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Let $\mathbb {F}_{q}$ be the finite field of $q$ elements. In this paper we obtain bounds on the following counting problem: given a polynomial $f(x)\in \mathbb {F}_{q} [x]$ of degree $k+m$ and a non-negative integer $r$ , count the number of polynomials $g(x)\in \mathbb {F}_{q} [x]$ of degree at most $k-1$ such that $f(x)+g(x)$ has exactly $r$ roots in $\mathbb {F}_{q}$. Previously, explicit formulas were known only for the cases $m=0, 1, 2$. As an application, we obtain an asymptotic formula on the list size of the standard Reed-Solomon code $[q, k, q-k+1]_{q}$. [ABSTRACT FROM AUTHOR]

Study Design: Cross-sectional study.Objective: To investigate the equivalence of electronic and paper version of self-report questionnaires for the assessment of disability, pain, fear of movement, depression, and physical activity of patients with chronic low back pain (LBP).Summary Of Background Data: Paper and electronic versions of self-report questionnaires are commonly used for assessment of patients with LBP. However, the equivalence of self-report questionnaires commonly used for assessment of patients with chronic LBP remains unclear.Methods: Seventy-nine individuals with chronic LBP seeking physiotherapy care were recruited. Participants attended the clinic twice with an interval of 1 week and completed the self-reported questionnaires in a random order. The following questionnaires were administered: Roland Morris Disability Questionnaire (RMDQ); 11-point numerical rating scale (NRS); Tampa Scale for Kinesiophobia (TSK); Center for Epidemiological Studies-Depression (CES-D), and Baecke Habitual Physical Activity Questionnaire (BPAQ). To investigate the equivalence between the two questionnaire versions, intraclass correlation coefficient with 95% confidence interval and Bland-Altman plotting was used.Results: The paper and electronic versions of the RMDQ, TSK, and CES-D showed good reliability and the showed moderate reliability. In contrast, the NRS showed poor reliability between the electronic and paper versions.Conclusion: Our findings support that the electronic version of the RMDQ, TSK, CES-D, and BPAQ can be administered in clinical and research settings for assessment of patients with chronic LBP. Nevertheless, electronic version of the NRS for assessment of pain intensity should not be used interchangeably in clinical practice in patients with chronic LBP.Level Of Evidence: 3. [ABSTRACT FROM AUTHOR]

This article describes the use of microfluidic paper-based analytical devices (μPADs) to perform quantitative chemical assays with internal standards. MicroPADs are well-suited for colorimetric biochemical assays; however, errors can be introduced from the background color of the paper due to batch difference and age, and from color measurement devices. To reduce errors from these sources, a series of standard analyte solutions and the sample solution are assayed on a single device with multiple detection zones simultaneously; an analyte concentration calibration curve can thus be established from the standards. Since the μPAD design allows the colorimetric measurements of the standards and the sample to be conducted simultaneously and under the same condition, errors from the above sources can be minimized. The analytical approach reported in this work shows that μPADs can perform quantitative chemical analysis at very low cost. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

A preparation of organic working standards for the online measurement of 13 C/ 12 C and 18 O/ 16 O ratios in biological material is presented. The organic working standards are simple and inexpensive C 3 and C 4 carbohydrates (sugars or cellulose) from distinct geographic origin, including white sugar, toilet and XEROX papers from Switzerland, maize from Ivory Coast, cane sugar from Brazil, papyrus from Egypt, and the core of the stem of a Cyperus papyrus plant from Kenya. These photosynthetic products were compared with International Atomic Energy standards CH-3 and CH-6 and other calibration materials. The presented working standards cover a 15 ‰ range of 13 C/ 12 C ratios and 9 ‰ for 18 O/ 16 O, with a precision 10. [ABSTRACT FROM AUTHOR]