Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1], the distortion Cψ : [0, 1] → [0, 1], Cψ(x, y) = ψ(C(ψ−1(x)), ψ−1(y)), is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ which ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in...

Electromagnetic production of J/ψ at ee colliders is investigated. It is expected to be as a further test of charmonium production of QED nature. We find that at the energies of CESR, BEPC, and TRISTAN (e.g. 4.0GeV ≤ √s ≤ 60GeV ), the contributions of the concerned electromagnetic processes to the J/ψ inclusive production are great, even dominant, thus they greatly effect the observation on the...

We argue that the critical behaviour near the point of " gradient catastrophe " of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation ii Ψ t + 2 2 Ψ xx + |Ψ| 2 Ψ = 0, 1, with analytic initial data of the form Ψ(x, 0;) = A(x) e i S(x) is approximately described by a particular solution to the Painlevé-I equation .

It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors. In [?], Darwiche and Pearl propose postulates for iterated revisions, noted (R*1) to (R*6) and (C1) to (C4). In particular, the postulate (C3) reads: (C3) If Ψ • α |= µ, then (Ψ • µ) • α |= µ. It will be shown that, in the presence (R*1) to (R*6), (C1) and (C3) imply: (* *) If Ψ • α |= µ,...

Ex. 17 Let us call the new system L, i.e. its axioms are all propositional tautologies (Axiom 1) plus the axioms 2> (Axiom 2) and 2φ∧2ψ → 2(φ∧ψ) (Axiom 3), and the rules modus ponens and φ→ ψ 2φ→ 2ψ We have to show that for all formulas φ `K φ ⇔ `L φ. ⇒: For this direction we have to show that L derives all axioms of K and all its rules. Axiom 1 of K is the same as Axiom 1 in L, thus we have no...

We suggest the ratio of the ψ′′(3770)/ψ′(3686) production cross sections as an unambiguous probe of the dominance of hard, pointlike physics in charmonium production. If hard physics dominates the charmonium production the ratio : σ(ψ ) σ(ψ) ≈ Γ(ψ→ll) Γ(ψ′→l+l−) ≈ 0.1 is independent of the process. We argue that since the dominant DD̄ decay mode of the ψ′′-meson can be detected with a high effic...