Wave propagation in layered model due to point-source loading in low-impedance medium

Dynamic photoelastic and moiré techniques were used to study the incident, reflected and refracted waves in a layered model. The model, consisting of two birefringent layers with an impedance ratio of approximately 2∶1, was subjected to point-source explosive loading in the low-impedance medium. The isochromatic and moiré-fringe patterns were photographed with a Cranz-Schardin multiplespark camera operating at a rate of 200,000 frames per second. Propagation and attenuation characteristics of waves in both layers were studied. The formation of head-waves at the interface was clearly evident. Stress determinations were made in some instances using photoelastic and moiré data.     

Elude de la réaction du β-aminocrotonitrile et du α-formyl phénylacétonitrile avec l'hydrazine: Synthèse d'amino-7 pyrazolo[1,5-a]pyrimidines

The three compounds C₈ H₁₀N₄ which arise from reaction of hydrazine and β-aminocrotonitrile have been identified: the formation of anazine, a 3(5)-amino 5(3)-methyl pyrazole derivative and a 7-amino pyrazolo [1,5-a] pyrimidine has been demonstrated. The relationships among these compounds and with the methyl-aminopyrazole have been studied.     

Finiteness property of pairs of 2×2 sign-matrices via real extremal polytope norms

This paper deals with the joint spectral radius of a finite set of matrices. We say that a set of matrices has the finiteness property if the maximal rate of growth, in the multiplicative semigroup it generates, is given by the powers of a finite product.Here we address the problem of establishing the finiteness property of pairs of $2\times 2$ sign-matrices. Such problem is related to the conjecture that pairs of sign-matrices fulfil the finiteness property for any dimension. This would imply, by a recent result by Blondel and Jungers, that finite sets of rational matrices fulfil the finiteness property, which would be very important in terms of the computation of the joint spectral radius. The technique used in this paper could suggest an extension of the analysis to $n\times n$ sign-matrices, which still remains an open problem.As a main tool of our proof we make use of a procedure to find a so-called real extremal polytope norm for the set. In particular, we present an algorithm which, under some suitable assumptions, is able to check if a certain product in the multiplicative semigroup is spectrum maximizing.For pairs of sign-matrices we develop the computations exactly and hence are able to prove analytically the finiteness property. On the other hand, the algorithm can be used in a floating point arithmetic and provide a general tool for approximating the joint spectral radius of a set of matrices.     

A new semifield of order 2

In [G. Lunardon, Semifields and linear sets of PG(1,q^t), Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order q²ⁿ,n>1 and n odd, with left nucleus F_qⁿ, middle and right nuclei both F_q² and center F_q. When n=3 this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1-34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87-104]. For n>3, no example of a semifield belonging to this family is known.In this paper we first prove that, when n>3, any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 2¹⁰ belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield.     

Shear banding in biphasic liquid-liquid systems

In this Letter, we present the first systematic report of shear-induced banding in microconfined biphasic liquid-liquid systems, i.e., formation of alternating regions of high and low volume fraction of dispersed-phase droplets in a parallel plate flow cell. Such a flow-driven, gap-dependent phenomenon is only observed at low values of the viscosity ratio between the dispersed and the continuous phase, and in a given range of the applied shear rate. Based on rheological measurements, band formation is found to be associated with a viscosity decrease as compared to the homogeneous, structureless case, thus showing that system microstructure is somehow evolving towards reduced viscous dissipation under shear flow.     

Violation of the Cauchy-Schwarz inequality in the macroscopic regime

We have observed a violation of the Cauchy-Schwarz inequality in the macroscopic regime by more than 8 standard deviations. The violation has been obtained while filtering out only the low-frequency noise of the quantum-correlated beams that results from the technical noise of the laser used to generate them. We use bright intensity-difference squeezed beams produced by four-wave mixing as the source of the correlated fields. We also demonstrate that squeezing does not necessarily imply a violation of the Cauchy-Schwarz inequality.