Dirac Operator on the Podleś Sphere

The spectral problem for the Dirac operator on the Podle sphere is discussed and solved in one of its possible formulations. The standard constructions for the Dirac operator on classical symmetric spaces and the spectrum of the Dirac operator on the classical two-dimensional sphere are recalled. The problem of defining a spinor structure on a quantum space is discussed and the definitions of a classical spinor structure and Dirac operator according to Ðurdevich are sketched. The Dirac operator for the Podles´ quantum sphere treated as a quotient space of SU(2) is constructed using the Woronowicz left-covariant calculus over this quantum group. The spectrum of the operator is obtained. Disagreement of its asymptotic behavior with Connes' axiom of noncommutative spectral geometry is stressed.     

Heat Trace and Spectral Action on the Standard Podleś Sphere

We give a new definition of dimension spectrum for non-regular spectral triples and compute the exact (i.e., not only the asymptotics) heat-trace of standard Podle? spheres \({S^2_q}\) for 0 < q < 1, study its behaviour when \({q\to 1}\) , and fully compute its exact spectral action for an explicit class of cut-off functions.     

Instantons on General Noncommutative R^4＊

We study the U(1) and U(2) instanton solutions of gauge theory on general nonocmmutative R^4,In all cases considered we obtain explicit results for the projection operators.In some cases we computed numberically the instanton charge and found that it is an integer independent of the noncommutative parametersθ1,2.     

On the noncommutative spin geometry of the standard Podleś sphere and index computations

The purpose of the paper is twofold: First, known results of the noncommutative spin geometry of the standard Podle? sphere are extended by discussing Poincaré duality and orientability. In the discussion of orientability, Hochschild homology is replaced by a twisted version which avoids the dimension drop. The twisted Hochschild cycle representing an orientation is related to the volume form of the distinguished covariant differential calculus. Integration over the volume form defines a twisted cyclic 2-cocycle which computes the q$q$-winding numbers of quantum line bundles.     

Noncommutative Geometry¶and Gauge Theory on Fuzzy Sphere

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left U(N+1) transformation of the field, where a field is a bimodule over the quantized algebra . The interaction with a complex scalar field is also given. Received: 21 January 1998 / Accepted: 4 February 2000     

1×4 MMI Splitter Based on Rib SOI Waveguide

In this paper, a 1×4 MMI splitter based on silicon-on-insulator (SOI) by effective index method and guide mode method is designed. The fabrication tolerance was analyzed. The device was fabricated and near-field output was obtained.     

Synthesis and Properties of Semicrystalline Copolyimides Based on 4,4′-Diaminodiphenylether and 1,3-Bis(4-aminophenoxy) Benzene

Copolyimides were prepared from 4,4′-diaminodiphenylether (4,4′-ODA), 1,3-bis(4-aminophenoxy) benzene (TPER), and pyromellitic dianhydride (PMDA) through a three-step imidization process with different monomer compositions. The copolymerization disrupted the molecular regularity and decreased the intermolecular interaction of the polyimide chains. The X-ray diffraction (XRD) results indicated the prepared copolyimides showed the same semicrystalline character, but had various crystallinity and crystal forms. The copolymerization also changed the crystal morphologies of the polyimides. With increasing TPER ratio, the copolyimides started to form spherulites and hedrites, which then tended to grow more perfectly as the TPER ratio was further increased. The solubility of the copolyimides and their dependence on the crystallnity and the chain flexibility was investigated. These copolyimides exhibited excellent thermal and thermo-oxidative stability.     

Growing Networks Based on the Mechanism of Addition and Deletion

We divide various fat-tailed degree distributions of real-world networks into five classes based on careful examination of experimental data. By taking account of the mechanism of addition and deletion of nodes in the growing network model with and without preferential attachment respectively, we obtain a11 the five classes of degree distributions, which is believed to shed some light on the dynamics of formation of complex network systems.     

Egorov’s Theorem for Transversally Elliptic Operators on Foliated Manifolds and Noncommutative Geodesic Flow

The main result of the paper is Egorov’s theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations. Mathematics Subject Classifications (2000) 58J40, 58J42, 58B34.     

White Organic Light-Emitting Devices Based on 2-（2-Hydroxyphenyl） Benzothiazole and Its Chelate Metal Complex

We present three kinds of organic light-emitting devices (OLED) fabricated to achieve the emission of bright and pure white light. Device A, with a double-layered structure using 2-(2-hydroxyphenyl) benzothiazole (HBT) and poly (N-vinylcarbazole) (PVK) as the emitting layer (EML) and the hole transport layer (HTL) respectively, could realize the blue-green light emission. Bis-(2-(2-hydroxyphenyl) benzothiazole)zinc (Zn(BTZ)2), synthesized with zinc acetate dihydrate and HBT to form a complex, is used as main EMLs in a similar structure to fabricate devices B and C. Bright and pure white light emissions can be obtained from device C which was fabricated with a green-white emitting host Zn(BTZ)2 and red dopant 5,6,11,12-tetraphenylnaphthacene (rubrene). The maximum quantum efficiency of device C could reach 0.63%, and the corresponding brightness and CIE coordinates were 4000cd/m^2 and (x=0.341, y=0.334) at the driving voltage of 20V.     

