Structure and Classification of Superconformal Nets

We study the general structure of Fermi conformal nets of von Neumann algebras on S ¹ and consider a class of topological representations, the general representations, that we characterize as Neveu–Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by taking the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2. Sebastino Carpi: Supported by MIUR, GNAMPA-INDAM and EU network “Noncommutative Geometry” MRTN-CT-2006-0031962 Yasuyuki Kawahigashi: Supported in part by the Grants-in-Aid for Scientific Research, JSPS. Submitted: March 3, 2008. Accepted: May 5, 2008.     

The Virasoro Algebra and Sectors with Infinite Statistical Dimension

We show that the sectors with lowest weight $ h \geq 0,\, h \neq j{^2},\, j \in {1\over2}\mathbb{Z} $ of the local net of von Neumann algebras on the circle generated by the Virasoro algebra with central charge c = 1 have infinite statistical dimension. Communicated by Klaus Fredenhagen submitted 28/11/02, accepted: 10/03/03     

Piperazine quaternary diammonium salts as additives to background electrolytes in capillary zone electrophoresis

The differential behavior of five different quaternary mono- and diammonium salts, among the 18 investigated, in modulating the electroendoosmotic flow (EOF) and analyte separations in capillary zone electrophoresis is evaluated. It is found that quaternary diammonium salts with positive charges separated by more than four carbon atoms, while exhibiting a very strong affinity for chromatographic silica beads, to the point of exhibiting Rf values close to zero, display, on the contrary, a very poor affinity for the silica wall of capillaries. Compounds separated only by a C2 unit (i.e., 1,4-dialkyl-1,4-diazoniabicyclo[2,2,2,]octane, salts 17 and 18) show high Rf values due to strong ion pair association. The unique behavior of quaternary monoammonium salts possessing an iodinated alkyl (butyl or octyl) tail (i.e., 1, 6, and 7) is attributed to their ability to be covalently affixed to the silica wall via alkylation of ionized silanols at alkaline pH values. They thus strongly modulate and typically invert the EOF, even when not present in the background electrolyte. On the contrary, all diammonium salts, devoid of such alkyl tails, are unable to modulate the EOF and to prevent analyte binding to the silica wall, since they are rapidly removed from the wall by the voltage gradient. However, if added in small amount to the background electrolyte, they offer excellent separations of mixtures of very similar organic acids and prevent any interaction with the capillary wall.     

Diffusion dynamics in small-world networks with heterogeneous consumers

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers’ probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets. This paper won the best student paper award at the North American Association for Computational Social and Organizational Science (NAACSOS) Conference 2005, University of Notre Dame, South Bend, Indiana, USA. Preceding versions of this paper have been presented to the Conference of the North American Association for Computational Social and Organizational Science (NAACSOS), 2005, University of Notre Dame, South Bend, USA and to the Conference of the European Social Simulation Association (ESSA), 2005, Koblenz, Germany. Sebastiano Alessio Delre received his Master Degree in Communication Science at the University of Salerno. After one year collaboration at the Institute of Science and Technologies of Cognition (ISTC, Rome, Italy), now he is a PhD student at the faculty of economics, University of Groningen, the Netherlands. His work focus on how different network structures affect market dynamics. His current application domain concerns Agent-Based Simulation Models for social and economic phenomena like innovation diffusion, fashions and turbulent market. Wander Jager is an associate professor of marketing at the University of Groningen. He studied social psychology and obtained his PhD in the behavioral and social sciences, based on a dissertation about the computer modeling of consumer behaviors in situations of common resource use. His present research is about consumer decision making, innovation diffusion, market dynamics, crowd behavior, stock-market dynamics and opinion dynamics. In his work he combines methods of computer simulation and empirical surveys. He is involved in the management committee of the European Social Simulation Association (ESSA). Marco Janssen is an assistant professor in the School of Human Evolution and Social Change and in the Department of Computer Science and Engineering at Arizona State University. He got his degrees in Operations Research and Applied Mathematics. During the last 15 years, he uses computational tools to study social phenomena, especially human-environmental interactions. His present research focuses on diffusion dynamics, institutional innovation and robustness of social-ecological systems. He combined computational studies with laboratory and field experiments, case study analysis and archeological data. He is an associate editor-in-chief of the journal Ecology and Society.     

