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).     

q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients

A purpose of this paper is to present a systemic study of some families of multiple q-Bernoulli numbers and polynomials by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤ _p . Moreover, the study of these higher-order q-Bernoulli numbers and polynomials implies some interesting q-analogs of Stirling number identities. This paper is supported by Jangjeon Research Institute for Mathematical Science (JRIMS-10R-2001).     

Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on ℤ p

The objective of the paper is to indicate a symmetry of the multivariate p-adic invariant integral on ℤ _p , which leads to a relation between the power sum polynomials and higher-order Euler polynomials. The present research has been conducted under the Research Grant of Kwangwoon University in 2008.     

On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers

In this paper, we construct a twisted q-partial zeta function and some twisted two-variable q-L-functions that interpolate q-Bernoulli numbers, β _n,ξ ^(h) (q), and Bernoulli polynomials, β _n,x,ξ ^(h) (x, q), respectively, at negative integers. Using these functions, we prove the existence of a p-adic interpolation function that interpolates the q-generalized polynomials β _n,x,ξ ^(h) (x, q) at negative integers. Consequently, we define a p-adic twisted q-L-function which is a solution of a question of Kim et al. This paper was supported by the Scientific Research Project Administration Akdeniz University.     

Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤ p

A systemic study of some families of q-Euler numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic p-adic integral on ? _p . The study of these higher-order q-Euler numbers and polynomials yields an interesting q-analog of identities for Stirling numbers.     

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.     

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.     

q-Fuzzy Spheres and Quantum Differentials on Bq[SU2] and Uq(su2)

We provide a new unified construction of the two-parameter Podleś two-spheres as characterised by a projector e with trace _q (e) = 1 + λ. In our formulation the limit in which q → 1 with λ fixed is the fuzzy sphere, while the limit λ → 0 with q fixed is the standard q-deformed sphere. We show further that the non-standard Podleś spheres arise geometrically as ‘constant time slices’ of the unit hyperboloid in q-Minkowski space viewed as the braided group B _q [SU ₂]. Their localisations are then isomorphic to quotients of U _q (su ₂) at fixed values of the q-Casimir precisely q-deforming the fuzzy case. We also use transmutation and twisting theory to introduce a C_q[G_\mathbb C]{C_q[G_\mathbb {C}]} -covariant differential calculus on general B _q [G] and U _q (g), with Ω(B _q [SU ₂]) and Ω(U _q (su ₂) given in detail. To complete the picture, we show how the covariant calculus on the 3D bicrossproduct spacetime arises from Ω(C _q [SU ₂]) prior to twisting.     

A note on p-adic Euler measure on ℤp

In this paper, we give some p-adic approximation of E _n,x for certain n. Finally we will treat p-adic l-function of Kubota-Leopoldt’s type Euler numbers and p-adic measure for Euler numbers.     

On the von Staudt-Clausen theorem for q-Euler numbers

The q-Euler numbers and polynomials were recently constructed [T. Kim, “The Modified q-Euler Numbers and Polynomials,” Adv. Stud. Contemp. Math., 16, 161–170 (2008)]. These q-Euler numbers and polynomials have interesting properties. In this paper, we prove a theorem of the von Staudt-Clausen type for q-Euler numbers; namely, we prove that the q-Euler numbers are p-adic integers. Finally, we prove Kummer-type congruences for the q-Euler numbers.     

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure (p = 1.00) and weakly diluted (p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.     

Contribution of three-electron diagrams of two-photon exchange to the energy of 2 s , 2 p 1/2, and 2 p 3/2 states of Li-like multiply charged ions

The contribution of three-electron diagrams of two-photon exchange to the energy of 2s, 2p _1/2, and 2p _3/2 states of Li-like ions is calculated. The consistent quantum-electrodynamic calculation is performed for the nuclear charge Z varying over a wide range with the correction for the finite size of the nucleus taken into account. All the contributions to the energy of the 2p _1/2−2s transition in Li-like ions with Z≥18 calculated to date are collected. __________ Translated from Optika i Spektroskopiya, Vol. 92, No. 3, 2002, pp. 375–384. Original Russian Text Copyright ? 2002 by Sysak, Erokhin, Shabaev.     

