On the linear wave regime of the Gross-Pitaevskii equation

We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.     

Solid-state ultraviolet irradiation of some maleimides and bismaleimides

The solid-state photoreactivity of a series of maleimides and bismaleimides is studied Various crystalline maleimides are found to dimerize on irradiation by ultraviolet light Based on this discovery, the photopolymerizability of the related bismaleimides in the crystalline state is examined. As a result it is found that some N,N,-alkylenebismaleimides polymerize into highly crystalline polymers. The polymers do not melt below their decomposition temperature (>300°C) and are practically insoluble in all solvents. The obtained irradiation products are different from the reaction products of the solution-phase photochemistry. Closely related bismaleimides, such as members of a homologous series, show substantial differences in their solid-state photochemical behavior; on excitation they either lead to polymers or are not reactive. This indicates that the solid-state photoreactivity of maleimides and bismaleimides is controlled by the geometry of their crystal structure.     

Medical diagnosis: Fuzzy sets and degrees of belief

A model simulating the medical diagnostic process is presented. Diagnostic groups are considered as fuzzy sets. Partial knowledge is quantified by belief functions. The process is considered as the evaluation by the clinician of his degree of belief concerning the belonging of his patient to a fuzzy set given fuzzy and partial informations.     

Probability of a fuzzy event: An axiomatic approach

Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh. They are based (1) on the postulate that the sum of the conditional probability of a fuzzy event and of its complement given any fuzzy event adds to one or (2) on soft independence for orthogonal sets with independent constitutive elements. A general postulate is also required concerning the complement of a fuzzy set. The classical definition of the operator representing the complement can also be deduced.     

Photocycloaddition polymerization. I. Preparation and characterization of poly-N,N′-polymethylenebisdichloromaleimides

The benzophenone-sensitized solution-phase photocycloaddition polymerization of N,N′-polymethylenebisdichloromaleimides has been investigated. It is shown that a polymer can be obtained by repeated 2π + 2π photocycloaddition process. The intrinsic viscosity of the products varies from 0.1 to 0.6 when the link between the two maleimide moieties contains more than six and simultaneously an uneven number of methylene units. The polymeric materials form transparent, flexible, noninflammable films and decompose at 310°C.     

How Does the Fluorination of the Linker Affect the Structural Chemistry of Trimesate-Based Metal-Organic Frameworks (MOFs)?

FMOFs, i.e. metal-organic frameworks with linkers with fluoro substituents, were supposed to show enhanced thermal and chemical stability as well as high gas affinity and hydrophobicity. However, at least for aromatic carboxylate ligands it was shown in a subsequent work that fluoro substituents weaken the C(phenyl)-COO^– bond and thus facilitate decarboxylation leading to a decreased chemical and thermal stability. Nonetheless, it was concluded that linker fluorination leads to a rich structural chemistry, as the torsion angle between the phenyl ring and the carboxylate group is significantly increased in these compounds. Here, we present the very first examples of four MOFs all based on Sr²⁺ cations and trimesate-based linkers with three different degrees of fluorination as well as the known non-fluorinated counterpart: [Sr(HL)(H₂O)] · n H₂O [ 1 : L = mF-BTC^3–, n = 0.5, P1 , Z = 2; 2 : L = dF-BTC^3–, n = 0.5, C2/c, Z = 8; 3 : L = pF-BTC^3–, n = 1.5, C2/c, Z = 8; 4 : L = BTC^3–, n = 0.5, P1 , Z = 2; BTC^3– ≡ 1,3,5-benzenetricarboxylate (trimesate); mF-BTC^3– ≡ monofluorinated trimesate, dF-BTC^3– ≡ difluorinated trimesate, pF-BTC^3– ≡ per-(tri-)fluorinated trimesate]. Whereas 1 and known 4 are found to crystallize in isotypic structures and 2 in a very similar structural arrangement [all CN(Sr²⁺) = 9], 3 with the highest degree of fluorination exhibits a completely different crystal structure [CN(Sr²⁺) = 8], which is already obvious from the different composition. It is shown that the torsion angles between the phenyl ring and the carboxylate groups play an important structure-directing role. DSC/TGA investigations confirm that with increasing fluorination the thermal stability is decreased. However, the release temperature of water, i.e. the affinity to water, increases with the number of fluoro substituents.     

Molecular Hydrogels from Bolaform Amino Acid Derivatives: A Structure–Properties Study Based on the Thermodynamics of Gel Solubilization

Insight is provided into the aggregation thermodynamics associated to hydrogel formation by molecular gelators derived from L ‐valine and L ‐isoleucine. Solubility data from NMR measurements are used to extract thermodynamic parameters for the aggregation in water. It is concluded that at room temperature and up to 55 °C, these systems form self‐assembled fibrillar networks in water with quite low or zero enthalpic component, whereas the entropy of the aggregation is favorable. These results are explained by considering that the hydrophobic effect is dominant in the self‐assembly. However, studies by NMR and IR spectroscopy reveal that intermolecular hydrogen bonding is also a key issue in the aggregation process of these molecules in water. The low enthalpy values measured for the self‐assembly process are ascribed to the result of a compensation of the favorable intermolecular hydrogen‐bond formation and the unfavorable enthalpy component of the hydrophobic effect. Additionally, it is shown that by using the hydrophobic character as a design parameter, enthalpy‐controlled hydrogel formation, as opposed to entropy‐controlled hydrogel formation, can be achieved in water if the gelator is polar enough. It is noteworthy that these two types of hydrogels, enthalpy‐versus entropy‐driven hydrogels, present quite different response to temperature changes in properties such as the minimum gelator concentration (mgc) or the rheological moduli. Finally, the presence of a polymorphic transition in a hydrogel upon heating above 70 °C is reported and ascribed to the weakening of the hydrophobic effect upon heating. The new soft polymorphic materials present dramatically different solubility and rheological properties. Altogether these results are aimed to contribute to the rational design of molecular hydrogelators, which could be used for the tailored preparation of this type of soft materials. The reported results could also provide ground for the rationale of different self‐assembly processes in aqueous media.