ≥ 1, from 2.5 , we have xn xn 1, then by 2...