Synthesis and temperature dependence of physical properties of four pyridinium-based ionic liquids: Influence of the size of the cation

In this paper, the ionic liquids 1,2-diethylpyridinium ethylsulfate, EEpyESO₄; 1-methylpyridinium methylsulfate, MpyMSO₄; 1,3-dimethylpyridinium methylsulfate, MMpyMSO₄; and 2-ethyl-1-methylpyridinium methylsulfate, EMpyMSO₄; were synthesized in our laboratory, and their experimental densities, speeds of sound, dynamic viscosities, and refractive indices were studied as a function of temperature at atmospheric pressure. Thermal expansion coefficient, molar volume, and molar refraction of these ionic liquids were calculated from the experimental density and refractive index values.     

Ueber Sparte?n

Ohne Zusammenfassung     

Application de la chélatométrie au dosage des esters et chlorures de mono-esters oxaliques

Esters and chlorides of oxalic mono-esters can be estimated volumetrically. After saponification precipitation is carried out by means of a calcium chloride solution, the excess of which is measured by chelatometry.     

Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known U_q(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2)) U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the U_q(sl(2)) previously discussed is disentangled. Received: 25 April 1996/Accepted: 20 July 1996     

Influence of Molar Mass and Concentration on the Thermogelation of Methylcelluloses

In this study, thermogelation of methylcelluloses is investigated in relation to the molar mass and concentration in aqueous medium. A large hysteresis between heating and cooling ramps was observed whatever the conditions. The heating process in particular was studied to analyze the two steps of gelation using rheometry. At low temperature, in the sol state, viscosity depends on the concentration and molar mass. Over 30°C a gel-like behavior was observed including two steps (the second step is a strong gel with phase separation) having storage moduli that are nearly independent of polymer molar mass but are directly related to polymer concentration.     

Multiplicity theorems for superlinear elliptic problems

In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions. This paper was completed while the first author was visiting the University of Aveiro as an Invited Scientist. The hospitality and financial support of the host institution are gratefully acknowledged. The second and third authors acknowledge the partial financial support of the Portuguese Foundation for Science and Technology (FCT) under the research project POCI/MAT/55524/2004.