Weighted Projective Lines as Fine Moduli Spaces of Quiver Representations

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their canonical bundles, and show that they are rarely tilting. We also give a moduli construction for these total spaces for weighted projective lines with three orbifold points.     

Optimal transmission of “television type” gaussian signals through a noiseless feedback channel

Using the methods and results of the theory of conditionally Gaussian filtering of stochastic processes and fields, an optimal scheme of “television type” signal transmission through a noiseless feedback channel is constructed under the usual power conditions, the signals being evolutionary Gaussian fields θ={θ_t(x)),tε[0,T),xεDεRⁿ . Explicit representations for optimal coding and decoding functionals, which are optimal in the sense of a special square criterion, and the expression for the error of signal reproduction are given.     

An Inexact PRP Conjugate Gradient Method for Symmetric Nonlinear Equations

In this article, without computing exact gradient and Jacobian, we proposed a derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric. This method is a generalization of the classical PRP method for unconstrained optimization problems. By utilizing the symmetric structure of the system sufficiently, we prove global convergence of the proposed method with some backtracking type line search under suitable assumptions. Moreover, we extend the proposed method to nonsmooth equations by adopting the smoothing technique. We also report some numerical results to show its efficiency.     

Primal mixed formulations for the coupling of FEM and BEM. Part I: linear problems

We apply the boundary integral equation method and a primal mixed finite element approach to study the weak solvability and Galerkin approximations of linear interior transmission problems arising in potential theory and elastostatics. The existence and uniqueness of solution of the resulting weak formulations and of the associated discrete schemes are derived by using the classical theory for variational problems with constraints. Suitable finite element subspaces of Lagrange type satisfying the compatibility conditions are utilized for defining the Galerkin scheme. The error analysis and corresponding rates of convergence are also provided.     

A perturbation theory for the discrete harmonic oscillator equation

This work deals with the existence, uniqueness and stability of solutions for the semilinear discrete harmonic oscillator equation on Banach spaces by using recent characterization of maximal regularity for a best difference approximation of the discrete harmonic oscillator equation.     

Harmonic and Probabilistic Approaches to Zeros of Riemann's Zeta Function

Probability concepts and results are closely related to the study of zeros of the classical Riemann zeta function and its affinity to Gaussian and Gamma distributions. This is elaborated in obtaining the functional and integral equations for the zeta and in the determination first of the nonzero sets and then sets containing almost all (i.e., for the CLT probability measure) nontrivial zeros of the zeta function ζ(·). Also probability distributions determined by the zeta, based on the behavior of their finite dimensional distributions of the ζ(σ +it), σ > 0; as t varies and particularly the results of Denjoy, slightly sharpened, and also one of Salem are included. Several related opinions and comments are discussed.     

Revisiting the defect structure of MAX phases: the case of Ti4AlN3

Microstructural study of as-grown Ti₄AlN₃ MAX phase has been performed by transmission electron microscopy. Dislocation walls, dislocation nucleation sites and stacking faults are described. In particular, diffraction contrast analysis combined with high-resolution images give a new insight into the nature of the stacking faults: contrarily to what is usually postulated, it is shown that the stacking faults possess a shear component in the basal plane. The stacking faults are created by the insertion of MX layers in the lattice via diffusion mechanisms. Their possible role on the deformation mechanism of MAX phases is discussed.     

Effect of Fe on the glass-forming ability,structure and devitrification behavior of Zr–Cu–Al bulk glass-forming alloys

We report on the glass-forming ability and devitrification behavior of Zr₆₀Cu₃₀Al₁₀, Zr₆₀Cu₂₅Al₁₀Fe₅ and Zr_62.5Cu_22.5Al₁₀Fe₅ bulk glass-forming alloys on heating. The effect of Fe addition on the structure of Zr–Al–Cu alloys is also discussed. Crystallization kinetics and structural changes in the glassy alloys were studied using X-ray diffraction, transmission electron microscopy, differential scanning and isothermal calorimetry methods. The results indicate that good glass-formers, such as Zr_62.5Cu_22.5Al₁₀Fe₅, are located somewhat beyond the equilibrium eutectic point. Possible phase separation in the supercooled liquid on heating and electron beam-induced in situ crystallization are observed and discussed.