The GSI oscillation mystery

In this talk, a short discussion of the GSI anomaly is given. We discuss the physics involved using a comparison with pion decay, and explain why the observed oscillations cannot be caused by standard neutrino mixing.     

On the enumeration of chains in regular chain-groups

Let N be a regular chain-group on E (see W. T. Tutte, Canad. J. Math.8 (1956), 13–28); for instance, N may be the group of integer flows or tensions of a directed graph with edge-set E). It is known that the number of proper Z_λ-chains of N (λ ∈ Z, λ ≥ 2) is given by a polynomial in λ, P(N, λ) (when N is the chain-group of integer tensions of the connected graph G, λP(N, λ) is the usual chromatic polynomial of G). We prove the formula: P(N, λ) = Σ_{[E′]∈O(N)⁺/～}Q(R_[E′](N), λ), where O(N)⁺ is the set of orientations of N with a proper positive chain, ～ is a simple equivalence relation on O(N)⁺ (sequence of reversals of positive primitive chains), and Q(R_[E′](N), λ) is the number of chains with values in [1, λ ? 1] in any reorientation of N associated to an element of [E′]. Moreover, each term Q(R_[E′](N), λ) is a polynomial in λ. As applications we obtain: P(N, 0) = (?1)^r(N)∥O(N)⁺/～∥; P(N, ?1) = (?1)^r(N)∥O(N)⁺∥ (a result first proved by Brylawski and Lucas); P(N, λ + 1) ≥ P(N, λ) for λ ≥ 2, λ ∈ Z. Our result can also be considered as a refinement of the following known fact: A regular chain-group N has a proper Z_λ-chain iff it has a proper chain in [?λ + 1, λ ? 1].     

List of subject

We report the high resolution emission (S₁ → S₀, T₁ → S₀) and laser single site singlet excitation (S₁ ← S₀) spectra for the various insertion sites of coronene in n-heptane cooled to 1.5 K. The observation of site splitting of doubly degenerate vibrations and weak electric dipole forbidden 0, 0 bands in the S₁ → S₀ and T₁ → S₀ spectra indicates that the ground state, the first excited singlet and lowest triplet states are all distorted. In these spectra, the intensity distribution of the various sites in the 0, 0 bands suggests that the distortion is different from site to site but similar in S₀, S₁ and T₁. Identical ordering of the sites in S₁ S₀ and S₁ S₀ spectra as well as the observation of weak shifts in the vibrational frequencies in the two states implies the absence of strong pseudo Jahn-Teller forces in the first excited singlet state. We propose, further, that this is also true for the triplet state. This conclusion is supported by the similarity in zero-field splitting parameters of coronene and deuterated coronene. Taken together, these results indicate strongly that the distortion of coronene in n-heptane is primarily crystal field induced and is not greatly changed upon excitation of the molecule to its lowest excited states.     

Structural study of the Diels-Alder reaction between tetrachlorodimethoxycyclopentadiene and the nickelocene-dimethyl acetylenedicarboxylate adduct. Crystal structures of the products

The cyclopentadienylnickel complex (2) and the parent dimethyl norbornadienedicarboxylate (4) each react with 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadiene (3) on the less hindred exo-face of the dienophile to produce anti-sequinorbornane adducts 5 and 6. X-ray crystal structures of these adducts have been determined and refined to R values of 0.029 and 0.042 respectively.     

Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.     

Global well-posedness,scattering and blow-up for the energy-critical focusing non-linear wave equation

We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static solution W which gives the best constant in the Sobolev embedding, the following alternative holds. If the initial data has smaller norm in the homogeneous Sobolev space H ¹ than the one of W, then we have global well-posedness and scattering. If the norm is larger than the one of W, then we have break-down in finite time.