中低能非全裸C离子与He原子的碰撞研究

采用反冲离子飞行时间-散射离子位置灵敏符合测量技术，测量了能量范围在0.7v₀—4.4v₀(v₀为玻尔速度)的碳离子C^q+(q=1—4)与He原子碰撞过程不同出射道靶原子的双电离与单电离截面比R，包括入射离子不损失电子(直接电离)的出射道(R_q,q),入射离子俘获一个电子的出射道(R_q,q-1)和入射离子损失一个电子的出射道(R_q,q+1)，并研究了R随入射C离子的能量及电荷态的变化关系.实验表明，对给定电荷态的入射离子，靶原子的双电离与单电离截面比R与出射道有很强的依赖关系，即R_q,q<R_q,q+1<R_q,q-1.直接电离出射道截面比R_q,q与入射离子电荷态几乎无关，而入射离子俘获一个电子的出射道和损失一个电子的出射道靶原子双电离与单电离截面比R_q,q-1和R_q,q+1却与入射离子电荷态有很强的关系.采用原子极化理论和电子屏蔽与反屏蔽作用对实验结果进行了解释. 关键词： 离子-原子碰撞 电离 截面比     

Lifting <Emphasis Type="Italic">q</Emphasis>-difference operators for Askey-Wilson polynomials and their weight function

We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H _n (x|q) of Rogers into the Askey-Wilson polynomials p _n (x; a, b, c, d|q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form ɛ _q (c _q D _q ) (where c _q are some constants), defined as Exton’s q-exponential function ɛ _q (z) in terms of the Askey-Wilson divided q-difference operator D _q . We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH _n (x|q) up to the weight function, associated with the Askey-Wilson polynomials p _n (x; a, b, c, d|q).     

Nonstandard U q(so3) and U q(so4): tensor products of representations, oscillator realizations and roots of unity

Nonstandard q-deformed algebras U _q(so₃) and U _q(so₄), which can be embedded into U _q(sl₃) and U _q(sl₄) and are coideals in them, are considered. It is shown how to multiply finite dimensional representations of U _q(so₃) when q is positive. Homomorphisms from U _q(so₃) and U _q(so₄) to the q-oscillator algebras are given. By making use of these homomorphisms, irreducible representations of U _q(so₃) and U _q(so₄) for q equal to a root of unity are obtained.     

Wavelet Transforms in Quantum Calculus

Abstract

This paper aims to study the q-wavelets and the q-wavelet transforms, using only the q-Jackson integrals and the q-cosine Fourier transform, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.     

Differences Among Three Deformed Oscillators

The differences among quon operators, q _a-math oscillator operators and q-deformed oscillator operators are pointed out. The q-deformed ocsillator and q _a-math oscillator are constructed in terms of q _q = 0 quon.     

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     

Some Special Functions of Noncommuting Variables

In this paper we deal with q-commuting variables x and y satisfying the relation xy = qyx + (q – 1)y ² with q complex, 0 < |q| < 1. We study various functional equations for q-exponentials and we deduce some identities for q-special functions involving q-commuting variab les.     

Representations of Multiparameter Quantum Groups

We construct representations of the quantum algebras U_q,q(gl(n)) and U_q,q(sl(n)) which are in duality with the multiparameter quantum groups GL_qq(n), SL_qq(n), respectively. These objects depend on n(n − 1)/2+ 1 deformation parameters q, q_ij (1 ≤ i< j ≤ n) which is the maximal possible number in the case of GL(n). The representations are labelled by n − 1 complex numbers r_i and are acting in the space of formal power series of n(n − 1)/2 non-commuting variables. These variables generate quantum flag manifolds of GL_qq(n), SL_qq(n). The case n = 3 is treated in more detail.

     

A new extended q-deformed KP hierarchy

Abstract

A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when q goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations.     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码,这族码具有参数［［n,n-2k,k+1］］_q,是q维量子系统上的码,q是任意素数的幂.这族码的最小距离达到了理论上限,因此,以码距来说,它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时,码都是存在的. 关键词： 量子Generalized Reed-Solomon码 量子MDS码 量子纠错码 量子信息     

Integrable Equations of the Form q t =L 1(x,t,q,q x,q xx )q xxx +L 2(x,t,q,q x,q xx )

Integrable equations of the form q _t =L ₁(x,t,q,q _x ,q _xx )q _xxx +L ₂(x,t,q,q _x ,q _xx ) are considered using linearization. A new type of integrable equations which are the generalization of the integrable equations of Fokas and Ibragimov and Shabat are given.     