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let λ _d (p) be the p monomer-dimer entropy on the d-dimensional integer lattice ℤ ^d , where p∈[0,1] is the dimer density. We give upper and lower bounds for λ _d (p) in terms of expressions involving λ _d−1(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of ℤ ^d is bounded above by λ _d (p). We compute the first three terms in the formal asymptotic expansion of λ _d (p) in powers of  \frac1d\frac{1}{d}. We prove that the lower asymptotic matching conjecture is satisfied for λ _d (p). Converted to a power series in p, our “formal” expansion shows remarkable validity in low dimensions, d=1,2,3, in which dimensions we give some numerical studies.     

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).     

Electrical and photovoltaic properties of Cd1? x Zn x S/ p -GaAs heterojunctions

Cd_1−x Zn _x S/p-GaAs heterojunctions for solar cell applications have been prepared by growing single crystal Cd_1−x Zn _x S epitaxial layers on (111)GaAs substrates through a vapour phase chemical transport method using the close-spaced geometry and H₂ as a transport agent. Electrical and photovoltaic properties of the heterojunctions have been investigated and discussed in connection with the main features of the growth technique. AM1 power conversion efficiencies up to 6.2% have been measured and possible improvements have been examined.     

Generalized q-Hermite Polynomials

We consider two operators A and A ⁺ in a Hilbert space of functions on the exponential lattice , where 0<q<1. The operators are formal adjoints of each other and depend on a real parameter . We show how these operators lead to an essentially unique symmetric ground state ψ₀ and that A and A ⁺ are ladder operators for the sequence . The sequence (ψ _n /ψ₀) is shown to be a family of orthogonal polynomials, which we identify as symmetrized q-Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When γ=0 the polynomials are the discrete q-Hermite polynomials of type II, studied in several papers on q-quantum mechanics. Received: 6 December 1999 / Accepted: 21 May 2001     

Measurement of electron-muon correlations from semi-leptonic D decay in 200 GeV p + p collisions at RHIC-PHENIX

Charm production is a valuable probe of the early stages of a heavy ion collision. Correlated electron-muon pairs are a signature of semi-leptonic D decays, and a measurement of D mesons provides information on charm quark energy loss in the hot medium. The energy loss of heavy quarks is still not fully understood, so it is vital to investigate different decay channels of charm mesons to better understand this process. Measurements of electron-muon pairs suffer less from background than e ⁺ e ⁻ or μ⁺μ⁻ pairs since neither direct lepton production nor resonance decays produce this type of correlated signal. Another advantage is that because electrons are measured in the central arms and muons are measured in the forward region in PHENIX, open charm can be probed in a rapidity region different from previous dilepton measurements. Studying electron-muon pairs in p + p collisions provides an important baseline for the study of these processes in d + Au and Au + Au collisions. The data in this analysis was obtained during the 2006 RHIC run of p + p collisions at 200 GeV. The current status of this analysis will be presented.     

Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ₂ (del Rey and Rodriguez Sánchez in Appl. Math. Comput., 2011, doi:). In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤ _p . For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata. More specifically, for any given values (from any fixed field ℤ _p ) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells. As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ₂ and ℤ₃.     

Quantum Geometry of Algebra Factorisations¶and Coalgebra Bundles

We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices M ₂(ℂ)=ℂℤ₂·ℂℤ₂. We also further extend the coalgebra version of theory introduced previously, to include frame resolutions and corresponding covariant derivatives and torsions. As an example, we construct q-monopoles on all the Podleś quantum spheres S ² _q,s . Received: 25 September 1998 / Accepted: 23 February 2000