Multi-parameter regularization techniques for ill-conditioned linear systems

Summary.  When a system of linear equations is ill-conditioned, regularization techniques provide a quite useful tool for trying to overcome the numerical inherent difficulties: the ill-conditioned system is replaced by another one whose solution depends on a regularization term formed by a scalar and a matrix which are to be chosen. In this paper, we consider the case of several regularizations terms added simultaneously, thus overcoming the problem of the best choice of the regularization matrix. The error of this procedure is analyzed and numerical results prove its efficiency. Received January 15, 2002 / Revised version received July 31, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 65F05 – 65F22     

Optical Space of the Reissner-Nordström Solutions

We present an exhaustive discussion of the embedding diagrams for the optical geometry of the Reissner-Nordström solutions. Whereas in the black hole sector there are no qualitative differences with respect to the Schwarzschild case, the diagrams are considerably different if naked singularities are present. Our treatment is sufficiently general that it can be applied also to any other static spherically symmetric spacetime.     

Dendrimers made of porphyrin cores and carbazole chromophores as peripheral units. Absorption spectra, luminescence properties, and oxidation behavior

Luminescent and redox-active porphyrin-based dendrimers of first and second generation have been synthesized, and their absorption spectra, photophysical properties, and oxidation behavior have been investigated, together with those of the corresponding aldehyde carbazole precursors. All the dendrimers contain a porphyrin core and carbazole-based chromophores as branches. The structural formulas of the new species are represented in Figures 1 and 2, with the corresponding schematizations. The absorption spectra of the aldehyde carbazole precursors A1-A6 in dichloromethane exhibit intense transitions in the UV region, centered on the carbazole and benzaldehyde subunits. The lowest-energy absorption bands receive contribution from charge-transfer transitions. Compounds A1-A6 are luminescent at room temperature in fluid solution; such a luminescence is attributed to twisted intramolecular charge-transfer excited states. The luminescence at 77 K in a rigid matrix is blue-shifted with respect to room-temperature emission and is assigned to locally excited states. Absorption spectra of the porphyrin-cored dendrimers P1-P6 appear additive as they are constituted by visible bands due to porphyrin absorption and bands in the UV region due to transitions centered on the carbazole-based branches. Emission spectra of P1-P6 both at 77 K and at room temperature are typical of porphyrin species and independent of excitation wavelength, indicating that the light collected by the peripheral chromophores is quantitatively transferred to the core. All the compounds exhibit a rich oxidation behavior in 1,2-dichloroethane solution, with reversible processes centered on the different carbazole subunits. Interaction between the different carbazole centers depends on the size of the spacer interposed.     

A comparative chemotaxonomic study on Vinca sardoa steam and Vinca difformis pourret

The phytochemical analysis of iridoidic fraction of the aerial parts of Vinca sardoa and Vinca difformis, gave the identification of loganic acid in V. difformis as unique iridoid glucoside, while loganin is also present in V. sardoa. The two taxa highly differ in alkaloids, so the chemotaxonomic classification in two different species is supported.     

On the Representation Theory of Virasoro Nets

We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the c=1 Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge c is in a certain subset of (1, ), including [2, ), and h(c–1)/24, the irreducible representation with lowest weight h of the corresponding Virasoro net has infinite statistical dimension. As a consequence we show that if the central charge c is in the above set and satisfies c25 then the corresponding Virasoro net has no proper local extensions of compact type.Supported in part by the Italian MIUR and GNAMPA-INDAM.