Mathematics

The effect of CO2 and of lactic acid (L.A.) on the extracellular (pHe) and intracellular pH (pHi) of ascites tumor cells (DS-carcinosarcoma) in rats was studied by in vitro equilibration of ascites with CO2 and alteration of lactic acid concentration. pHi was determined by the distribution of DMO. The effects of lactic acid and CO2 on pH were additive and could be expressed as pHe = 8.872 - 0.745 logPCO2 - 0.0355 (L.A.) (R = 0.867, n = 201) pHi = 8.218 - 0.436 logPCO2 - 0.0275 (L.A.) (R = 0.812, n = 143) delta pHi/delta pHe was dependent on the way pHe was changed: If the change in pHe was due to lactic acid, delta pHi/delta pHe was 0.91; if it was due to CO2 delta pHi/delta pHe was 0.625. pHi exceeded pHe if either PCO2 and/or the concentration of lactic acid was raised above a critical level. The results render it questionable to predict intracellular pH values within solid tumor from pH measurements within the extracellular fluid.

In this article we replicate and extend findings from Duncan et al. (2007). The 1st study used Canada-wide data on 1,521 children from the National Longitudinal Survey of Children and Youth (NLSCY) to examine the influence of kindergarten literacy and math skills, mother-reported attention, and mother-reported socioemotional behaviors on 3rd-grade math and reading outcomes. Similar to Duncan et al., (a) math skills were the strongest predictor of later achievement, (b) literacy and attention skills predicted later achievement, and (c) socioemotional behaviors did not significantly predict later school achievement. As part of extending the findings, we incorporated a multiple imputation approach to handle missing predictor variable data. Results paralleled those from the original study in that kindergarten math skills and Peabody Picture Vocabulary Test-Revised scores continued to predict later achievement. However, we also found that kindergarten socioemotional behaviors, specifically hyperactivity/impulsivity, prosocial behavior, and anxiety/depression, were significant predictors of 3rd-grade math and reading. In the 2nd study, we used data from the NLSCY and the Montreal Longitudinal-Experimental Preschool Study (MLEPS), which was included in Duncan et al., to extend previous findings by examining the influence of kindergarten achievement, attention, and socioemotional behaviors on 3rd-grade socioemotional outcomes. Both NLSCY and MLEPS findings indicated that kindergarten math significantly predicted socioemotional behaviors. There were also a number of significant relationships between early and later socioemotional behaviors. Findings support the importance of socioemotional behaviors both as predictors of later school success and as indicators of school success.

This study aims to describe the role of Assessment as Learning for pre-service mathematics teachers in designing mathematical test instruments. Assessment as Learning is useful as a quality control tool for the designed mathematics test instrument. This is qualitative research with a phenomenological approach, involving four pre-service mathematics teachers. Data were obtained through the design of mathematical test instruments and in-depth interviews with the participants. The test instruments designed was then adjusted to the results of the interview. The research results reveal that Assessment as Learning is important in supporting students to monitor the results of their work; environmental aspects are the most difficult aspects to be integrated into mathematical problems; students have more difficulty in completing Peer-Assessment than Self-Assessment; the problems raised in the economic aspects are only around prices, and Self-Assessment and Peer-Assessment are very helpful in detecting errors and deficiencies in the questions designed. It is concluded that Assessment as Learning helps and supports pre-service mathematics teachers in designing mathematics test instruments to create good quality mathematics test instruments. This research contributes to pre-service mathematics teachers conducting the Assessment as Learning to minimize errors in the mathematical test instruments.

International research has pointed out the importance of integrating mathematical modeling and inquiry processes into the teaching and learning of mathematics. This paper aims to present an integrative model that enables analyzing the characteristics inquiry and modeling processes share in the same model with a view to using them when designing and implementing interdisciplinary teaching sequences. After presenting a synthesis of the literature review, our theoretical approach to inquiry and modeling for the analysis of an interdisciplinary teaching sequence will be introduced. We focus here on the case of an inquiry situation in an archaeological context where mathematics and history are interrelated. It was implemented at secondary school level with students aged 13–14. We use this particular case study to analyze the appearance of both processes, in order to look for coincidences, concatenations and synergies. The main result is an integrative model for the joint analysis of both...

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construc...

The literature in mathematics education identifies a traditional formal mechanistic-type paradigm in Integral Calculus teaching which is focused on the content to be taught but not on how to teach it. Resorting to the history of the genesis of knowledge makes it possible to identify variables in the mathematical content of the curriculum that have a positive influence on the appropriation of the notions and procedures of calculus, enabling a particularised way of teaching. Objective: The objective of this research was to characterise the anthology of the integral seen from the epistemic complexity that composes it based on historiography. Design: The modelling of epistemic complexity for the definite integral was considered, based on the theoretical construct “epistemic configuration”. Analysis and results: Formalising this complexity revealed logical keys and epistemological elements in the process of the theoretical constitution that reflected epistemological ruptures which, in th...

Different groups of Papuans and New Guineans have used a wide variety of devices and techniques, as well as systems of numeration, to tally and, less frequently, to record quantities of goods and multiples of people, shells, days (until a meeting or ceremony), and animals. It is as yet impossible to provide a comprehensive guide to the counting systems of Papua and New Guinea or to provide a key to their geographic distribution as K. W. Galis has done for West Irian. Readers who wish to enquire into the systems employed by specific groups of people or into the distribution of a particular method or device should consult the bibliography that follows. This article is confined to a survey of the kinds of tallying, recording, and counting systems used, with examples only of each major type provided.

In this paper, we study the nonlinear coupled system of equations with fractional integral boundary conditions involving the Caputo fractional derivative of orders θ 1  and  θ 2 and Riemann–Liouville derivative of orders ϱ 1  and  ϱ 2 with the p -Laplacian operator, where n − 1 < θ 1 , θ 2 , ϱ 1 , ϱ 2 ≤ n , and n ≥ 3 . With the help of two Green’s functions G ϱ 1 w , ℑ , G ϱ 2 w , ℑ , the considered coupled system is changed to an integral system. Since topological degree theory is more applicable in nonlinear dynamical problems, the existence and uniqueness of the suggested coupled system are treated using this technique, and we find appropriate conditions for positive solutions to the proposed problem. Moreover, necessary conditions are highlighted for the Hyer–Ulam stability of the solution for the specified fractional differential problems. To confirm the theoretical analysis, we provide an example at the end.

A precise prediction of Bitcoin price is an important aspect of digital financial markets because it improves the valuation of an asset belonging to a decentralized control market. Numerous studies have studied the accuracy of models from a set of factors. Hence, previous literature shows how models for the prediction of Bitcoin suffer from poor performance capacity and, therefore, more progress is needed on predictive models, and they do not select the most significant variables. This paper presents a comparison of deep learning methodologies for forecasting Bitcoin price and, therefore, a new prediction model with the ability to estimate accurately. A sample of 29 initial factors was used, which has made possible the application of explanatory factors of different aspects related to the formation of the price of Bitcoin. To the sample under study, different methods have been applied to achieve a robust model, namely, deep recurrent convolutional neural networks, which have shown t...

MATERIAL: Estimation of glomerular filtration rate (eGFR) is the most widely accepted marker of renal function. Precise calculation is not routinely performed in clinical practice. Several methods have been developed for eGFR: creatinine clearance (CCr) calculation ...

... Oral Submucous Fibrosis: Review on Etiopathogenesis Sunita N Dyavanagoudar* Department of Oral Pathology, Sri Hassanamba Dental College and Hospital, Vidyanagar, Hassan, Karnataka, India Journal of Cancer Science & Therapy - Open Access ...