In his Comment [1] to my paper [2] Rutenberg notes that " the basis of my analysis of conserved scalar phase-ordering dynamics, to apply only the global conservation constraint dxψ = N, (1) is incorrect ". Because " for physical conserved systems, which evolve by mass transport, the stronger local conservation law embodied by continuity equation " ∂ψ/∂t = −∇j. (2) This question needs clarificat...

ion An abstraction (V , ψ,F) is given by: • V : a finite set of observables, • ψ: a mapping from V → R into V ] → R, • F: a C∞ mapping from V ] → R into V ] → R; such that: • ψ is linear with positive coefficients, and for any sequence (xn) ∈ (V → R+)N such that (||xn||) diverges towards +∞, then (||ψ(xn)||) diverges as well (for arbitrary norms || · || and || · ||), • the following diagram com...

Theorem 2: Let H be as in Theorem 1 of Ref. [2]. Then H is pseudo-Hermitian if and only if it is Hermitian with respect to an inner product 〈〈 , 〉〉 that supports a positivesemidefinite basis [3] including the eigenvectors of H . In particular, for every eigenvector ψ of H , 〈〈ψ|ψ〉〉 ≥ 0; if the corresponding eigenvalue is real and nondefective (algebraic and geometric multiplicities are equal), ...

Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions ψ : G → Ud such that Pr[ψ(xy) = ψ(x) ψ(y)] is large, or more generally Ex,y ‖ψ(xy)− ψ(x) ψ(y)‖22 is small, where x, y are uniformly random elements ...

The ψ = ψ(3770) resonance is expected to be mainly cc̄(1D1), but tensor forces and coupling to charmed particle pairs can mix it with ψ(2S1) and other states. Implications of this mixing for decays of ψ to non-charmed final states are discussed. (i) The ratio Γ(ψ → γ + χc2)/Γ(ψ′′ → γ + χc0) is expected to be highly suppressed if ψ is a pure D-wave state, and is enchanced by mixing. (ii) The expe...

First observations of the Bs → ψ(2S)η, B0 → ψ(2S)π+π− and Bs → ψ(2S)π+π− decays are made using a dataset corresponding to an integrated luminosity of 1.0 fb−1 collected by the LHCb experiment in proton–proton collisions at a centre-of-mass energy of √ s = 7 TeV. The ratios of the branching fractions of each of the ψ(2S) modes with respect to the corresponding J/ψ decays are B(Bs →ψ(2S)η) B(Bs →...

We review the current status of heavy quarkonium production phenomenology based on nonrelativistic effective field theories, focusing spintriplet S -wave states such as J/ψ, ψ (2 ), and ϒ. present some representative examples for mechanisms proposed in literature, which vary significantly depending choice data employed analyses. then discuss rôle polarization discriminating between different po...

THEOREM A. Let (X, τ) be a Hausdorff topological space and Ψ : X →]−∞,+∞], Φ : X → R two functions. Assume that there is r > infX Ψ such that the set Ψ (]−∞, r]) is compact and first-countable. Moreover, suppose that the function Φ is bounded below in Ψ(]−∞, r]) and that the function Ψ+ λΦ is sequentially lower semicontinuous for each λ ≥ 0 small enough. Finally, assume that the set of all glob...

Given a single copy of a quantum state |ψ〉, the no cloning theorem greatly limits the amount of information which can be extracted from it. On the other hand, given only a procedure which verifies the state, for example access to a measurementM = {I−|ψ〉〈ψ|, |ψ〉〈ψ|}, even distinguishing I−|ψ〉〈ψ| from the identity takes exponential time. In this paper, we consider the scenario in which we are giv...