Solution of fuzzy equations with extended operations

Assuming that 1 is any operation defined on a product set X × Y and taking values on a set Z, it can be extended to fuzzy sets by means of Zadeh's extension principle. Given a fuzzy subset C of Z, it is here shown how to solve the equation $\text{A 1 B = C}$ (or $\text{A 1 B ? C}$) when a fuzzy subset A of X (or a fuzzy subset B of Y) is given. The methodology we provide includes, as a special case, the resolution of fuzzy arithmetical operations, i.e. when 1 stands for +, ?, × or ÷, extended to fuzzy numbers (fuzzy subsets of the real line). The paper is illustrated with several examples in fuzzy arithmetic.     

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork that are such that the meshwork's energy is a function F(el)[A(xi)] not of the real microscopic membrane area A, but of a smoothed membrane's area A(xi), which corresponds to the area of the membrane coarse grained at the mesh size xi. We show that the meshwork modifies the membrane tension sigma both below and above the scale xi, inducing a steep crossover of amplitude deltasigma=dF(el)/dA(xi). The predictions of our model account for the fluctuation spectrum of red blood cell membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane areas. We also predict an observable tension jump for membranes decorated with polymer "brushes."     

Eigen fuzzy sets and fuzzy relations

When R is a fuzzy relation between the elements of a finite set X, the fuzzy sets A of X such that R ° A = A (MAX-MIN composition) are called eigen fuzzy sets. The main result of this paper is the determination of the greatest eigen fuzzy set associated with a given fuzzy relation and we give three methods illustrated by an example. We then state that the greatest eigen fuzzy set associated with $\text{R}\text{?}$, the transitive closure of R, is exactly the one associated with R. Finally we describe how to obtain all fuzzy relations keeping invariant a given fuzzy set.     

Structure des peroxydates obtenus par action de lóxygene moleculaire sur des organometalliques derives du bromure de crotyle

Butenylmagnesium, butenylzinc and butenylaluminium bromides are oxidized at low temperature (?80 and ?100°C). The qualitative and quantitative studies of the reaction products after reduction by PPh₃, LiAlH₄ and n-BuMgBr show that the secondary structure is dominant in the peroxides formed.     

Modal Overlap Factor of a beam with an acoustic black hole termination

An Acoustic Black Hole (ABH) effect is a passive vibration reduction technique which takes advantage of properties of wave propagation in thin structures of varying thickness. A practical implementation of ABH on a uniform beam consists in an extremity whose thickness follows a power-law profile covered by a very thin layer of additional damping material. A modal analysis based on a High Resolution technique shows that the ABH significantly increases the Modal Overlap Factor (MOF) of the beam, thus reducing the resonant behaviour of the structure. Further investigations, including a two-dimensional numerical model of the structure based on the finite difference method, show that this MOF can be explained by an increase of the modal density and a high damping of a number of modes of the structure due to the ABH.     

Iodonium Ion-Mediated Mannosylations of Myo-Inositol : Synthesis of a Mycobacteria Phospholipid Fragment

Abstract

Iodonium ion-mediated glycosylation of 1-O-allyl-3,4,5-tri-O-benzyl-6-O-para-methoxybenzyl-D/L-myo-inositol by ethyl 2-O-benzoyl-3,4,6-tri-O-benzyl-l-thio-α-D-mannopyranoside gave, after removal of the para-methoxybenzyl group and column chromatography, an α/β-mixture of the individual diastereoisomeric disaccharides. Subsequent stereospecific glycosylation of the α(1-2) linked mannopyranosyl-D-myo-inositol enantiomorph by the same ethyl 1-thiomannopyranoside donor afforded, after debenzoylarion, benzylation and subsequent deallylation the partially benzylated 2,6-dimannopyranosyl-D-myo-inositol derivative, the HO-1 position of which was phosphorylated, via the H-phosphonate method, with 1,2-dipalmitoyl-sn-glycerol. Oxidation of the intermediate phosphonate diester, and subsequent hydrogenolysis of the O-benzyl groups, furnished the target compound 1-O-(1,2-dipalmitoyl-sn-glycero-3-phosphoryl)-2,6-di-O-α-D-mannopyranosyl-D-myo-inositol.     

Dynamics of communal vocalizations in a social songbird, the zebra finch (Taeniopygia guttata)

Colonies or communities of animals such as fishes, frogs, seabirds, or marine mammals can be noisy. Although vocal communication between clearly identified sender(s) and receiver(s) has been well studied, the properties of the noisy sound that results from the acoustic network of a colony of gregarious animals have received less attention. The resulting sound could nonetheless convey some information about the emitting group. Using custom-written software for automatic detection of vocalizations occurring over many hours of recordings, this study reports acoustic features of communal vocal activities in a gregarious species, the zebra finch (Taeniopygia guttata). By biasing the sex ratio and using two different housing conditions (individual versus communal housing), six groups of zebra finches were generated, with six different social structures that varied both in terms of sex-composition and proportion of paired individuals. The results showed that the rate of emission and the acoustic dynamic both depended on the social structure. In particular, the vocal activity of a group of zebra finches depended mainly on the number of unpaired birds, i.e., individuals not part of a stably bonded pair.