A Method for q-Calculus

Abstract

We present a notation for q-calculus, which leads to a new method for computations and classifications of q-special functions. With this notation many formulas of q-calculus become very natural, and the q-analogues of many orthogonal polynomials and functions assume a very pleasant form reminding directly of their classical counterparts.

The first main topic of the method is the tilde operator, which is an involution operating on the parameters in a q-hypergeometric series. The second topic is the q-addition, which consists of the Ward–AlSalam q-addition invented by Ward 1936 [102, p. 256] and Al-Salam 1959 [5, p. 240], and the Hahn q-addition.

In contrast to the the Ward–AlSalam q-addition, the Hahn q-addition, compare [57, p. 362] is neither commutative nor associative, but on the other hand, it can be written as a finite product.

We will use the generating function technique by Rainville [76] to prove recurrences for q-Laguerre polynomials, which are q-analogues of results in [76]. We will also find q-analogues of Carlitz’ [26] operator expression for Laguerre polynomials. The notation for Cigler’s [37] operational calculus will be used when needed. As an application, q-analogues of bilinear generating formulas for Laguerre polynomials of Chatterjea [33, p. 57], [32, p. 88] will be found.     

Asymptotic Approximations in Quantum Calculus

Abstract

This paper aims to study the asymptotic approximation of some functions defined by the q-Jackson integrals, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical methods by giving their q-analogues. In particular, a q-analogue of the Watson’s lemma is discussed and new asymptotic expansions of the q?j _α Bessel function and of the q-complementary error function are established.     

An extension of the Borel-Weil construction to the quantum groupU q (n)

The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU _q(n). Thisq-BW construction uses a recursion procedure forU _q(n) in which the fiber of the bundle carries an irrep ofU _q(n–1)×U _q(1) with sections that are holomorphic functions in the homogeneous spaceU _q(n)/U _q(n–1)×U _q(1). Explicit results are obtained for theU _q(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007     

q-conformally covariant q-Minkowski space-time and invariant equations

We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original.     

q-Generalized Euler numbers and polynomials

Recently, B. A. Kupershmidt constructed reflection symmetries of q-Bernoulli polynomials (see [12]). In this paper, we study new q-extensions of Euler numbers and polynomials by using the method of Kupershmidt. We also investigate the properties of symmetries of these q-Euler polynomials by using q-derivatives and q-integrals.     

增加光子奇偶q相干态的高阶压缩效应

通过数值计算研究了增加光子奇q相干态a_q^+m|α>_q^o和增加光子偶q相干态a_q^+m|α>_q^e的高阶压缩效应.结果表明:当q较小时,态a_q^+m|α>_q^o和a_q^+m|α>_q^e都能呈现出强烈的奇次方阶压缩效应,但无偶次方阶压缩效应,而且奇次方阶压缩随m的增大而增强.当m=0时a_q^+m|α>_q^o和a_q^+m|α>_q^e为光场振幅偶次幂的最小测不准态,但当m≠0时它们不是光场振幅偶次幂的最小测不准态.     

Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Whereas the first part of this paper dealt with the relaxation in the β-regime, this part investigates the final relaxation (α-relaxation) of a simulated polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of ideal mode-coupling theory (MCT). The temperature range covers the onset of a two-step relaxation behaviour down to a temperature merely 2% above . We monitor the incoherent intermediate scattering function as well as the coherent intermediate scattering function of both a single chain and the melt over a wide range of wave numbers q. Upon approaching the coherent α-relaxation time of the melt increases strongly close to the maximum q _max of the collective static structure factor S_q and roughly follows the shape of S_q for q q _max. For smaller q-values corresponding to the radius of gyration the relaxation time exhibits another maximum. The temperature dependence of the relaxation times is well described by a power law with a q-dependent exponent in an intermediate temperature range. Deviations are found very close to and far above , the onset of which depends on q. The time-temperature superposition principle of MCT is clearly borne out in the whole range of reciprocal vectors. An analysis of the α-decay by the Kohlrausch-Williams-Watts (KWW) function reveals that the collective KWW stretching exponent and KWW relaxation time show a modulation with S_q. Furthermore, both incoherent and coherent KWW times approach the large-q prediction of MCT already for q > q _max. At small q, a q^-3 power law is found for the coherent chain KWW times similar to that of recent experiments.