We wish to describe the motion of a rarefied gas, consisting of a very large number of identical particles, moving in a three-dimensional space. For (t, x, ξ) ∈ [0,∞[×IR3 × IR, we consider a function f(t, x, ξ) describing the density of particles at time t, at the point x, having speed ξ. In alternative, we may also think of f(t, x, ξ) as the probability of finding a particle with speed ξ near ...

Given a closed subspace S of a Hilbert space H and a bounded linear operator A ∈ L(H) which is positive, consider the set of all A-selfadjoint projections onto S P(A,S) = {Q ∈ L(H) : Q2 = Q , Q(H) = S , AQ = Q∗A}. In addition, if H1 is another Hilbert space, T : H → H1 is a bounded linear operator such that T ∗T = A and ξ ∈ H, consider the set of (T,S) spline interpolants to ξ: sp (T,S, ξ) = {η...

Stability-based methods for scenario generation in stochastic programming are reviewed. In particular, we briefly discuss Monte Carlo sampling, Quasi-Monte Carlo methods, quadrature rules based on sparse grids and optimal quantization. In addition, we provide some convergence results based on recent developments in multivariate integration. The method of optimal scenario reduction and technique...

In this note we prove a relation between the Riemann Zeta function, ζ and the ξ function (Krein spectral shift) associated with the Harmonic Oscillator in one dimension. This gives a new integral representation of the zeta function and also a reformulation of the Riemann hypothesis as a question in L1(R). ∗Part of talk presented at the Conference on Harmonic Analysis, 13-15 March 1997, Ramanuja...

Global polarization of Ξ and Ω hyperons has been measured for the first time in Au+Au collisions at sNN=200 GeV. The measurements Ξ− Ξ¯+ hyperon have performed by two independent methods, via analysis angular distribution daughter particles parity violating weak decay Ξ→Λ+π, as well measuring Λ hyperon, polarized transfer from its parent. polarization, obtained combining results methods average...

The probability distribution of random walks on linear structures generated by random walks in d-dimensional space, Pd(r, t), is analytically studied for the case ξ ≡ r/t1/4 ≪ 1. It is shown to obey the scaling form Pd(r, t) = ρ(r)tξfd(ξ), where ρ(r) ∼ r 2−d is the density of the chain. Expanding fd(ξ) in powers of ξ, we find that there exists an infinite hierarchy of critical dimensions, dc = ...

Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...

The Born cross sections and effective form factors for process e+e−→Ξ−Ξ¯+ are measured at eight center-of-mass energies between 2.644 3.080 GeV, using a total integrated luminosity of 363.9 pb−1 e+e− collision data collected with the BESIII detector BEPCII. After performing fit to section e+e−→Ξ−Ξ¯+, no significant threshold effect is observed.Received 19 October 2020Accepted 11 December 2020DO...