Orthogonality of polynomials in several variableswith respect to a positiveBorelmeasure supported on an algebraic set is themain theme of this paper.As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in ter...

In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. ...

Heterostructure material that acts as resonant tunneling system is a major scientific challenge in applied physics. Herein, we report a resonant tunneling system, quasi-2D Cu(2)O/SnO(2) p-n heterostructure multi-layer film, prepared by electrochemical deposition in a quasi-2D ultra-thin liquid layer. By applying a special half-sine deposition potential across the electrodes, Cu(2)O and SnO(2) s...

In this paper, we define several ideal versions of Cauchy sequences and completeness in quasimetric spaces. Some examples are constructed to clarify their relationships. We also show that: (1) if a quasi-metric space (X, ?) is I-sequentially complete, for each decreasing sequence {Fn} nonempty I-closed sets with diam{Fn} ? 0 as n ?, then ?n?N Fn single-point set; (2) let I be P-ideal, every pre...

Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...

The existing constructions of space-time codes or modulation have mainly focused on two ideal situations: either quasi-static or rapid fading channels. In this paper, we consider the design of robust space-time modulation for time-correlated Rayleigh fading channels. We show that the space-time signals of square size achieving full diversity in quasi-static fading channels can also achieve the ...

LetR be a ring andM a rightR-module with S= End(MR). The moduleM is called almost principally quasi-injective (or APQ-injective for short) if, for any m∈M, there exists an S-submodule Xm of M such that lMrR(m) = Sm ⊕ Xm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any s∈ S, there exists a left ideal Xs of S such that lS(ker(s)) = Ss ⊕ Xs. In thi...

An algorithm is proposed to include Pauli exclusion principle in Monte Carlo simulations. This algorithm has significant advantages to implement in terms of simplicity, speed, and memory storage; therefore it is ideal for the three-dimensional device simulators. The authors show that even in moderately high applied fields, one can obtain the correct electronic distribution. They give the correc...

A new soft X-ray double crystal monochromator beamline is designed and will be constructed at BL-13. Special care is paid for the degree of parallelism of the beam and the beam size at the focal point. We propose to use two toroidal mirrors, one for producing a parallel beam and another for focusing the beam at the sample position. Although a toroidal mirror is not ideal to produce a parallel b...

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of mechanical problems. However, the classical FEM is not well suited for the treatment of large deformation problems since excessive mesh distortions require remeshing. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used t...