Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

Eigenvalues of the Kählerian Dirac Operator

We get estimates on the eigenvalues of the Kählerian Dirac operator in terms of the eigenvalues of the scalar Laplace–Beltrami operator. In odd complex dimension, these estimates are sharp, in the sense that, for the first eigenvalue, they reduce to Kirchberg's inequality.     

A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds

On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution—a class of bivector fields generalizing twisted Poisson structures that we study in detail.     

Fe doping induced enhancement in room temperature ferromagnetism and selective cytotoxicity of CeO2 nanoparticles

In the present study, structural, optical, magnetic properties as well as cytotoxicity of undoped and Fe doped Ceria (CeO₂) nanoparticles synthesized by simple soft chemical method have been reported. SEM and XRD results have shown that the synthesized samples are comprised of ultrafine spherical nanoparticles having single phase cubic fluorite structure of CeO₂. Raman spectroscopy results have depicted a red shift in F_2g mode with Fe doping which reveals enhancement in the oxygen vacancies. The optical band gap calculated from UV–visible absorption spectra has been found to vary unsystematically with Fe doping which is associated with the creation of impurity level and abundance in oxygen vacancies with Fe doping. The oxygen vacancies have introduced the room temperature ferromagnetism (RTFM) in undoped and Fe doped CeO₂ nanoparticles. The saturation magnetization (M_s) value of pristine CeO₂ nanoparticles has been found to be 0.00083 emu/g which is increased up to 0.0126 emu/g for 7% Fe doped nanoparticles. For cytotoxicity tests, the synthesized nanoparticles induced effects on Neuroblastoma cancer cells & HEK-293 healthy cells have been analyzed via CCK-8 analysis. It has been observed that the prepared undoped and Fe doped CeO₂ nanoparticles have nontoxic nature towards healthy cells while they are extremely toxic towards cancerous cells. Furthermore, the anticancer activity is found to enhance with Fe doping. The selective toxicity and enhancement in anticancer activity with Fe doping has observed to be strongly correlated with reactive oxygen species (ROS) generation.     

On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

非线性RL电路的暂态特性

对一个可解的非线性ＲＬ电路模型的暂态过程进行了研究，得到非线性ＲＬ电路的一些普遍特性，加深了加ＲＬ电路中的有关概念的理解，对教学有一定的参考价值。     

Weyl-Ordered Operator Moyal Bracket by Virtue of Method of Integral Within an Weyl Ordered Product of Operators

The Moyal bracket is an exemplification of Weyl's correspondence to formulate quantum mechancis in terms of Wigner function. Here we present a formalism of Weyl-ordered operator Moyal bracket by virtue of the method of integral within a Weyl ordered product of operators and the Weyl ordering operator formula.     

Affine A3^（1） N = 2 Monopole as the D Module and AiTine ADHMN Sheaf

A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse afiine rapidity parameters μ and μ^-1. The Dirac wave function scattering in this background also factorized respectively into the （anti）holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conformal affine massive field. We find explicit Nahm transformation matrix （Fourier Mukai transformation） between the Higgs YM BPS （fiat） bundles （1） modules） and the affinized blow up ADHMN twistors （perverse sheafs）. Thus we establish the algebra for the ＇t Hooft Hecke operators in the Hecke correspondence of the geometric Langlands program.     

A characterization of the Hamiltonian

The classical Hamiltonian ) of the very classical quantum harmonic oscillator, which is regarded as a germ of the most of what comes about in quantum mechanics, can be sublimed to an abstract operator in a separable Hilbert space. Having this done one may ask for a condition which would allow it to be identified among operators of a suitable class. This class is that corresponding to three diagonal matrices and the property which makes the action successful is a kind of diagonal invariance (up to change of basis) within the class in question.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.