Use Of Simultaneous Equations Research Articles

Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems

Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and teaching context, with specific reference to using mathematical modelling. Since mathematical modelling is a fairly new teaching strategy used in mathematics teaching some teachers may be ignorant of the skills and competencies required for learners to solve problems efficiently. A mixed-methods approach to this study was decided upon and a case study design used within an interpretative paradigm in an effort to ascertain the levels of mathematical modelling competencies of a non-random sample of 20 Grade 10 learners. Participant learners who attended a Western Cape school were requested to solve a set of word problems involving the use of simultaneous equations. Task based activities and observations were used as a means to collect data, as well as semi-structured interviews to gauge participating learners’ views and experiences. Qualitative content analysis methods were employed together with basic descriptive statistical methods.Contribution: Research findings reveal the limited competence and abilities of the participating Grade 10 learners to make sense of, understand or constructively progress in solving contextual problems, and the challenges they experience to progress through particular stages of the modelling process, such as building and solving models and interpreting the solutions thereof.

Precise estimation of chlorophyll a, b and carotenoid content by deconvolution of the absorption spectrum and new simultaneous equations for Chl determination.

The precise determination of photosynthetic pigment content in green organisms, chlorophylls (Chls) and carotenoids (Cars), is important to investigate many photosynthetic processes such as responses to environmental fluctuations or to gene mutations, as well as to interpret biochemical and structural results obtained on purified membranes and photosynthetic complexes. The most utilized methods for determination by spectrophotometry of Chl content in solution, usually 80% acetone, are based on the use of simultaneous equations. The advantages are the easiness and speed over chromatography, which also requires less common equipment. The disadvantage is that issues in sample preparation or in the measurement are not detectable, which could lead to wrong results. Here we propose a fast, accurate and (almost) error-proof method to measure Chl a, Chl b and also total Car content in a solution of pigments extracted from tissue, membranes or purified complexes. The method is based on the fit of the absorption spectrum of the acetone extract using the spectra of purified pigments as references. We show how this method allows a more precise and accurate estimation of pigment content as compared to classical equations, even in incorrectly prepared acetone solutions. Moreover, the method allows the discovery of artifacts in sample preparation or measurement and thus drastically reduces the risk of mistakes. Examples obtained on purified complexes are also discussed. Based on newly acquired Chl spectra, we also propose a new set of improved simultaneous equations that provide slightly different but more reliable results in comparison with the currently used equations.

Factors that influence the financial literacy of young Spanish consumers

AbstractThis study examines the development of mathematical and financial literacy skills amongst 471 students in Spain. Most studies on this topic have looked at either one or the other skill but they have not examined the relationship between the two. The use of simultaneous equations has enabled us to do so. The aim of the paper is to disentangle the factors determining the financial skills of young consumers in Spain. To do this, the PISA Financial Literacy Assessment conducted by the OECD in 2012 is used. Our paper’s main contribution lies in the methodological way to deal with the empirical challenges overshadowing our study. Particularly, our methodological strategy is defined by the application of a multi‐level model of simultaneous equations (MSiEM). This method allows us to take into account the simultaneous determination of math and financial skills at school and the nested structure of the database. This MSiEM permits the identification of the determinants of financial skills, differentiating between the influences operating at school level from those at student level. A first conclusion is that the development of financial abilities of young consumers is mediated by their mathematical skills. A second conclusion, in accordance with those of other international studies, is the importance of the family on the financial literacy of 15‐year‐old Spanish students. The family, a first‐order determinant in reading, science and math scores, is also a key variable in the development of financial skills. Finally, school type (public vs. private) does not display any effect on either the financial or math performance of Spanish young people.

Do Promoter Holding and Firm Performance Exhibit Endogenous Relationship? An Analysis from Emerging Market of India

Firm ownership structure has a strong influence on its long-term performance and financial literature documents that high concentration of promoter ownership has a positive bearing on firm performance. This study is an attempt to analyze relationship between promoter’s holding and firm performance in an emerging market setting of India. The study specifically examines the endogeneity problem through use of simultaneous equations. To ensure robustness in addition to accounting-based measures (ROA and ROE), a market-based performance measure (Tobin’s Q) has been employed. Panel data of 2148 firm-year observations are analyzed from 2003 to 2015 for 179 companies listed on India’s broad-based market Index, the S&P BSE 500. The results indicate presence of non-linear relationship between the firm performance and promoter’s holdings. Specifically, the study documents the relationship to be of U curve nature and clearly finds evidence of endogenous relationship between promoter’s holding and firm performance.

