Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics.Comment: 17 page

Magnetic and Transport Properties of Fe-Ag granular multilayers

Results of magnetization, magnetotransport and Mossbauer spectroscopy measurements of sequentially evaporated Fe-Ag granular composites are presented. The strong magnetic scattering of the conduction electrons is reflected in the sublinear temperature dependence of the resistance and in the large negative magnetoresistance. The simultaneous analysis of the magnetic properties and the transport behavior suggests a bimodal grain size distribution. A detailed quantitative description of the unusual features observed in the transport properties is given

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Detection of zero anisotropy at 5.2 AU during the November 1998 solar particle event: Ulysses Anisotropy Telescopes observations

International audienceFor the first time during the mission, the Anisotropy Telescopes instrument on board the Ulysses spacecraft measured constant zero anisotropy of protons in the 1.3-2.2 MeV energy range, for a period lasting more than three days. This measurement was made during the energetic particle event taking place at Ulysses between 25 November and 15 December 1998, an event characterised by constant high proton fluxes within a region delimited by two interplanetary forward shocks, at a distance of 5.2 AU from the Sun and heliographic latitude of 17°S. We present the ATs results for this event and discuss their possible interpretation and their relevance to the issue of intercalibration of the two telescopes

Influence of sintering temperature and pressure on crystallite size and lattice defect structure in nanocrystalline SiC

Microstructure of sintered nanocrystalline SiC is studied by x-ray line profile analysis and transmission electron microscopy. The lattice defect structure and the crystallite size are determined as a function of pressure between 2 and 5.5 GPa for different sintering temperatures in the range from 1400 to 1800 degrees C. At a constant sintering temperature, the increase of pressure promotes crystallite growth. At 1800 degrees C when the pressure reaches 8 GPa, the increase of the crystallite size is impeded. The grain growth during sintering is accompanied by a decrease in the population of planar faults and an increase in the density of dislocations. A critical crystallite size above which dislocations are more abundant than planar defects is suggested

The measurement of dissolved oxygen today - tradition and topicality

Today, the determination of the dissolved oxygen content of natural waters is practically an essential duty whenever background data is collected for investigations of a hydrobiological, ecological, and nature or environmental protection viewpoint. If the method by which the measurements are carried out is concerned, it can be stated that the 120 year old, classical Winkler-method is inevitable even today. However the development of hydroecological sciences have laid claim to such expectations that the necessity of in situ oxygen determinations have become increasingly important. In our work we present the survival of the traditional Winkler-method in the present practice, we review all those viewpoints which have facilitated the widespread application of in situ oxygen determinations as well as the methods of all the measurements that are presently regularly applied in the investigations of natural waters

The Routing of Complex Contagion in Kleinberg's Small-World Networks

In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after $k \ge 2$ neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where we can activate one node at one time step with the goal of activating the targeted node in the end. We consider decentralized routing scheme where only the weak ties from the activated nodes are revealed. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all nodes that could be activated are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in $n$ (the number of nodes in the network) for all range of $\alpha$ both in expectation and with high probability (in particular, $\Omega(n^{\frac{1}{\alpha+2}})$ for $\alpha \le 2$ and $\Omega(n^{\frac{\alpha}{2(\alpha+2)}})$ for $\alpha > 2$ in expectation), while the routing time of simple contagion has polylogarithmic upper bound when $\alpha = 2$. Our results indicate that complex routing is harder than complex diffusion and the routing time of complex contagion differs exponentially compared to simple contagion at sweetspot.Comment: Conference version will appear in COCOON 201

On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance