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.      

Contact Classification of Linear Ordinary Differential Equations: I

It is known that a linear ordinary differential equation of order n3 can be transformed to the Laguerre–Forsyth form y ⁽ⁿ⁾= _i=3 ⁿ a _n–i (x)y ^(n–i) by a point transformation of variables. The classification of equations of this form in a neighborhood of a regular point up to a contact transformation is given.     

Strong conjugation actions induced by flags of exact Borel subalgebras

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u^-1eCeu.     

Extraction of subsystems “Majorized” by the rademacher system

In this paper it is proved that from any uniformly bounded orthonormal system {f _n} _n=1 ^∞ of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni} _i ^{Emphasis>=1/∞} majorized in distribution by the Rademacher system on [0, 1]. This means that {

Almost-Sure Results for a Class of Dependent Random Variables

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by _d ⁺ —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.     

Théorie de Kasparov équivariante et groupo?des I

Let be a locally compact topological groupoid, A and B two C*-algebras endowed with a continuous action of . We define an operator K-theory group K K (A,B). We describe two basic properties of this theory: the existence of a Kasparov product and functoriality with respect to groupoid cocycles.     

Periodic solutions of damped differential systems with repulsive singular forces

We consider the periodic boundary value problem for the singular differential system: where , , and . The singular potential is of repulsive type in the sense that as . Under Habets-Sanchez's strong force condition on at the origin, the existence results, obtained by coincidence degree in this paper, have no restriction on the damping forces . Meanwhile, some quadratic growth of the restoring potentials at infinity is allowed.

     

Reducibility and nonreducibility between equivalence relations

We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.

     

Contact Transformations and Local Reducibility of ODE to the Form y‴=0

Orbits of the ODE y=0 in corresponding jet bundles are investigated. Explicit relations for the right-hand side of an arbitrary 3-order ODE necessary and sufficient for the existence of a contact transformation reducing this equation locally to the form y=0 are obtained.     

On Some Rings of Arithmetical Functions

In this paper, we consider several constructions which from a given B-product * _B lead to another one We shall be interested in finding what algebraic properties of the ring are shared also by the ring . In particular, for some constructions the rings R _B and will be isomorphic and therefore have the same algebraic properties.