The cross section for ultra-high energy neutrino-nucleon scattering is very sensitive to the parton distributions at very small values of Bjorken x (x ≤ 10−4). We numerically investigate the effects of modifying the behavior of the gluon distribution function at very small x in the DGLAP evolution equation. We then use the Color Glass Condensate formalism to calculate the neutrino-nucleon cross...

where the inf is taken over all admissible sequences. We also let dX(T ) denote the diameter of T with respect to norm ‖·‖X . For the remainder of this section we make the definitions πrx = argminy∈Tr‖y − x‖X and ∆rx = πrx− πr−1x. Throughout this section we let ‖ · ‖ denote the `2→2 operator norm in the case of matrix arguments, and the `2 norm in the case of vector arguments. Krahmer, Mendelso...

As a continuation of [7], we introduce the notions of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras and study some related properties. In the section 3, we investigate the compactness in a TBCI-algebra X and quotient TBCI-algebra X=I where I is a topological ideal of X. In the section 4, we introduce the notion of topological homomorphisms...

the s-kinetic energy of the system, their proof strategy consists in showing that (1) the quadratic kinetic energy K2 is finite, (2) the influence graph is eventually constant, and (3) the 1-kinetic energy K1 is finite, which immediately implies the convergence of the sequence of position vectors (x(t))t∈N. To show the finiteness of K2, we present a simple proof in Section 2 which is based on a...

Let n, x be positive integers satisfying 1 < x < n. Let Hn,x be a group admitting a presentation of the form 〈a, b | a = b = (ba) = 1〉. When x = 2 the group Hn,x is the familiar dihedral group, D2n. Groups of the form Hn,x will be referred to as generalized dihedral groups. It is possible to associate a cubic Cayley graph to each such group, and we consider the problem of finding the isoperimet...

This paper continues the work [6]. For a Polish group G the notions of G-continuous functions and whirly actions are further exploited to show that: (i) A G-action is whirly iff it admits no nontrivial spatial factors. (ii) Every action of a Polish Lévy group is whirly. (iii) There exists a Polish monothetic group which is not Lévy but admits a whirly action. (iv) In the Polish group Aut (X,X, ...

According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve Γ, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of Γ. It is proven that, for a generic X , the Abel-Jacobi map of the family of elliptic sextics...

BaFe12-xCrxO19 (x = 0.0, 0.1, 0.2, 0.3, and 0.4) ferrite ceramics were prepared by a sol-gel method using spruce sapwoods as the templates. The prepared materials were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), and a magnetic property measurement system (MPMS). The prepared materials maintained a multilayer wall structure of spruce sapwoods. All samples presen...