Firstly, the second term v of (4) in [1] is zero-mean complex Gaussian with v∼N c (0, σ 2 v I NM), where σ v = (1/ √ L)σ w. Also, the σ 2 w in (8) should be changed to σ 2 v. Secondly, if we have Q-independent pulses, the Fisher information matrix in (9) should be [2] J(ξ) = Qtr R −1 η (ξ) ∂R η (ξ) ∂ξ R −1 η (ξ) ∂R η (ξ) ∂ξ. (1) The corresponding formulas of CRB in the appendix should be revise...

Proof of Proposition 1. With a slight abuse of notation, let us denote by D d the set of multivariate stochastic processes such that the aggregate demand equals d. Accordingly, Problem (5) can be decomposed as follows: ρ(y) = max d∈P max D∈D d max z∈F R(z, D) − R(y, D) = max d∈P max z∈F max D∈D d R(z, D) + max D∈D d −R(y, D). Let ξ j be the realized sales under a booking policy z when the deman...

Let X be a nonsingular algebraic curve of genus g ≥ 3, and M ξ the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d coprime and d > n(2g − 2). We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. Let W ξ (L) denote the vector bundle over M ξ defined as the direct image π * (U ξ ⊗ p * 1 L) where U ξ is a universal vector bu...

The two heavy quarks in a baryon which contains two heavy quarks and a light one, can constitute a scalar or axial vector diquark. We study electromagnetic radiations of such baryons, (i) Ξ(bc)1 → Ξ(bc)0 + γ, (ii) Ξ∗(bc)1 → Ξ(bc)0 + γ, (iii) Ξ ∗∗ (bc)0 (1/2, l = 1) → Ξ(bc)0 + γ, (iv) Ξ∗∗ (bc)0(3/2, l = 1) → Ξ(bc)0 + γ and (v) Ξ ∗∗ (bc)0 (3/2, l = 2) → Ξ(bc)0 + γ, where Ξ(bc)0(1) ,Ξ ∗ (bc)1 are ...

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...

We aim at clarifying the relationship between laws of large numbers for fuzzy sets or possibility distributions and laws of large numbers for fuzzy or possi-bilistic variables. We contend that these two frameworks are different and present the relationships between them that explain why this fact was unrecognized so far. A classical result in Probability Theory is the law of large numbers. If ξ...

A comparison problem for volumes of convex bodies asks whether inequalities fK(ξ) ≤ fL(ξ) for all ξ ∈ S imply that Voln(K) ≤ Voln(L), where K,L are convex bodies in R, and fK is a certain geometric characteristic of K. By linear stability in comparison problems we mean that there exists a constant c such that for every ε > 0, the inequalities fK(ξ) ≤ fL(ξ) + ε for all ξ ∈ S imply that (Voln(K))...

We consider the nonlinear Sturm-Liouville problem −(p(x)u′(x))′ + q(x)u(x) = f(x, u(x), u′(x)), in (0, π), (1) c00u(0) + c01u ′(0) = 0, c10u(π) + c11u ′(π) = 0, (2) where p ∈ C1[0, π], q ∈ C0[0, π], with p(x) > 0, x ∈ [0, π], and ci0 + ci1 > 0, i = 0, 1. We suppose that f : [0, π] × R2 → R is continuous and there exist increasing functions ζl, ζu : [0,∞) → R, and a constant B, such that limt→∞ ...

R. Rimányi defined the incidence class of two singularities η and ξ as [η]|ξ, the restriction of the Thom polynomial of η to ξ. He conjectured that (under mild conditions) [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η. Generalizing this notion we define the incidence class of two orbits η and ξ of a representation. We give a sufficient condition (positivity) for ξ to have the property that [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η for any ot...

We report measurements of Ξ and Ξ + hyperon absolute yields as a function of rapidity in 158 GeV/c Pb+Pb collisions. At midrapidity, dN dy = 2.29± 0.12 for Ξ, and 0.52 ± 0.05 for Ξ+, leading to the ratio of Ξ+/Ξ−=0.23±0.03. Inverse slope parameters fitted to the measured transverse mass spectra are of the order of T ≈ 300 MeV near mid-rapidity. The estimated total yield of Ξ particles in Pb+Pb ...