Mathematical Papers Research Articles

In Memoriam: Slavik Jablan 1952–2015

After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]

Correction to “Voevodsky’s motives and Weil reciprocity,” Duke Math. J. 162 (2013), 2751–2796

We correct a mistake in Section 2.4 of the said paper. In [1, Section 2.4], we wrote: “The category Z Span is isomorphic to the full subcategory of Cor consisting of smooth k-schemes of dimension 0.” Tom Bachmann kindly pointed out to us that this statement is incorrect. Here we clarify the relationship between the two categories and show that it does not affect any argument about cohomological Mackey functors (the only Mackey functors appearing in [1]). We retain the notation of [1]. 1 Let Cor0 be the full subcategory of Cor given by 0-dimensional smooth schemes (D etale k-schemes). If f W X ! Y is a surjective morphism of degree d of etale k-schemes, then we have the formula in Cor0, f i f D d: (1) 2 There is a canonical functor W Z Span!Cor0 (2) which is the identity on objects and sends a span (2.1) from [1], X g Z f ! Y; (3) to f i g. DUKE MATHEMATICAL JOURNAL Vol. 164, No. 10, © 2015 DOI 10.1215/00127094-3146068 Received 23 October 2014. Revision received 14 March 2015. 2010 Mathematics Subject Classification. Primary 19E15; Secondary 19A22, 18D10.

Encouraging Citizenship in Science Education: Continuing Questions and Hopeful Possibilities

AbstractThis special issue of the Canadian Journal of Science, Mathematics and Technology Education invokes questions intended to further the discourse of citizenship in science and mathematics education, such as, How do we define citizen and democracy? Is our call for student action hypocritical? Does positioning school science through the work of Ranciere present a “straw man” argument for change? To what extent does the ghost of John Dewey animate and inform a “wild pedagogy” in science education? Challenging the view of the science and mathematics curriculum as a barrier to overcome, this article argues that possibilities for developing citizenship and critical thinking can be found and developed in existing curriculum formations and practices of school science and mathematics education.

On multi-index fixed charge bi-criterion transportation problem

In this paper, we propose an algorithm for solving a multi-index fixed charge bi-criterion transportation problem and present a method for finding the optimum trade-off pair among efficient cost–time trade-off pairs. The proposed algorithm minimizes variable and fixed costs simultaneously to yield an optimal basic feasible solution. The results of the computational experiments suggests that our algorithm is better than the one proposed by Ahuja and Arora (Indian Journal of Pure and Applied Mathematics, 32(5) 739-746, 2001). We also provide an algorithm to obtain an initial basic feasible solution of the multi-index transportation problem that may be used as a better initial solution for other existing procedures to enhance convergence to the optimal solution.

Mathematical Modeling of Multi-Physics Electrochemical Devices

Electrochemical devices such as batteries and electrochemical solar cells are often described as multi-physics devices. This is a catch-all term meant to convey the fact that these devices are inherently multi-scale, multi-component and multi-phase in nature and that their operation involves complicated interfacial charge transfer and bulk solid and solution phase charge transport. Consequently, the development of accurate and meaningful mathematical models and numerical simulations for such devices is a complex task. Such modelling however, can play a vital role in the optimization of these devices via the identification of the key parameters that control their operational behaviour for a range of conditions and material configurations. In this presentation we will consider examples from some of the authors previous(1-10) and current work on the mathematical modelling of multi-physics electrochemical devices such as battery electrodes, solar cells and nano-diodes to highlight the challenges, approaches and outcomes of such modelling. REFERENCES T. W. Farrell, C. P. Please, D. L. S. McElwain and D. A. J. Swinkels, J. Electrochem. Soc., 147, 4034 (2000).T. W. Farrell and C. P. Please, J. Electrochem. Soc., 152, A1930 (2005).M.A. Penny, T.W. Farrell and G.D. Will, Sol. Energy Mat. & Sol. Cells, 92, 24-37, 2008.Troy Farrell and Steven Psaltis, in Physics of Nanostructured Solar Cells, eds. V. Badescu and M. Paulescu, pp. 327-353, Nova Science Publishers, Inc., New York, ISBN: 978-1-60876-110-4, 2010.S. Dargaville and T.W. Farrell, J. Electrochem. Soc., 157, A830 (2010).S. T. P. Psaltis and T. W. Farrell, J. Electrochem Soc., 158, A33 (2010).S. Dargaville and T.W. Farrell, Electrochimica Acta, 94 (1), pp. 143-158 (2013).S. Dargaville and T.W. Farrell, Electrochimica Acta, 111 , pp. 474-490 (2013).S. Dargaville and T.W. Farrell, Journal of Computational and Applied Mathematics, 273, pp 255-244 (2014).S. Psaltis, T. Farrell, K. Burrage, P. McCabe, T. Moroney, I. Turner and S. Mazumder, “Mathematical Modelling of Gas Production and Compositional Shift of a CSG Field: Local Mo del Development”, submitted to Energy (2014).

Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

ABSTRACTThis paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.

Nonsoluble and non-p-soluble length of finite groups

Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. We prove that λ(G) is bounded in terms of the maximum 2-length of soluble subgroups of G, and that λ(G) is bounded by the maximum Fitting height of soluble subgroups. For an odd prime p, the non-p-soluble length λ p (G) is introduced, and it is proved that λ p (G) does not exceed the maximum p-length of p-soluble subgroups. We conjecture that for a given prime p and a given proper group variety V the non-p-soluble length λ p (G) of finite groups G whose Sylow p-subgroups belong to V is bounded. In this paper we prove this conjecture for any variety that is a product of several soluble varieties and varieties of finite exponent. As an application of the results obtained, an error is corrected in the proof of the main result of the second author’s paper Multilinear commutators in residually finite groups, Israel Journal of Mathematics 189 (2012), 207–224.

Erratum to “On the strong metric dimension of the strong products of graphs”

Abstract The original version of the article was published in Open Mathematics (formerly Central European Journal of Mathematics) 13 (2015) 64–74. Unfortunately, the original version of this article contains a mistake: in Lemma 2.17 appears that for any C1-graph G and any graph H, β (G ⊠ H) ≤ β (G)(β(H)+1), while should be β (G ⊠ H) ≤ β(H) (β(G)+1). In this erratum we correct the lemma, its proof and some of its consequences.

RETRACTED: <i>The Modified Simple Equation Method and Its Applications in Mathematical Physics and Biology</i>

Short Retraction Notice The paper does not meet the standards of "American Journal of Computational Mathematics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused. Editor guiding this retraction: Prof. Hari M. Srivastava (EiC of AJCM) The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

CJM celebrates 25 years of publication of its new series

This year, Carpathian Journal of Mathematics (CJM) reaches an important milestone – 25 years of publication of its new series. Following an already well established tradition of marking the main anniversary moments of the journal by an editorial, see [Berinde, V., Anniversary: Ten years of publication of the new series of Buletin Ştiinţific, Bul. Ştiinţ. Univ. Baia Mare, Ser. B., Matematică-Informatică, 16 (2000), No. 1, i–ii] and [Berinde, V., Carpathian Journal of Mathematics: Celebrating 20 years of publication of the new series, Carpathian J. Math., 26 (2010), No. 2, i–vi], it is the main aim of this note to present a detailed account of what has been achieved since the previous anniversary editorial written five years ago.

