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Xiaoxia Wang

Publications and source records attributed to Xiaoxia Wang.

36 records · Page 2Linked to original sources
arXiv2021

Some q-supercongruences on double and triple sums

In this paper, we investigate a number of $q$-supercongruences on double and triple sums. By means of a lemma devised by El Bachraoui and its generalization, we transform some $q$-supercongruences on double and triple sums into the $q$-supercongruences of the square and cube of truncated basic hypergeometric series.Our main tools still involve the `creative microscoping' method introduced by Guo and Zudilin, a lemma designed by Guo and Li and the Chinese remainder theorem.

math.NT↗
arXiv2021

Some q-supercongruences from Rahman's summation formula

Inspired by the recent work on $q$-congruences and the quadratic summation formula of Rahman, we provide some new $q$-supercongruences. By taking $q\to 1$ in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hamme's (G.2) supercongruence for $p\equiv 1 \pmod 4$. We also formulate some related challenging conjectures on supercongruences and $q$-supercongruences.

math.CO↗
arXiv2020

$q$-Supercongruences from the $q$-Saalschütz identity

In terms of the $q$-Saalschütz identity and the Chinese remainder theorem for coprime polynomials, we establish some $q$-supercongruences modulo the third power of a cyclotomic polynomial. In particular, we give a $q$-analogue of a formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773--808].

math.CO↗
arXiv2020

q-analogues of the G.2 Supercongruence of Van Hamme

Motivated by the recent research of congruences and $q$-congruences, we provide two different $q$-analogues of the (G.2) supercongruence of Van Hamme through the `creative microscoping' method, which was devised by Guo and Zudilin. It is a remarkable fact that this is the first time to give direct $q$-analogues of (G.2). In addition, we propose a conjecture related to Swisher's Dwork-type supercongruence (G.3).

math.NT↗
arXiv2018

Development and validation of Critical Thinking Disposition Inventory for Chinese medical college students (CTDI-M)

PURPOSE: Critical thinkers in medical context must be not only "able" but also "willing" to think critically. To develop and conduct psychometric testing of Critical Thinking Disposition Inventory which measure the critical thinking disposition of Chinese medical college students. METHODS: The study was conducted in two stages: (a) item generation and exploratory factor analysis (EFA) and (b) testing of psychometric properties (construct validity, split-half reliability and Cronbach's alpha, and test-retest reliability. The subjects were composed of 441 undergraduate medical and nursing students from a medical university in China. Test-retest reliability of the instrument was determined at two-week interval. Data was analyzed with SPSS13.0. RESULTS: Preliminary 264 items were obtained using an open-ended questionnaire; from which 61 items were reviewed through half open-ended questionnaire, and finally 18 items were chosen. Eighteen final items were sorted into 3 factors, which were identified as "Open-mindedness ", "Systematicity/analyticity" and "Truth seeking". The cumulative percent of variance was 57.66%. The Cronbach's alpha was 0.924 and the factors' alphas ranged from 0.824-0.862. Correlational analysis indicated moderate to high correlations between the subscales and total scores of the CTDI-CM. Our results indicated that open-mindedness and systematicity/analyticity were higher for medical students than nursing students. CONCLUSIONS: This study conducted in a Chinese medical college student population demonstrated a reliable and valid instrument for clinical thinking disposition, which measured motivation and cognitive components. The effect of enrollment year and major on the profiles of critical thinking dispositions was identified, emphasizing the importance of applying specialized teaching to students of different majors.

physics.ed-ph↗
arXiv2018

Recursion formulas of q-Appell functions

Recently, Opps, Saad and Srivastava gave the recursion formulas of Appell's function F2. The first author of this paper then established the recursion formulas for Appell functions F1, F2, F3 and F4 by the contiguous relations of hypergeometric series. In this paper, the authors will present the recursion formulas for q-Appell functions $Φ^{(1)}, Φ^{(2)}, Φ^{(3)}$ and $Φ^{(4)}$ as the q-analogies of F1, F2, F3 and F4's relations.

