Multiple positive radial solutions on annuli for nonlinear Neumann problems with large growth

We consider a classical semilinear elliptic equation with Neumann boundary conditions on an annulus in R ^N . The nonlinear term is the product of a radially symmetric coefficient with a pure power. We prove that if the power is sufficiently large, the problem admits at least three distinct positive and radial solutions. In case the coefficient is constant, we show that none of the three solutions is constant. The methods are variational and are based on the study of a suitable limit problem.     

Optimal enough?

An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular application, portfolio optimisation. We demonstrate that the randomness of the ‘optimal’ solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample. Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample only to financially meaningless improvements and unpredictable changes (noise) in performance.     

Generalized Cauchy difference iterative forecasting model for wind speed based on fractal time series

Nonlinear Dynamics - The local irregularity and global correlation of wind speed can be described by the fractal dimension D and the Hurst parameter H. However, the existing mathematical models...     

About the synthesis of N-1-substituted 3-aminopyrroles. A comparison

A general method for the preparation of 3-amino-1-methylpyrroles in excellent yields is reported. The key step involves the N-methylation of the nitro derivatives 2 , under phase transfer catalysis conditions.     

Drifted Laplace operators on homogeneous trees

We determine the spectrum and the resolvent operator of a drifted Laplace operator on a homogeneous tree, obtaining qualitatively different results according to the sign of the drift in the direction of a boundary point.

     

Electrochemical sensor for the detection and presumptive identification of quinolone and tetracycline residues in milk

A novel application of an electrochemical biosensor is here employed as analytical method for the detection and presumptive identification of antimicrobial drug residues in milk. The measurement was based on carbon dioxide production rate in relation to inhibition of microbial grow (Escherichia coli ATCC 11303). In this pilot study quinolone and tetracycline residues have been taken into consideration because use of these last in livestock production has been identified as area of particular concern. The experimental approach and analytical method developed appear adequate for the purpose, and compared to older screening methods as, for example, the microbial inhibition assays and immunoassays, offers the advantages of (i) very short analysis time (about 120 min); (ii) smaller sample amount (approximately 0.5 mL); (iii) no sample treatment (iv) good precision; and (v) the possibility of following, in a continuous manner, the inhibition process. Moreover, sensitivity of electrochemical biosensor system is resulted very high considering that for all quinolones and tetracyclines investigated it has been possible detect a residue concentration below or equal to 25 μg L⁻¹. Under this point of view, it must be considered that the maximum residue limits fixed by UE for quinolones and tetracyclines in milk are, at present, all higher of this concentration.     

Semilocal rings with Engel conditions

The relation between the Engel structure of a semilocal ring and that of its multiplicative group is investigated. Suppose that every local ring whose multiplicative group satisfies an m-Engel condition for some positive integer m is an f (m)-Engel ring for some function f . It is proved that under this condition a corresponding statement holds for every semilocal ring which is generated by its multiplicative group. Received: 20 September 2005     

A basic relation between invariants of matrices under the action of the special orthogonal group

The first fundamental theorem of invariant theory for the action of the special orthogonal group onm tuples of matrices by simultaneous conjugation is proved in [2]. In this paper, as a first step in the direction of establishing the second fundamental theorem, we study a basic identity betweenSO(n, K) invariants ofm matrices.