Triviality of φ 4 4 and all that in a hierarchical model approximation

The infrared behavior of lattice _d ⁴ ,d 4, and dipole gases ind 1 is rigorously shown to be Gaussian within the context of a hierarchical approximation. Methods are developed to generalize the result beyond this approximation.On leave of absence from the Department of Mathematical Methods of Physics, University, 00-682 Warsaw, Hoza 74, Poland.     

Comment on “Quantum Key Distribution and Quantum Authentication Based on Entangled State”

Shi et al. (Phys. Lett. A 281:83–87, 2001) proposed a scheme which allows simultaneous realization of quantum key distribution and quantum authentication. However, this study points out a weakness in Shi et al.’s scheme, in which a malicious user can impersonate a legitimate participant without being detected. Furthermore, an improved scheme is proposed to avoid this weakness.     

A Chaotic Communication Scheme Based on Generalized Synchronization and Hash Functions

A new chaotic communication scheme based on generalized chaotic synchronization (GCS) and hash function transpositions is presented. The communication scheme has nonsymmetric secrete keys and its ability is similar to traditional digital signatures, i.e. a receiver can convince himself whether or not the sender‘s message contents have been modified. As a direct application of the scheme, a GCS system is designed by using Chen‘s chaotic circuit and is studied in some detail. The numerical simulation shows that this Chen GCS system has high security and is fast and reliable for secure lnternet communications.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

Hypersensitivity in the Luminescence and 4f?C4f Absorption Properties of Mono- and Dinuclear EuIII and ErIII Complexes Based on Fluorinated ??-Diketone and Diimine/ Bis-Diimine Ligands

The results of our investigation on the sensitized luminescence properties of three Eu(III) ??-diketonate complexes of the form [Eu₂(fod)₆(??-bpm)], [Eu(fod)₃(phen)] and [Eu(fod)₃(bpy)] and 4f?C4f absorption properties of their Er(III) analogues ( fod = anion of 6,6,7,7,8,8,8- heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2??-bipyrimidine, phen = 1,10-phenanthroline and bpy = 2,2??-bipyridyl) in a series of non-aqueous solvents are presented. The Eu(III) complexes are highly luminescent and their luminescence properties (intensity and band shape) are sensitive to the changes in the inner coordination sphere of the Eu(III) ion. The luminescence intensity of the mononuclear complexes in pyridine is drastically decreased. The coordination structure of the complexes in pyridine is transformed into a more symmetrical one which results into a slow radiative rate of the emission from the complexes. The ancillary ligands, phen and bpy are found better co-sensitizers as compared to the bpm to sensitize Eu(III)-luminescence. The 4f?C4f absorption properties (oscillator strength and band shape) of the Er(III) complexes demonstrate that ⁴G_11/2 ?? ⁴I_11/2 and ²H_11/2 ?? ⁴I_15/2 hypersensitive transitions of Er(III) are very sensitive in some coordinating solvents which reflects complex?Csolvent interaction in solution. The hypersensitive transitions of [Er(fod)₃(phen)] remain unaffected in any of the solvents and this complex retains its bulk composition in solution. The erbium complexes as well as the Er(fod)₃ chelate are invaded by DMSO. This solvent enters the inner coordination sphere by replacing heterocyclic ligand and the complexes acquire similar structure [Er(fod)₃(DMSO)₂] in this solvent. The results reveal that the luminescence and absorption properties of lanthanide complexes in solution can be controlled by tuning the coordination structure through ancillary ligands and donor solvents. This work shall prove useful in designing new biological applications with such probes.     

Fabrication of Degradable Bone-Like Substitutes Based on Poly-L-lactide and β-tricalcium Phosphate

Composite bone-like substitutes composed of poly-L-lactide (PLLA) and β-tricalcium phosphate (β-TCP) (average particle size: 4.43 μm) were fabricated and the properties were investigated. β-TCP was prepared by wet chemical precipitation, followed by calcining at 800°C. Composite films were obtained by completely mixing dissolved PLLA with granules of β-TCP; the agglomerated β-TCP powder granules were distributed homogeneously in the PLLA matrix. PLLA/β-TCP composite materials were obtained by cold and hot pressing the composite film at a pressure of 130 MPa and temperature of 185°C–195°C. With increase of the amount of β-TCP powder, the bending strength of the composites decreased while the bending modulus increased. The fracture mechanism of the composites was significantly influenced by the content of β-TCP powder, from ductile fracture to brittle fracture as the β-TCP powder content increased.