Let φ(x1, . . . , xh, y) = u1x1 + · · · + uhxh + vy be a linear form with nonzero integer coefficients u1, . . . , uh, v. Let A = (A1, . . . , Ah) be an h-tuple of finite sets of integers and let B be an infinite set of integers. Define the representation function associated to the form φ and the sets A and B as follows: R (φ) A,B (n) = card ({(a1, . . . , ah, b) ∈ A1 × · · · × Ah × B : φ(a1, ....

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...

Retroviruses specifically package full-length, dimeric genomic RNA (gRNA) even in the presence of a vast excess of cellular RNA. The "psi" (Ψ) element within the 5'-untranslated region (5'UTR) of gRNA is critical for packaging through interaction with the nucleocapsid (NC) domain of Gag. However, in vitro Gag binding affinity for Ψ versus non-Ψ RNAs is not significantly different. Previous salt...

Results are reported based on samples of 58 million J/ψ and 14 million ψ(2S) decays obtained by the BESII experiment. Improved branching fraction measurements are determined, including branching fractions for J/ψ → πππ, ψ(2S) → πJ/ψ, ηJ/ψ, ππJ/ψ, anything J/ψ, and ψ(2S) → γχc1, γχc2 → γγJ/ψ. The decay J/ψ → ωππ is studied. At low ππ mass, a large, broad peak due to the σ is observed, and its po...

In this article, we propose two algorithms for determining the Nielsen-Thurston classification of a mapping class ψ on a surface S. We start with a finite generating set X for the mapping class group and a word ψ in 〈X〉. We show that if ψ represents a reducible mapping class in Mod(S) then ψ admits a canonical reduction system whose total length is exponential in the word length of ψ. We use th...

In this paper we characterize those accessible V-categories that have limits of a specified class. We do by introducing the notion companion C for class weights Ψ, as collection special types colimit diagrams are compatible with Ψ. then Ψ-limits accessibly embedded and C-virtually reflective in presheaf V-category, C-models sketches. This allows us to recover standard theorems locally presentab...

These notes are written as a supplement to [1, Sect. 16.1&16.3], but can be read independently. 1 Demystifying Induction Consider a loop of the form while B do C od, and assume that we know 1 ψ is established by the preamble of the loop (1) if with B true, ψ holds prior to C, then ψ also holds after C (2) Then we can infer that ψ is an invariant of the loop. (3) That is, each time control reach...

e + e − experiments producing charmonium are reviewed. It is found that the contribution of the continuum amplitude via virtual photon was neglected in almost all the experiments and the channels analyzed. It is shown that the contribution of the continuum part may affect the final results significantly in ψ(2S) and ψ(3770) decays, while the interference between continuum and resonance amplitud...

e + e − experiments producing charmonium are reviewed. It is found that the contribution of the continuum amplitude via virtual photon was neglected in almost all the experiments and the channels analyzed. It is shown that the contribution of the continuum part may affect the final results significantly in ψ(2S) and ψ(3770) decays, while the interference between continuum and resonance amplitud...

We prove that the Bohmian arrival time of the 1D Schrödinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet Ψ, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time tK ij (Ψ). We derive the inequality tB ...