Equivalence among different formalisms in the Tsallis entropy framework

In a recent paper [T. Wada, A.M. Scarfone, Phys. Lett. A 335 (2005) 351] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear Fokker-Planck equation (NFPE). By means of time-scale conversion, it is shown that there exists a “correspondence” among the self-similar solutions of the NFPEs associated with the different Tsallis formalisms. The time-scale conversion is related to the corresponding Lyapunov functions of the respective NFPEs.     

Efficient polymer white-light-emitting diodes with a single-emission layer of fluorescent polymer blend

Efficient polymer white-light-emitting diodes (WPLEDs) have been fabricated with a single layer of fluorescent polymer blend. The device structure consists of ITO/PEDOT/PVK/emissive layer/Ba/Al. The emissive layer is a blend of poly(9,9-dioctylfluorene) (PFO), phenyl-substituted PPV derivative (P-PPV) and a copolymer of 9,9-dioctylfluorene and 4,7-di(4-hexylthien-2-yl)-2,1,3-benzothiadiazole (PFO-DHTBT), which, respectively, emits blue, green and red light. The emission of pure and efficient white light was implemented by tuning the blend weight ratio of PFO: P-PPV: PFO-DHTBT to 96:4:0.4. The maximum current efficiency and luminance are, respectively, 7.6 cd/A at 6.7 V and 11930 cd/m² at 11.2 V. The CIE coordinates of white-light emission were stable with the drive voltages.     

A littlewood-paley inequality for the Carleson operator

The Carleson operator is closely related to the maximal partial sum operator for Fourier series. We study generalizations of this operator in one and several variables.     

Cantor families of periodic solutions for wave equations via a variational principle

We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities.     

The critical curve for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux

This paper deals with the critical curve of the non-Newtonian polytropic filtration equation coupled via nonlinear boundary flux. The critical global existence curve is obtained by constructing various self-similar supersolutions and subsolutions. Furthermore, we get some new results on the critical Fujita curve.     

Even and odd diagonals in doubly stochastic matrices

The existence of even or odd diagonals in doubly stochastic matrices depends on the number of positive elements in the matrix. The optimal general lower bound in order to guarantee the existence of such diagonals is determined, as well as their minimal number for given number of positive elements. The results are related to the characterization of even doubly stochastic matrices in connection with Birkhoff's algorithm.     

A method for the resolution of the Jacobi equation <Emphasis Type="Italic">Y</Emphasis>″ + <Emphasis Type="Italic">RY</Emphasis> = 0 on the manifold <Emphasis Type="Italic">Sp</Emphasis>(2)/<Emphasis Type="Italic">SU</Emphasis>(2)

In this paper a method for the resolution of the differential equation of the Jacobi vector fields in the manifold V ₁ = Sp(2)/SU(2) is exposed. These results are applied to determine areas and volumes of geodesic spheres and balls. Work partially supported by DGI (Spain) and FEDER Projects MTM 2004-06015-C02-01 and MTM 2007-65852 (first author) and by Research Project PGIDIT05PXIB16601PR (second author). Authors’ addresses: A. M. Naveira, Departamento de Geometría y Topología. Facultad de Matemáticas, Avda. Andrés Estellés, N1, 46100 – Burjassot, Valencia, Spain; A. D. Tarrío Tobar, E. U. Arquitectura Técnica, Campus A Zapateira. Universidad de A Coru?a, 15192 – A Coru?a, Spain     

Synchronization of delayed fuzzy cellular neural networks based on adaptive control

This Letter studies synchronization of delayed fuzzy cellular neural networks with all the parameters unknown. To enhance the coupled strength dynamically and be more suitable for the reality, we add fuzzy theory to the traditional cellular neural networks. By the Lyapunov-Lasall principle of functional differential equations, some new stability criteria are obtained via adaptive control. To the best of our knowledge, there has few work studying fuzzy cellular neural networks. Moreover, the approaches developed here extend the ideas and techniques derived in recent literatures. In the end, an example and its simulation were given to illustrate the simpleness and effectiveness of our main results.     

Bicyclic graphs for which the least eigenvalue is minimum

The spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with minimum least eigenvalue among all connected bicyclic graphs of order n. Also, we determine the unique graph with maximum spread in this class for each n?28.     

Local currents for the GL(N,C) self-dual Yang-Mills equation

By using a simple Bäcklund-like transformation which linearizes the GL(N, C) self-dual Yang-Mills equation, an infinite number of local conservation laws for this equation are constructed. In the SL(N, C) case, the currents become trivial, which explains why these currents are not found in SU(N) gauge theory.