Self-focusing in new kerr media: Large thermal nonlinearity in metallotetraphenylporphins

A large optical nonlinearity of thermal origin has been observed in acetone solutions of a series of tetraphenylporphin, TPPH₂, MnTPP(CH₃CO₂ ^–), FeTTPCI^-, CoTPP, NiTPP, and CuTPP. The nonlinear Kerr coefficient is sensitively dependent on the nature of central metals in the compounds. The Mn compound exhibits the largest coefficient, 6 × 10^–5 esu, for 514 nm laser wavelength. The use of prophins offers increased flexibility in the preparation of different Kerr media.Presented at the International Workshop on Squeezed and Correlated States in Quantum Optics, Moscow, December 3–7, 1990.     

Improved Surface and Adhesion Properties of Wood-Polyethylene Composite by Treatment with Argon–Oxygen Low Pressure Plasma

Ar:O₂ low pressure plasma (Ar:O₂ LPP) surface treatment is proposed for increasing the surface energy and improve the adhesion of wood-polyethylene composite. The treatment time was varied between 20 and 90 s and the configuration of the shelves inside the plasma chamber (direct and secondary downstream) was also changed. Ar:O₂ LPP treatment during 30–40 s created new surface carbon–oxygen groups, increased the surface energy, mainly its polar component, reduced roughness and caused ablation of wood-polyethylene composite, irrespective of the configuration of the shelves inside the plasma chamber. The increase of the treatment time above 40 s did not cause additional surface modifications. Adhesion of the wood-polyethylene composite was noticeably increased when was treated with Ar:O₂ LPP. The surface modifications of Ar:O₂ LPP treated wood-polyethylene composite were partially lost during 24 h after treatment.     

Synthesis of Densely Packaged,Ultrasmall Pt02 Clusters within a Thioether‐Functionalized MOF: Catalytic Activity in Industrial Reactions at Low Temperature

The gram‐scale synthesis, stabilization, and characterization of well‐defined ultrasmall subnanometric catalytic clusters on solids is a challenge. The chemical synthesis and X‐ray snapshots of Pt⁰₂ clusters, homogenously distributed and densely packaged within the channels of a metal–organic framework, is presented. This hybrid material catalyzes efficiently, and even more importantly from an economic and environmental viewpoint, at low temperature (25 to 140 °C), energetically costly industrial reactions in the gas phase such as HCN production, CO₂ methanation, and alkene hydrogenations. These results open the way for the design of precisely defined catalytically active ultrasmall metal clusters in solids for technically easier, cheaper, and dramatically less‐dangerous industrial reactions.     

Valorization of food waste based on its composition through the concept of biorefinery

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Prime ideals in polynomial rings in several indeterminates

If is a prime ideal of a polynomial ring , where is a field, then is determined by an irreducible polynomial in . The purpose of this paper is to show that any prime ideal of a polynomial ring in -indeterminates over a not necessarily commutative ring is determined by its intersection with plus polynomials.

     

Hausdorff measures and dimension on

We consider the Hausdorff measures , , defined on with the topology induced by the metric

for all . We study its properties, their relation to the ``Lebesgue measure" defined on by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some examples.

     

Some Properties of the Bel and Bel-Robinson Tensors

The properties of the Bel and Bel-Robinson tensors seem to indicate that they are closely related to the gravitational energy-momentum. We present some new properties of these tensors which might throw some light onto this relationship. First, for any spacetime we find a decomposition of the Bel tensor in terms of the Bel-Robinson tensor and two other tensors, which we call the pure matter super-energy tensor and the matter-gravity coupling super-energy tensor. We show that the pure matter super-energy tensor of any Einstein-Maxwell field is simply the square of the usual energy-momentum tensor. This, together with the fact that the Bel-Robinson tensor has dimensions of energy density square, leads us to the definition of square root for the Bel-Robinson tensor: a two-covariant symmetric traceless tensor with dimensions of energy density and such that its square gives the Bel-Robinson tensor. We prove that this square root exists if and only if the spacetime is of Petrov type O, N or D, and its general expression is explicitly presented. The properties of this new tensor are examined and some interesting explicit examples are analyzed. Of particular interest are an invariant function that appears in the spherically symmetric metrics and an expression for the energy carried out by pure plane gravitational waves. We also examine the decomposition of the whole Bel tensor for Vaidya's radiating metric and Kerr-Newman's solution. Finally, we generalize the definition of square root to a factorization of the Bel-Robinson tensor and get the general solution for all Petrov types.