Perturbation foundation of <Emphasis Type="Italic">q</Emphasis>-deformed dynamics

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians; one originates from the perturbation expansion of the potential in one configuration space, the other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved. The first is Equivalence Theorem I: Perturbation expressions of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. The general Equivalence Theorem II is: for any potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied. Received: 6 September 2002 / Revised version: 21 October 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: jzzhang@physik.uni-kl.de, jzzhang@ecust.edu.cn     

<Emphasis Type="Italic">q</Emphasis>-deformed Coherent States on a Circle

Coherent states for the q-deformed quantum mechanics on a circle are introduced.     

Exact Results for Topological Strings on Resolved <Emphasis Type="Italic">Y</Emphasis><Superscript><Emphasis Type="Italic"> p</Emphasis>,<Emphasis Type="Italic">q</Emphasis></Superscript> Singularities

We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y ^p,q manifolds and give rise via M-theory compactification to SU(p) gauge theories on . As an application we present a detailed study of the local case and compute open and closed genus zero Gromov-Witten invariants of the orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes. The mirror curve in this case is the spectral curve of the relativistic A ₁ Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y ^p,q geometries.     

A <Emphasis Type="Italic">q</Emphasis>-deformed particle algebra with a unique <Emphasis Type="Italic">d</Emphasis>-dimensional representation

We present an algebra generated by a single pair of creation and annihilation operators b and b*. We prove that the algebra has a unique d-dimensional representation. Physically this algebra corresponds to a system where there are at most d − 1 particles in a state with otherwise same quantum numbers.     

<Emphasis Type="Italic">q</Emphasis>-plane-wave solutions of <Emphasis Type="Italic">q</Emphasis>-Weyl gravity

The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given. The text was submitted by the authors in English.     

Identities involving values of Bernstein, <Emphasis Type="Italic">q</Emphasis>-Bernoulli,and <Emphasis Type="Italic">q</Emphasis>-Euler polynomials

In this paper, we give relations involving values of q-Bernoulli, q-Euler, and Bernstein polynomials. Using these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler, and Bernstein polynomials.     

Thermal Radiation Laws of a <Emphasis Type="Italic">q</Emphasis>-deformed Boson System in <Emphasis Type="Italic">m</Emphasis> Dimensions

Within the theoretical framework of multidimensional space and q bosons, we generalize our hypothesis of regarding the CMBR as the radiation of q bosons, and investigate the thermal radiation laws of a q boson system in m dimensions. Utilizing the new radiation laws, we make a numerical calculation and the results show that these new laws have some special features. We consider that this work may provide more insight into the theory of q bosons and the study on the CMBR.     

A note on <Emphasis Type="Italic">q</Emphasis>-Bernstein polynomials

Recently, Simsek-Acikgoz [17] and Kim-Jang-Yi [9] have studied the q-extension of Bernstein polynomials. In the present paper, we suggest q-extensions of Bernstein polynomials of degree n which differ from the q-Bernstein polynomials of Simsek-Acikgoz [17] and Kim-Jang-Yi [9]. Using these q-Bernstein polynomials, we derive fermionic p-adic integral representations of several q-Bernstein-type polynomials. Finally, we investigate identities between q-Bernstein polynomials and q-Euler numbers.     

Free <Emphasis Type="Italic">q</Emphasis>-deformed relativistic wave equations by representation theory

In a representation theoretic approach a free q-relativistic wave equation must have the property that the space of solutions is an irreducible representation of the q-Poincaré algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-gamma matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the q-Maxwell equations are computed explicitly.Received: 8 May 2002, Revised: 14 July 2003, Published online: 29 August 2003     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Cosmology from <Emphasis Type="Italic">q</Emphasis>-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by q ^(a) with label a), we have obtained, in the low-energy limit, a particular type of f(R) model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological f(R) models on physical grounds. The text was submitted by the authors in English.     

