Outer operators for the noncommutative symmetric hardy spaces associated with finite subdiagonal algebra

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.     

Synthesis of 5-[(2-hydroxynaphthalen-1-yl)diazenyl]isophthalic acid and its application to electrocatalytic oxidation and determination of adrenaline,paracetamol, and tryptophan

In this study,Au nanoparticles/poly 5-[(2-hydroxynaphthalen-l-yl)diazenyl]isophthalic acid film modified glassy carbon electrode(AuNPs/poly(NDI)/GCE) has shown excellent electrocatalytic activity toward the oxidation of adrenaline(ADR),paracetamol(PAC),and tryptophan(Trp).The bare glassy carbon electrode(GCE) fails to separate the oxidation peak potentials of these molecules,while the poly(NDI) film modified electrode can resolve them.Electrochemical impedance spectroscopy(EIS)indicates that the charge transfer resistance of the bare electrode decreases as 5-[(2-hydroxynaphthalen-l-yl)diazenyl]isophthalic acid is electropolymerized on the bare electrode.Furthermore,EIS exhibits enhancement of electron transfer kinetics between analytes and the electrode after electrodeposition of Au nanoparticles.Differential pulse voltammetry results show that the electrocatalytic current increases linearly in the ranges of 0.01-680.0 μmol L~1 for ADR,0.05-498.0 μmol L~1 for PAC,and 3.0-632.0 μmol L~1 for Trp;with detection limits(S/N = 3) of 0.009 μmol L~1,0.005 μmol L~1,and 0.09 μmol L~1 for ADR,PAC,and Trp,respectively.The proposed method has been successfully applied for simultaneous determination of ADR,PAC,and Trp in biological samples.     

On geodesic mappings of equidistant generalized Riemannian spaces

In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.     

Simple connectedness of hyperplane complements in some geometries related to buildings

For a class of parapolar spaces that includes the geometries E6,4, E7,7, and E8,1 with lines of size at least three, the metasymplectic spaces with lines of size at least four, and the polar line Grassmannians with lines of size at least four except D4,2(3), we show that the subgraph of the point-collinearity graph induced on the complement of a hyperplane is simply connected. We also show that these parapolar spaces have Veldkamp lines.     

Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?^{n+ 1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?^{n+ 1}) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?^{n+ 1, 1}). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.     

Quasi-periodic stability of normally resonant tori

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.     

Spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations

We study the spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations by separately calculating the contribution to the excitation rate of vacuum fluctuations and a cross term which involves both vacuum fluctuations and radiation reaction, and demonstrate that although the spontaneous excitation for the atom in its ground state would occur in vacuum, such atoms in circular motion do not perceive a pure thermal radiation as their counterparts in linear acceleration do since the transition rates of the atom do not contain the Planckian factor characterizing a thermal bath. We also find that the contribution of the cross term that plays the same role as that of radiation reaction in the scalar and electromagnetic fields cases differs for atoms in circular motion from those in linear acceleration. This suggests that the conclusion drawn for atoms coupled with the scalar and electromagnetic fields that the contribution of radiation reaction to the mean rate of change of atomic energy does not vary as the trajectory of the atom changes from linear acceleration to circular motion is not a general trait that applies to the Dirac field where the role of radiation reaction is played by the cross term.