The relationship between non-audit fees and audit quality: dealing with the endogeneity issue

Purpose – The purpose of this paper is to explore whether the provision of non-audit services (NAS) by public accounting firms undermines audit quality. The study addresses this question by testing for an association between the provision of consulting services and auditor independence in listed companies. Design/methodology/approach – The authors study if the magnitude of non-audit fees explains variations in earnings management by looking at the joint determination of non-audit fees, audit fees, and abnormal accruals using the SURE-regression estimation method. Findings – Evidence from tested models suggests that audit services quality is uncompromised by the provision of NAS. In other words, high non-audit fees do not necessarily result in poor quality financial reporting. Research limitations/implications – A different research methodology and a different sample (e.g. non-listed companies) may lead to differing results. As the paper analyses only one country, generalizability of the results might be a limitation. There is no need to increase legal restrictions on the provision of consulting services by public accounting firms in order to better safeguard audit quality. Practical implications – Consulting clients may be more confident to hire both audit and NAS with the same firm and can make a case before the general Shareholders’ meeting. By providing both audit and NAS, consulting firms obtain knowledge spillovers and synergies while appealing highly qualified professionals. Originality/value – The use of simultaneous equations (SURE-regression) to establish the auditor-client relation allows us to better model theoretical relations between audit fees, non-audit fees, and abnormal accruals. Likewise, joint modeling takes account of correlations between the error terms of the individual models, yielding more efficient estimates than ordinary least squares. Performing this analysis in a non-Anglo-American country with low litigation risk is also a valuable contribution to extant literature.

Culture and Trade in the European Union

Since its origin, the European Union has focused on removing barriers to the full integration of its members’ economies. While formal institutions have been adapted, informal social norms may have also changed. In this paper, variables from the World Values Survey are used to estimate the cultural distance between countries to examine the extent to which cultural distance and bilateral trade are related. Cultural distance reflects the differences between two countries’ norms and beliefs. It is predicted that cultural distance reduces trade while trade reduces cultural distance. Fixed-effects regressions for exports and cultural distance show that, contrary to the prediction, cultural distance raises trade and trade raises cultural distance. However, these results are questionable due to the potential problem of endogeneity. Once the problem of endogeneity is addressed with the use of simultaneous equations, the results show that, in fact, cultural distance has no effect on trade, while trade reduces cultural distance.

Consequences of financial reporting quality on corporate performance: Evidence at the international level

This paper examines the consequences of Financial Reporting Quality (FRQ) on Corporate Performance, using three proxies of FRQ: (i) earnings quality; (ii) conservatism; and (iii) accruals quality. Our purpose is to analyze the effect of a good FRQ on financial performance (FP) measured by the market to book ratio. To this end, the proposed hypotheses are tested on an unbalanced sample of 1, 960 international non-financial listed companies from 25 countries and the special administrative region of Hong-Kong for the period 2002-2010. The use of simultaneous equations for the panel data, via the GMM estimator proposed by Arellano and Bond (1991), highlights the positive effect of financial reporting quality (FRQ) on financial performance. This result is robust according to the different measurements of FRQ (earnings quality, accruals quality and accounting conservatism) and for an aggregated measure for the previous three proxies of FRQ. The empirical evidence shows that this relationship is moderated by the level of corruption perception in the country of origin of the company, the adoption of IFRS, the accounting system used in the country and the influence of the economic cycle.

Responsabilidad social corporativa vs. responsabilidad contable

The aim of this paper is to analyze if sustainable companies show a higher quality of the accounting information, identified by the lower tendency to carry out earnings management. This relationship is tested for an unbalanced sample of 1960 multinational non-financial listed companies from 26 countries for the period 2002–2010. The use of simultaneous equations for panel data, via the GMM estimator proposed by Arellano and Bond (1991), highlights the existence of a negative relationship between both variables. The results obtained are robust for different measures of earnings management and corporate social responsibility.

Proactive management of political risk and corporate performance: The case of Spanish multinational enterprises

The present study analyzes the relationship between the political risk assumed by Spanish multinational enterprises in their internationalization strategies and their performance over a five-year period, from 2000 to 2005. Significant evidence is obtained of a positive and simultaneous relationship between political risk and performance through the use of simultaneous equations applied to a sample of 164 firms. These results are consistent with the premises of the Prospect Theory and with the traditional financial and economic theory grounded in risk aversion. They also explain the proactive use of political risk, to the extent that greater risk results in greater performance, which in turn contributes the amount of resources that are needed to undertake investments in countries with greater risk.

