New Operator Identities and Integration Formulas Regarding to Hermite Polynomials Obtained via the Operator Ordering Method

Based on the technique of integration within an ordered product (IWOP) of operators we show that the operator ordering method can lead us to derive new operator identities and new integration formulas regarding to Hermite polynomials. Work supported by specialized research fund for the doctoral progress of higher education of China.     

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two－Variable Hermite Polynomials

Based on the technique of integration within an ordered product of operators,we derive new bosonic operators‘ ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials Hm,n,and vice versa,In doing so,some concise normally (antinormally)ordering operator identities,such as a^ma^n=:Hm,n(a,a):,a^na^m=(-i)^m n:Hm,n(ia,ia):are obtained.     

Application of a ‘Jacobi Identity’ for Vertex Operator Algebras to Zeta Values and Differential Operators

We explain how to use a certain new Jacobi identity for vertex operator algebras, announced in a previous paper (math.QA/9909178), to interpret and generalize S. Bloch's recent work relating values of the Riemann zeta function at negative integers to a certain Lie algebra of operators.     

Mutual transformations between the P–Q,Q–P,and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.     

Comparison Theorems for Eigenvalues of Elliptic Operators and the Generalized Pólya Conjecture

We establish comparison theorems for eigenvalues between higher order elliptic equations on compact manifolds with boundary. As an application, it follows that if the Pólya conjecture is true then so is the generalized Pólya conjecture proposed by Ku et al. (J Differ Equ 97:127–139, 1992). We also obtain new lower bound for the eigenvalues of higher order elliptic equations on bounded domains in a Euclidean space.     

The primary and secondary acceptors in bacterial photosynthesis III. Characterization of the quinone radicals Q A − ⋅ and Q B − ⋅ by EPR and ENDOR

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques were used to investigate the electronic structure of the primary (Q _A ^?? ) and secondary (Q _B ^?? ) ubiquinone electron acceptors in reaction centers (RCs) of the photosynthetic bacteriumRhodobacter sphaeroides. To reduce the EPR linewidth, the high-spin Fe²⁺ present in native RCs was replaced by diamagnetic Zn²⁺. Experiments were performed both on frozen solutions and single crystals at microwave frequencies of 9, 35 and 94 GHz. Differences in the EPR/ENDOR spectra were observed for Q _A ^?? and Q _B ^?? , which are attributed to different environments of the quinones in the RC. The differences exhibited themselves in: (i) the g-tensors, (ii) the¹⁷O and¹³C hyperfine coupling (hfc) constants of the quinones labeled at the carbonyl group, (iii) the¹H-hfcs of the quinone ring and (iv) the exchangeable protons hydrogen bonded to the carbonyl oxygens. From these results and from H/D exchange experiments, the following conclusions were drawn: both Q _A ^?? and Q _B ^?? have at least two hydrogen bonds of different strengths to the carbonyl oxygens. The hydrogen bonds for Q _A ^?? are stronger and more asymmetric than for Q _B ^?? . For Q _A ^?? the stronger bond (to O₄) was assigned to His(M219) and the weaker (to O₁) to Ala(M260). For Q _B ^?? the stronger bond (to O₄) was assigned to His(L190), with several weaker bonds (to O₁) to Ser(L223), Ile(224) and Gly(L225). From the temperature dependence of the hfcs of the exchangeable protons some dynamic properties of the RC were deduced. Hfcs with more distant nitrogens were observed by electron spin echo envelope modulation (ESEEM). For Q _A ^?? they were assigned to N_δ of His(M219) and to the peptide backbone nitrogen of Ala(M260) and for Q _B ^?? to N_δ of His(L190). These interactions indicate the extent of the electron wave function, which is important for the understanding of the electron transfer mechanism. Based on the magnetic resonance results, the function of the quinone acceptors in the reaction center is discussed.     

Cartan–Weyl Dirac and Laplacian Operators,Brownian Motions: The Quantum Potential and Scalar Curvature,Maxwell’s and Dirac-Hestenes Equations,and Supersymmetric Systems

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q     

The surface passivation of Cd1−xZnxTe as to ZnS thickness and pre-heating

The dielectric material of ZnS is used for the surface passivation of the CdZnTe. The surface morphology and the optical property of ZnS/CdZnTe structure according to variation of ZnS thickness is analyzed by AFM and low temperature photoluminescence (PL) measurement, respectively. As the results, it shows that the change of PL spectra of CdZnTe as to ZnS thickness indicates the significant alteration of electronic states near the interface of ZnS/CdZnTe. From the result of improvement for optical property of CdZnTe at ZnS thickness of 200 nm, it is known that the thickness is an essential condition for the passivation of CdZnTe. Also, the measurement of C–V for the MIS structure of Au/ZnS/CdZnTe is done to study the interface trap state of ZnS/CdZnTe structure as to pre-heating of CdZnTe. Therefore, it is shown that the pre-heating of CdZnTe is an essential process of the passivation in order to reduce the trap state. Seventy-seven Kelvin PL measurement is studied for the pre-heating condition of the CdZnTe surface. It is known that the optimum condition of pre-heating temperature and time is 200 °C and 60 min, respectively. And the result of I–V measurement shows that the surface leakage current of CdZnTe is considerably reduced after the passivation of ZnS with these conditions. It means that the electronic property of the interface should be improved after the passivation process.     