math.CO↗
arXiv2017

Evaluations of series of the $q$-Watson, $q$-Dixon, and $q$-Whipple type

Using $q$-series identities and series rearrangement, we establish several extensions of $q$-Watson formulas with two extra integer parameters. Then they and Sears' transformation formula are utilized to derive some generalizations of $q$-Dixon formulas and $q$-Whipple formulas with two extra integer parameters. As special cases of these results, many interesting evaluations of series of $q$-Watson,$q$-Dixon, and $q$-Whipple type are displayed.

math.CA↗
arXiv2015

Comments on "New generating relations for products of two Laguerre polynomials"

By utilizing a two-dimensional extension of a very general series transform given by Bailey, Exton [Indian J. pure appl. Math. 24 (6) (1993), 401-408] deduced a very general double generating relation of a product of a pair of Laguerre polynomials and obtained a number of useful relations with elementary functions, Bessel functions, Hermite polynomials and single series expansions of pairs of Laguerre polynomials. Unfortunately, some of the results given by Exon contain errors and thus this is the aim of this short note to provide the corrected form of these results.

math.CA↗
arXiv2015

New Laplace transforms for the generalized hypergeometric functions 2F2 and 3F3

Motivated by the new Laplace transforms for the Kummer's confluent hypergeometric functions $_1F_1$ obtained recently by Kim et al. [Math $\&$ Comput. Modelling, 55 (2012), pp. 1068--1071], the authors aim is to establish so far unknown Laplace transforms of rather general case of generalized hypergeometric functions $_2F_2(x)$ and $_3F_3(x)$ by employing extensions of classical summation theorems for the series $_2F_1$ and $_3F_2$ obtained recently by Kim et al. [Int. J. Math. Math. Sci., 309503, 26 pages, 2010]. Certain known results obtained earlier by Kim et al. follow cases of our main findings.

math.CA↗
arXiv2015

Er3+-doped Na0.5Bi0.5TiO3 Ferroelectric Thin Films with Enhanced Electrical Properties and Strong Green Up-conversion Luminescence

Ferroelectric materials with up-conversion luminescence (UCL) properties have potential opto-electric applications for display and sensing etc. Here, we demonstrate strong green UCL and enhanced electrical properties in Er3+-doped Na0.5Bi0.5TiO3 thin films. The thin films are prepared via using a modified chemical solution deposition method. These thin films are phase-pure and crystallized in perovskite structure. The largest remnant polarization (Pr) and highest dielectric constant are obtained from Na0.5Bi0.49Er0.01TiO3 thin films, and their values are 0.22 C/m2 and 1166, respectively. Meanwhile, strong green UCL at 525 nm and 548 nm are observed in Er3+-doped thin films. They are attributed to 2H11/2 to 4I15/2 and 4S3/2 to 4I15/2 transitions of Er3+ ions. These thin films have potentials in optoelectrical device applications.

cond-mat.mtrl-sci↗
arXiv2014

Generalizations of Andrews' curious identities

According to the method of series rearrangement, we establish two generalizations of Andrews' curious $q$-series identity with an extra integer parameter. The limiting cases of them produce two extensions of Andrews' curious $_3F_2(\frac{3}{4})$-series identity with an additional integer parameter. Meanwhile, several related results are also given.

math.CO↗
arXiv2013

Series expansions for $1/π^m$ and $π^m$

By means of the telescoping method, we establish two sum- mation formulas on sine function. As the special cases of them, several interesting series expansions for $1/π^m$ and $π^m$.

math.CO↗
arXiv2013

A new proof of Andrews' conjecture for $_4ϕ_3$-series

In terms of Sear's transformation formula for $_4ϕ_3$-series, we give new proofs of a summation formula for ${_4ϕ_3}$-series due to Andrews [2] and another summation formula for${_4ϕ_3}$-series conjectured in the same paper. Meanwhile, other several related results are also derived.

math.CO↗
arXiv2013

Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral

By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's $_6ψ_6$-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations of Ramanujan's reciprocity formula. Then we utilize also Milne's identity to deduce a multi-variable generalization of the Askey-Wilson integral.

math.CA↗