The chequered history of the development and use of simultaneous equations for the accurate determination of chlorophylls a and b.

Over the last half century, the most frequently used assay for chlorophylls in higher plants and green algae, the Arnon assay [Arnon DI (1949) Plant Physiol 24: 1-15], employed simultaneous equations for determining the concentrations of chlorophylls a and b in aqueous 80% acetone extracts of chlorophyllous plant and algal materials. These equations, however, were developed using extinction coefficients for chlorophylls a and b derived from early inaccurate spectrophotometric data. Thus, Arnon's equations give inaccurate chlorophyll a and b determinations and, therefore, inaccurate chlorophyll a/b ratios, which are always low. This paper describes how the ratios are increasingly and alarmingly low as the proportion of chlorophyll a increases. Accurate extinction coefficients for chlorophylls a and b, and the more reliable simultaneous equations derived from them, have been published subsequently by many research groups; these new post-Arnon equations, however, have been ignored by many researchers. This Minireview records the history of the development of accurate simultaneous equations and some difficulties and anomalies arising from the retention of Arnon's seriously flawed equations.

Monitoring of electrical activity, ionic homeostasis (DC potential), and changes in extracellular concentration of catechols and indoles in the rat striatum : Obrenovitch T.P., Christofi G., Fonseca M., and Symon L. Gough-Cooper Department of Neurological Surgery, Institute of Neurology, Queen Square, WC1N 3BG, England

The possibilities for using fast-scan voltammetric detectors in flow injection analysis for individual and multicomponent determination of phenolic compounds are explored. A cyclic voltammetric unit for potential scans is connected to a three-electrode cell (carbon-paste working electrode, silver/silver chloride reference electrode and glassy-carbon auxiliary electrode). The resolution and hence the selectivity obtainabel from the electrode processes can be improved by derivatizing the current/potential recordings. Individual and simultaneous determinations of phenol, guaiacol and 2,4-dichlorophenol at levels lower than 1 μg ml−1 can be achieved by judicious selection of measurement potentials, and in worst cases, by use of simultaneous equations.

Simultaneous determination of phenolic compounds in water by normal and derivative flow injection/cyclic votammetry

The possibilities for using fast-scan voltammetric detectors in flow injection analysis for individual and multicomponent determination of phenolic compounds are explored. A cyclic voltammetric unit for potential scans is connected to a three-electrode cell (carbon-paste working electrode, silver/silver chloride reference electrode and glassy-carbon auxiliary electrode). The resolution and hence the selectivity obtainabel from the electrode processes can be improved by derivatizing the current/potential recordings. Individual and simultaneous determinations of phenol, guaiacol and 2,4-dichlorophenol at levels lower than 1 μg ml −1 can be achieved by judicious selection of measurement potentials, and in worst cases, by use of simultaneous equations.

Solving problems by equations

Abstract Traditionally, the answer to problems of resection, intersection and ranging is obtained by “solving triangles”. Nowadays, with programmed computing, a much more elegant and automatic solution is achieved through the use of simultaneous equations. This approach not only provides a much better understanding of the problem, it also readily yields interesting “add-on” benefits, such as the precision of the solution. This paper aims at demonstrating the power of simultaneous equations and uses resection by directions as an example.

A Comparison of Data Reduction Techniques for Line-Excited Optoacoustic Analysis of Mixtures

The use of discrete line laser excitation for the optoacoustic analysis of gas mixtures holds promise as a formidable analytical tool. However, this technique presents challenging demands on the data reduction process to increase the reliability of the analytical results. The problems unique to this method which make data reduction difficult are discussed. Use of simultaneous equations, multivariate least-squares, and a new iterative coefficient weighted least-squares approach are compared. Data indicating the relative performance of these methods are presented.

Properties of the lumen membrane of the cortical thick ascending limb of Henle's loop of rabbit kidney.

