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.     

Constructing the Co cyclic Structures for Crossed Copro duct Coalgebras

In this paper, we construct a cocylindrical object associated to two coal-gebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct c...     

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.     

多重调和Bergman空间上径向Toeplitz算子的交换性

In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space.     

One-Pot Synthesis and Fungicidal Activities of Derivatives of Imidazo [2,1-b]-1,3,4-thiadiazol-5(6H)-one

The isothiocyanates 2, obtained from aza-Wittig reactions of vinyliminophosphoranes 1 with CS ₂ , reacted with hydrazine to give 3-amino-2-thioxo-4-imidazolidinones 4. One-pot reactions of 4, aromatic isocyanates, Ph ₃ P, C ₂ Cl ₆ , and Et ₃ N generated imidazo[2,1-b]-1,3,4-thiadiazol-5(6H)-ones 7. Compound 7 exhibited good fungicidal activities, especially against Sclerotinia sclerotiorum de Bary and Botrytis Cinerea Pers.