The main properties and peculiarities of the Earth’s motion relative to the center of mass

The methods of theoretical and celestial mechanics and mathematical statistics have been used to prove that the Earth’s motion relative to the center of mass, the polar wobble, in the principal approximation is a combination of two circumferences with a slow trend in the mean position corresponding to the annual and Chandler components. It has been established that the parameters (amplitude and phase shift) of the annual wobble are stable, while those of the Chandler component are less stable and undergo significant variations over the observed time intervals. It has been proven that the behavior of these polar motion parameters is attributable to the gravitational-tidal mechanisms of their excitation.     

The Lp-Theory of the Spectral Shift Function,¶the Wegner Estimate, and the Integrated Density¶of States for Some Random Operators

We develop the L ^p -theory of the spectral shift function, for p≥ 1, applicable to pairs of self-adjoint operators whose difference is in the trace ideal ℐ _p , for $0 < p≤ 1. This result is a key ingredient of a new, short proof of the Wegner estimate applicable to a wide variety of additive and multiplicative random perturbations of deterministic background operators. The proof yields the correct volume dependence of the upper bound. This implies the local H?lder continuity of the integrated density of states at energies in the unperturbed spectral gap. Under an additional condition of the single-site potential, local H?lder continuity is proved at all energies. This new Wegner estimate, together with other, standard results, establishes exponential localization for a new family of models for additive and multiplicative perturbations. Received: 27 July 2000 / Accepted: 1 November 2000     

The adoption and mechanism of KIO4 for redox-equilibrated stabilization of FeO4 2− as an equalizer in water

The inherent thermodynamic instability of FeO₄ ²⁻ in water restricts its applications in water treatment, battery, and organic synthesis. The objective of this paper was to research and develop an additive for stabilization and mechanism of aqueous FeO₄ ²⁻ solution on the basis of a choice of the redox equilibration. In this study, it was found that FeO₄ ²⁻ in water was stabilized by the right match and adoption of KIO₄ called an equalizer. The redox thermodynamic analysis and dynamic experimental results show that the adoption of KIO₄ equalizer greatly increased lifetime of FeO₄ ²⁻ in water by orders of magnitude. The stabilization mechanism is attributed to occur via the effect of redox equilibrium of the FeO₄ ²⁻ and the IO₄ ⁻ species, as well as the formation of an oxidizing chemical environment. This study opens up possibilities for stabilization of solid ferrate compounds, for example, for use in the water treatment and super-iron battery.

     

The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch–Gordan Coefficients

We discuss the procedure of different partitions in the finite set of N integer numbers and construct generic formulas for a bijective map of real numbers s _y , where y = 1, 2,…, N, N = \( \underset{k=1}{\overset{n}{\varPi}}{X}_k, \) and X _k are positive integers, onto the set of numbers s(y(x ₁, x ₂,…, x _n )). We give the functions used to present the bijective map, namely, y(x ₁, x ₂, …, x _n ) and x _k (y) in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of “hidden gates” for a single qudit is proposed. We obtain the entropic-information inequalities for an arbitrary finite set of real numbers and consider the inequalities for arbitrary Clebsch–Gordan coefficients as an example of the found relations for real numbers.     

Long Range Scattering and Modified Wave Operators for the Maxwell-Schrödinger System I. The Case of Vanishing Asymptotic Magnetic Field

 We study the theory of scattering for the Maxwell-Schr?dinger system in space dimension 3, in the Coulomb gauge. In the special case of vanishing asymptotic magnetic field, we prove the existence of modified wave operators for that system with no size restriction on the Schr?dinger data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators. The method consists in partially solving the Maxwell equations for the potentials, substituting the result into the Schr?dinger equation, which then becomes both nonlinear and nonlocal in time, and treating the latter by the method previously used for the Hartree equation and for the Wave-Schr?dinger system. Received: 1 August 2002 / Accepted: 9 December 2002 Published online: 14 March 2003 RID="⋆" ID="⋆" Unité Mixte de Recherche (CNRS) UMR 8627 Communicated by P. Constantin     

New Bäcklund transformations for the third and fourth Painlevé equations to equations of second order and higher degree

We give new Bäcklund transformations for the third and fourth Painlevé equations, to equations of second order and higher degree.     

A New Formula for the Spectra of Axial Symmetric and Transition Nuclei and a Quantity to Identify the Nuclear γ Deformation

The analytical limits of a speacial potential of the Bohr Hamiltonian are discussed in detail.A new formula for the axial symmetric,triakial deformed and the γ-soft nuclei is presented.The nuclear γ deformation can be identified with this formula.The calculations of some nuclear yrast lines seproduce the experiment al results very Well,and the degree of the nuclear γ deformation is obtained.