On the multiple <Emphasis Type="Italic">q</Emphasis>-Genocchi and Euler numbers

The purpose of this paper is to present a systematic study of some families of multiple q-Genocchi and Euler numbers by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤ _p . The investigation of these q-Genocchi numbers and polynomials of higher order leads to interesting identities related to these objects. The results of the present paper cover earlier results concerning ordinary q-Genocchi numbers and polynomials. This paper is supported by Jangjeon Research Institute for Mathematical Science (JRIMS-11R-2007).     

Polynomial Realization of <Emphasis Type="Italic">s</Emphasis>l<Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2) and Fusion Rules at Exceptional Values of <Emphasis Type="Italic">q</Emphasis>

Representations of the sℓ_q(2) algebra are constructed in the space of polynomials of real (complex) variable for q^N=1. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated.     

The <Emphasis Type="Italic">q</Emphasis>-boson-fermion realizations of the quantum superalgebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">osp</Emphasis>(1/2))

We show that our construction of realizations for algebras and quantum algebras can be generalized to quantum superalgebras too. We studyan example of quantum superalgebra U _q (osp(1/2)) and give the boson-fermion realization with respect to one pair of q-boson operators and one pair of fermions.     

Analysis of the spectrum of the Zn-like Kr VII ion: Highly excited 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">d</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">s</Emphasis> configurations

The spectrum of the Zn-like Kr VII ion, excited in a capillary discharge and recorded with a high resolution in the wavelength range of 300–1000 Å, was studied. Previously performed identification of the transitions from the levels of the 4s4f, 4s5s, 4s5p, and 4s5d configurations is confirmed and extended, and the energies of these levels are specified. The (4p ²+4s4d)?4p4d and (4p ²+4s5s)?4p5s transitions are identified for the first time, and the energies of all the levels of the 4p4d and 4p5s configurations are determined. The results of the analysis performed are confirmed by semiempirical calculations in terms of the Hartree-Fock method. These results are also shown to conform to the experimental data obtained for lighter ions of the Zn I isoelectronic sequence.     

The multi-dimensional <Emphasis Type="Italic">q</Emphasis>-deformed bosonic Newton oscillator and its inhomogeneous quantum invariance group

We obtain the inhomogeneous invariance quantum group for the multi-dimensional q-deformed bosonic Newton oscillator algebra. The homogenous part of this quantum group is given by the multiparameter quantum group $ GL_{X;q_{ij} } $ GL_{X;q_{ij} } of Schirrmacher where q _ij’s take some special values. We find the R-matrix which gives the non-commuting structure of the quantum group for the two dimensional case.     

Ferromagnetism and ferroelectricity in Eu<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = <Emphasis Type="Italic">O</Emphasis>, <Emphasis Type="Italic">S</Emphasis>): pressure effects

Ferromagnetism and ferroelectricity in Eu monochalcogenides have been investigated by ab initio density functional theory in the DFT+U approach. Exchange interaction parameters and Curie temperatures under pressure are studied and discussed using Heisenberg Hamiltonian with first and second-nearest-neighbor interactions. The calculations showed that the hydrostatic pressure perfectly improves the Curie temperature (EuO: T _C = 175 K; EuS: T _C = 33.8 K) and in the other hand it cannot induce the spontaneous polarization (P _s ). The effect of uniaxial and biaxial pressure is also studied. Although the uniaxial strains slightly increases the Curie temperature, it ensures the ferrolectricity in these systems by producing a spontaneous polarization of the order of P _s (EuO) = 57.50 μC/cm² and P _s (EuS) = 42.86 μC/cm² with pressures of 5% and 4%, respectively. The search for new model systems is a necessity to better understand the physics related to multiferroïc materials and to consider possible applications.     

Multiple two-variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">q-L</Emphasis>-function and its behavior at <Emphasis Type="Italic">s</Emphasis> = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

Energy dependence of Cronin momentum in saturation model for <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">A</Emphasis> and <Emphasis Type="Italic">A</Emphasis> + <Emphasis Type="Italic">A</Emphasis> collisions

The energy dependence of the Cronin momentum for p + A and A + A collisions in the saturation model are calculated. This dependence is consistent with simple dimensional considerations and can be used to test the validity of the saturation model. It gives the possibility to distinguish the different variants of the saturation model with precise experimental data and to measure the x dependence of the saturation momentum.