Inclusive strange particle production in π+p interactions at 16 GeV/c

The production of $\text{K}{}_{\mathrm{S}}{}^0\text{, Λ}\text{and}\text{Λ}$ is measured in π⁺p reactions at 16 GeV/c. The total strange particle cross section is found to be 4.0 ± 0.3 mb, about 20% of the inelastic cross section. Cross sections for single strange particles and for strange particle pairs are determined, both inclusively and as functions of the charged multiplicity. Relative production rates for different strange particle combinations are compared with the prediction of the isospin statistical model. Inclusive spectra for single particles are studied and it is found the K_S⁰ are produced mostly in the forward hemisphere, most probably by fragmentation of the incident pion into $\text{K}\text{K}\text{π}$. The Λ are mostly backwards, probably deriving from fragmentation of the proton into ΛK pairs. The $\text{Λ}$ tend to be produced forwards, but evidence is found for central $\text{Λ}\text{Λ}$ production. Distributions in rapidity of the Λ particles from π⁺p interactions are compared in terms of the factorisation hypothesis. Results are given on the Λ transversal polarisation.     

A chemical method for the convenient surface functionalisation of polymers

A method for the application of carbenes as reactive intermediates for surface modification of polymeric substrates has been developed; the efficacy of the process has been demonstrated by irreversible dyeing of polystyrene, polythene, nylon, silica, and controlled pore glass, and to a limited extent, polytetrafluoroethylene.     

A spectral approach for the exact observability of infinite-dimensional systems with skew-adjoint generator

Let A be a possibly unbounded skew-adjoint operator on the Hilbert space X with compact resolvent. Let C be a bounded operator from D(A) to another Hilbert space Y. We consider the system governed by the state equation with the output y(t)=Cz(t). We characterize the exact observability of this system only in terms of C and of the spectral elements of the operator A. The starting point in the proof of this result is a Hautus-type test, recently obtained in Burq and Zworski (J. Amer. Soc. 17 (2004) 443-471) and Miller (J. Funct. Anal. 218 (2) (2005) 425-444). We then apply this result to various systems governed by partial differential equations with observation on the boundary of the domain. The Schrödinger equation, the Bernoulli-Euler plate equation and the wave equation in a square are considered. For the plate and Schrödinger equations, the main novelty brought in by our results is that we prove the exact boundary observability for an arbitrarily small observed part of the boundary. This is done by combining our spectral observability test to a theorem of Beurling on nonharmonic Fourier series and to a new number theoretic result on shifted squares.     

Orientation de la réaction d'alkylation des pyrazoles dans des conditions neutres et en catalyse par transfert de phase

The n-butylation and N-benzylation of nine pyrazoles bearing different substituents in positions 3 and 5 have been studied in neutral and basic medium (phase transfert catalysis). The orientation of the reaction depends strongly on the method used when the position 3 (or 5) of the starting pyrazole bears a substituent with a lone pair in ortho position (pyrazolyl or pyridyl). The different products have been identified by proton nmr.     

Spontaneous formation of vesicles of diblock copolymer EO6BO11 in water: a SANS study

Small angle neutron scattering (SANS) is used to study the structures formed in water by a diblock copolymer EO6BO11 (having 6 ethylene oxide, EO, and 11 butylene oxide, BO, units). The data show that polymer solutions over a broad concentration range (0.05-20 wt %) contain vesicular structures at room temperature. Interestingly, these vesicles could be formed without any external energy input, such as extrusion, which is commonly required for the formation of other block copolymer or lipid vesicles. The EO6BO11 vesicles are predominantly unilamellar at low polymer concentrations, whereas at higher polymer concentrations or temperatures there is a coexisting population of unilamellar and multilamellar vesicles. At a critical concentration and temperature, the vesicular structures fuse into lyotropic arrays of planar lamellar sheets. The findings from this study are in broad agreement with the work of Harris et al. (Langmuir, 2002, 18, 5337), who used electron microscopy to identify the vesicle phase in the same system.     

Comparison of graphs associated to a commutative Artinian ring

Let R be a commutative ring with \(1\ne 0\) and the additive group \(R^+\). Several graphs on R have been introduced by many authors, among zero-divisor graph \(\Gamma _1(R)\), co-maximal graph \(\Gamma _2(R)\), annihilator graph AG(R), total graph \( T(\Gamma (R))\), cozero-divisors graph \(\Gamma _\mathrm{c}(R)\), equivalence classes graph \(\Gamma _\mathrm{E}(R)\) and the Cayley graph \(\mathrm{Cay}(R^+ ,Z^*(R))\). Shekarriz et al. (J. Commun. Algebra, 40 (2012) 2798–2807) gave some conditions under which total graph is isomorphic to \(\mathrm{Cay}(R^+ ,Z^*(R))\). Badawi (J. Commun. Algebra, 42 (2014) 108–121) showed that when R is a reduced ring, the annihilator graph is identical to the zero-divisor graph if and only if R has exactly two minimal prime ideals. The purpose of this paper is comparison of graphs associated to a commutative Artinian ring. Among the results, we prove that for a commutative finite ring R with \(|\mathrm{Max}(R)|=n \ge 3\), \( \Gamma _1(R) \simeq \Gamma _2(R)\) if and only if \(R\simeq \mathbb {Z}^n_2\); if and only if \(\Gamma _1(R) \simeq \Gamma _\mathrm{E}(R)\). Also the annihilator graph is identical to the cozero-divisor graph if and only if R is a Frobenius ring.     

Cyclicity in the Dirichlet space

Let be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We give a new sufficient condition, not far from the known necessary condition, for a function f∈ to be cyclic, i.e. for {pf: p is a polynomial} to be dense in . The proof is based on the notion of Bergman–Smirnov exceptional set introduced by Hedenmalm and Shields. Our methods yield the first known examples of such sets that are uncountable. One of the principal ingredients of the proof is a new converse to the strong-type inequality for capacity.