Pool-Frenkel effect and high frequency dielectric constant determination of semiconducting P2O5-Li2MoO4-Li2O and P2O5-Na2MoO4-Na2O bulk glasses

The ternary 70P₂O₅-10Li₂MoO₄-20Li₂O and 70P₂O₅-10Na₂MoO₄-20Na₂O glasses, prepared by the press-melt quenching technique, were studied at temperatures between 298 and 418 K for their high dc electric field properties. For the above purpose, the effect of a strong electric field on the dc conduction of these amorphous bulk samples was investigated using the gap-type electrode configuration. At low electric fields, the current-voltage (I — V) characteristics have a linear shape, while at high electric fields (> 10³ V/cm), bulk samples show nonlinear effects (nonohmic conduction). Current-voltage curves show increasing departure from Ohm’s law with increasing current density, leading to critical phenomena at a maximum voltage (threshold voltage), known as switching (switch from a low-conduction state to a higher-conduction state at threshold voltage). The Pool-Frenkel high-field effect was observed at electrical fields of about 10³–10⁴ V/cm; then the lowering factor of the potential barrier, the high frequency dielectric constant, and the refractive index of these glasses were determined.      

On Sets that Meet Every Hyperplane in n-Space in at Most n Points

A simple proof that no subset of the plane that meets everyline in precisely two points is an F-set in the plane is presented.It was claimed that this result can be generalized for setsthat meet every line in either one point or two points. No proofof this assertion is known, however. The main results in thispaper form a partial answer to the question of whether the claimis valid. In fact, it is shown that a set that meets every linein the plane in at least one but at most two points must bezero-dimensional, and that if it is -compact then it must bea nowhere dense G-set in the plane. Generalizations for similarsets in higher-dimensional Euclidean spaces are also presented.     

Products of conjugacy classes in Chevalley groups I. Extended covering numbers

This paper is concerned with products of conjugacy classes in Chevalley groups. We prove that in any quasisimple Chevalley groupG proper or twisted, over any field, the extended covering number is bounded above linearly in terms of the rank ofG, that is, for some constante, for any Chevalley groupG, the product of anye · rank(G) non-central classes covers all ofG. We give estimates for the constante in different cases. The authors gratefully acknowledge the support of EPSRC through a Visiting Fellowship number GR/M58542 and a Research grant number GR/L92174.     

Topological equivalence of discontinuous norms

We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR ^Nsuch that for everyr>0,h maps the Hilbert cube [−r, r] ^N precisely onto the “elliptic cube” . This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR ^N.The result is obtained by means of the Bing Shrinking Criterion. Research supported in part by a grant from NSF-EPSCoR Alabama.     

Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights

We present two approaches to the spectral studies for infinite Jacobi matrices with monotonic or near-to-monotonic weights. The first one is based on the subordination theory due to Khan and Pearson [17] combined with the detailed analysis of the transfer matrices for the solutions of the formal eigenequation. The second one uses an extension of the commutator approach developed by Putnam in [19]. Applying these methods we prove the absolute continuity for several classes of weights and diagonals. For some other cases we prove the emptiness of the point spectrum. The results are illustrated with examples and compared with the results of Dombrowski [7]-[13], Clark [2] and of Máté and Nevai [18]. We show that some of our results are stronger.The research of the first author has been supported by the KBN grant PB 2 P03A 002 13.     

Tilting theory and the finitistic dimension conjectures

Let be a right noetherian ring and let be the class of all finitely presented modules of finite projective dimension. We prove that findim iff there is an (infinitely generated) tilting module such that pd and . If is an artin algebra, then can be taken to be finitely generated iff is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø.

     

Relative Asymptotic Efficiency of the Maximum Pseudolikelihood Estimate for Gauss–Markov Random Fields

A general version of the maximum pseudolikelihood estimate of parameters within the class of Gauss–Markov random fields is stated in a rigorous way. Its asymptotic properties, namely the consistency, the asymptotic normality, and the relative asymptotic efficiency are studied. Explicit formulas for the asymptotic covariance matrix are given, and a decrease of efficiency is proved. A numerical example is added to show that the efficiency can be improved by enlarging the range of the conditional distribution used in the estimator. This revised version was published online in June 2006 with corrections to the Cover Date.     

A bivariate extension of Bleimann-Butzer-Hahn operator

Let C(R2+ ) be a class of continuous functions f on R2+. A bivariate extension L.(f ,x,y) of BleimannButzer-Hahn operator is defined and its standard convergence properties are given. Moreover, a local analogue of Voronovskaja theorem is also given for a subclass of C(R2+).     

Magnetic Study of Doped Ba Ferrites Prepared by Citrate Method

The M-type barium ferrite is doped with either Co²⁺-Ti⁴⁺ or Co²⁺-Zr⁴⁺ pairs to reduce its intrinsically high uniaxial magnetic anisotropy in order to make fine particles for magnetic recording. The magnetic parameters were investigated by magnetic measurements and the Mössbauer spectroscopy. Compounds (BaF) obtained from BaCo _x (Ti,Zr) _x Fe_12-2x O₁₉ with 0x1.0 have been prepared by the modified citrate method with the initial ratio of Ba:Fe equal to 1:10.8. The substitution of Co - Ti or Co - Zr for Fe³⁺ ions affects mainly the positions 2a and 4f ₂. Ba ferrite with the substitution x 0.8 is promising for perpendicular recording media applications.