On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

A note on theβ-measure for digraph competitions

Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization of theβ-measure.     

Functionalized organosilica microspheres via a novel emulsion-based route

Thiol-functionalized organosilica microspheres were synthesized via a two-step process: (1) acid-catalyzed hydrolysis and condensation of 3-mercaptopropyltrimethoxysilane (MPTMS), followed by (2) base-catalyzed condensation, which led to the rapid formation of emulsion droplets with a narrow size distribution. These droplets continued to condense to form solid microspheres. Solution (29)Si NMR and optical microscopy were applied to study the mechanism of this novel synthetic route. Solid-state (29)Si NMR, SEM, zeta potential titration, and Coulter counter measurements were used to study the bulk and surface properties and to determine the particle size distributions of the final microspheres. Compared to conventional St?ber silica particles, these microspheres were shown to have a lower degree of cross-linking (average degree of condensation, r = 1.25), a larger average size (up to 6 microm), and a higher isoelectric point (pH = 4.4). Confocal microscopy of dye-labeled microspheres showed an even distribution of dye molecules throughout the interior, characteristic of a readily accessible and permeable organosilica network. These findings have implications for the production of functionalized solid supports for use in catalysis and biological applications, such as optically encoded carriers for combinatorial synthesis.     

Liquid crystal oligomers: going beyond dimers

This review focuses on structure-property relationships in liquid crystal oligomers, which consist of molecules containing two or more mesogenic units linked via flexible spacers essentially in a linear fashion and so does not consider, for example, liquid crystal dendrimers and tetrapodes. Previous reviews have tended to focus mainly on liquid crystal dimers in which just two mesogenic units are interconnected by a single spacer. By contrast, this review is largely devoted to higher oligomers such as liquid crystal trimers and tetramers containing three or four mesogenic units connected by two or three spacers, respectively.     

Twist-Bend Nematic Glasses: The Synthesis and Characterisation of Pyrene-based Nonsymmetric Dimers

A selection of pyrene-based liquid crystal dimers have been prepared, containing either methylene-ether or diether linked spacers of varying length and parity. All the diether linked materials, CBOnO.Py (n=5, 6, 11, 12), exhibit conventional nematic and smectic A phases, with the exception of CBO11O.Py which is exclusively nematic. The methylene-ether linked dimer, CBnO.Py, with an even-membered spacer (n=5) was solely nematogenic, but odd-members (n=6, 8, 10) exhibited both nematic and twist-bend nematic phases. Replacement of the cyanobiphenyl fragment by cyanoterphenyl giving CT6O.Py, gave elevated melting and nematic-isotropic transition temperatures, and SmA and SmC_A phases were observed on cooling the nematic phase. Intermolecular face-to-face associations of the pyrene moieties drive glass formation, and all these materials have a glass transition temperature at or above room temperature. The stability of the glassy twist-bend nematic phase allowed for its study using AFM, and the helical pitch length, P_TB, was measured as 6.3 and 6.7 nm for CB6O.Py and CB8O.Py, respectively. These values are comparable to the shortest pitch of a twist-bend nematic phase measured to date.     

The effect of a concurrent cognitive task on cortical potentials evoked by unpredictable balance perturbations

Background  

Although previous studies suggest that postural control requires attention and other cognitive resources, the central mechanisms responsible for this relationship remain unclear. To address this issue, we examined the effects of altered attention on cortical activity and postural responses following mechanical perturbations to upright stance. We hypothesized that cortical activity would be attenuated but not delayed when mechanical perturbations were applied during a concurrent performance of a cognitive task (i.e. when attention was directed away from the perturbation). We also hypothesized that these cortical changes would be accompanied by alterations in the postural response, as evidenced by increases in the magnitude of anteroposterior (AP) centre of pressure (COP) peak displacements and tibialis anterior (TA) muscle activity. Healthy young adults (n = 7) were instructed to continuously track (cognitive task) or not track (control task) a randomly moving visual target using a hand-held joystick. During each of these conditions, unpredictable translations of a moving floor evoked cortical and postural responses. Scalp-recorded cortical activity, COP, and TA electromyographic (EMG) measures were collected.     

Photochemistry and Thermal Decarboxylation of α-Phosphoryloxy-p-nitrophenylacetates

α-Carboxy-4-nitrobenzyl phosphate 4 and its derived monomethyl phosphate ester 5 were synthesized and purified by anion-exchange chromatography. A gradient of LiCl was necessary for elution of the anion-exchange column to avoid unexpected thermal decarboxylation that occurred during vacuum evaporation when the volatile triethylammonium bicarbonate buffer was used. Photolysis of each compound was accompanied by decarboxylation, and 4 released inorganic phosphate with near-100% stoichiometry. Time-resolved infrared spectroscopy of the photolysis reaction, coupled with density functional theory calculations of vibrational frequencies, enabled us to infer a mechanism for the photolytic pathway, although there was some evidence for a second pathway also being operative. In contrast to the results for 4 , photolysis of 5 appeared to release little or no monomethyl phosphate.