Previous data suggest the cotransport of Na+, Cl−, and K+ across the lumen membrane of the cortical thick ascending limb (cTAL) of rabbit nephron. For this cotransporter to operate K+ recycling across the lumen membrane has to be postulated. The present data focus on the conductivity properties of the lumen membrane. Methods for impaling individual cells of in vitro perfused cTAL segments are described. The meanPD across the lumen membrane (PD1) is 76 mV (lumen positive). Rapid increase in lumen perfusate K+ concentration (3.6→18.6 mmol · l−1) leads to a depolarization ofPD1 by 20 mV. Ba2+ (3 mmol · l−1) added to the lumen perfusate inhibits the K+ conductive pathway of the lumen membrane, and consequently increases the voltage divider ratio (current pulse induced voltage deflection across the lumen membrane divided by that across the basolateral membrane) from 2 to 36 as well as transepithelial resistance from 34 to 46 Ω cm2. From these changes, and with the use of simultaneous equations of the VDR and of Kirchhoff's law, the resistances of the lumen membrane (88 Ω cm2), of the basolateral membrane (47 Ω cm2), and of the paracellular shunt pathway (47 Ω cm2) can be calculated. Using these estimates of the individual resistances and using the observed change inPD1 in the K+ concentration step experiments (29±3 mV per decade in K+ concentration change) an apparent transference number of the lumen membrane for K+ in the order of 0.9–1.0 can be calculated. This indicates that the lumen membrane is essentially K+ conductive. This conclusion is strengthened further by the results of another series in which no evidence for a Cl− conductive pathway in the lumen was obtained. The data of this study can be used to calculate the intracellular K+ activity of some 90–100 mmol ·l−1. For this K+ activity the K+ diffusion from cell to lumen equals the carrier mediated uptake from lumen to cell. This indicates that an essentially complete recycling of K+ across the lumen membrane of the cTAL segment is feasible.

Computing Mineral Compositions of Sedimentary Rocks from Chemical Analyses

ABSTRACT Methods are given for computing the gross mineral compositions of sedimentary rocks. The methods are based on the use of simultaneous equations which are written to express the distribution of Al2O3 and K2O among various mineral constituents, principally clay and potassium feldspar. This approach has been used in studies of sedimentary rocks and sandstone-type uranium ores on the Colorado Plateau in which clay and potassium feldspar are the principal aluminous and potassic constituents. The methods may be modified for use in studying sedimentary materials in which other aluminous and potassic constituents are present. If the composition of the clay in the rocks which are being studied is largely unknown, the mineral compositions of the rocks may not be computed precisely. However, if the composition of the clay is known within limits it is possible to compute ranges of concentration for each mineral constituent. The ranges are broad where the rocks contain abundant clay of little-known composition, but are less broad where the rock is clay-poor or where the approximate composition of the clay can be presumed. It is not necessary to consider the complete composition of the clay to compute the gross mineral composition of the rock. The methods may also be used to interpret some chemical characteristics of the clay in the rocks being studied from certain aspects of their known mineral and chemical composition.

Dissimilation of 6-phosphogluconate by azotobacter vinelandii

A system for splitting 6-phosphogluconate to glyceraldehyde-3-phosphate and pyruvate at the rate of approximately 72 μmoles/h/46 mg enzyme protein has been demonstrated in extracts of Azotobacter vinelandii O. Part of the glyceraldehyde-3-phosphate formed appears to recycle through aldolase, fructose diphosphatase, and phosphohexoisomerase to G-6-P; the rest is converted into pyruvate through triose phosphate dehydrogenase and enolase. The ratio of conversion by these two pathways is limited by the level of triose phosphate dehydrogenase which is unknown in this organism. The use of simultaneous equations to determine the concentrations of trioses and hexoses in mixtures after reaction with anthrone reagent is proposed. Good confirmation of this method was obtained when it was checked with mixtures of these compounds in known concentrations.

The Use of Simultaneous Equations in Business Problems

ROBLEM in interlocking departmental charges in cost accounting led to the study on which this article is ased. The solution presented in the text consisted of successive distributions, and the process was carried out until the required accuracy was attained. Since the problem is presented in detail later, it may be stated briefly here that the limit of the process was evaluated. This limit proved to be a simple formula which could be used in finding answers to similar problems. This solution was fairly satisfactory, so an attempt was made to derive a similar formula for more than two departments rather than to search for an entirely different method of solving the problem. The solution was extended to three departments by the process of summing infinite series but, since the work involved in further extension would be very great, the solution for each of the unknowns was examined more closely. These were in fractional form and the numerators and denominators appeared to be the expansions of determinants such as might arise in the solution of simultaneous equations, but a different constant factor appeared in each numerator. When each unknown was divided by the corresponding factor, a system of linear equations in the new unknowns could be set up from the determinants. With these equations before him, the writer suddenly realized that if he had studied the problem carefully and stated the conditions in mathematical form he could have stated these equations directly from the conditions of the problem. It is interesting to analyze some of the conditions which might cause a person who is familiar with simultaneous equations to fail to recognize the problem as one in which a system of linear equations might be useful. Besides the misleading nature of the solution in the text, one might include in such a list lack of familiarity