English

The aim of the present study was to evaluate the postharvest behavior of tangerine coated with different pectin concentrations during storage under controlled temperature (22°C ± 0.1). Fruits with green color (± 90% of the surface) were divided into four groups: fruits without any coating (T1) and fruits coated with pectin solution at 4 g / 100 g (T2), 6 ml / 100 ml (T3) and 8 g / 100 ml (T4). Tangerines were evaluated during the storage period (0, 3, 6, 9, 12 and 15 days) for the following parameters: vitamin C, soluble solids (SS), total titratable acidity (TTA), mass loss, turgidity pressure and external appearance through colorimetric analysis. In general, coated fruits showed lower mass loss over the storage period. The polynomial model was the model that best suited the experimental data. Regarding to the physico-chemical characteristics, the citrus fruits and non-climacteric, showed little variation in the treatments and changes that have occurred and which can be explained by the variability of the fruits used. In general, the fruit treated with different concentrations of pectin kept green for longer period and with this feature of the fruits, is better accepted by the consumer. Keywords: Citrus deliciosa Tenore, pectin, coatings, coloring, mathematical models African Journal of Biotechnology , Vol 13(52) 4702-4710

Corrigendum and addendum: modeling weakly nonlinear acoustic wave propagation

This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.

Editorial: Science, Technology, Engineering and Mathematics (STEM) education in Malaysia

This Special Issue of Eurasia Journal of Mathematics, Science and Technology Education presents the current research trend of Science Technology, Engineering and Mathematics (STEM) education in Malaysia. As many may argue, a quality STEM education should be able to provide wider opportunities for students to develop their competencies in not only Science, but also Technology, Engineering and Mathematics and its related areas. A successful STEM education equips students with STEM core competencies in sequences that are built upon one another and can be applied within the context of real world application. The acquisition of STEM core competencies will gradually nourish them to be critical and creative thinkers, uplift their scientific literacy, and more importantly stimulate themselves to be creative innovators. These are among the main reasons why STEM education has been an area of great interest in Malaysia just like in any other countries in this world

Time series analysis of real-time music perception: approaches to the assessment of individual and expertise differences in perception of expressed affect

We use time series analysis methods to detect differences between individuals and expertise groups in continuous perceptions of the arousal expressed by Wishart's electroacoustic piece Red Bird. The study is part of a project in which we characterise dynamic perception of the structure and affective expression of music. We find that individual series of perceptions of expressed arousal often show considerable periods of stasis. This may challenge conventional time series methodologies, so we test their validity by application of a general linear autoregressive moving average (GLARMA) approach, which supports it. Acoustic intensity is a dominant predictor of perceived arousal in this piece. We show that responses are time-variant and that animate sounds influence the conditional variance of perceived arousal. Using vector autoregression and cross-sectional time series analysis (which preserves the integrity of each individual response series), we find differences between musical expertise groups (non-musicians, musicians, and electroacoustic musicians). Individual differences within each group are greater than those between expertise groups. The companion paper applies the developed methods to all four pieces in our overall project (Dean, R.T., F. Bailes, and W.T.M. Dunsmuir. 2014. “Shared and Distinct Mechanisms of Individual and Expertise-Group Perception of Expressed Arousal in Four Works.” Journal of Mathematics and Music 8 (3): 207–223). An Online Supplement is available at http://dx.doi.org/10.1080/17459737.2014.928752.

Retraction notice

Retraction notice

Changing Institutional Research Productivity of United States’ Science Education Programs: 2000s v. 1990s

The purpose of this study was to identify the major science education programs in the United States, where the science education researchers published their research during the first decade of the twenty-first century. This research study of the scholarly productivity of science education programs at United States’ institutions of higher education is compared with the last decade of 1990s (Barrow, Settlage, & Germann, 2008). Each issue of the eight research journals (Journal of Research is Science Teaching, Science Education, International Journal of Science Education, Journal of Science Teacher Education, School Science and Mathematics, Journal of Computers in Math and Science Teaching, Journal of Science Education and Technology, and Journal of Elementary Science Education) published in the 2000s provided the author(s) and their institutional affiliation. The resultant ranking of raw and weighted counts for the top 30 U.S science educations programs shows variation in journals where research was published. There were almost 50% of the 2000s top 30 institutions which were not listed for the 1990s. Potential explanations for variations and uses for ranking are discussed.

In memoriam:Jonathan Rogawski

Jonathan Rogawski is no more. In loving memory, his friends and collaborators and admirers have contributed to this garland of articles that you will find in the pages to follow. He was of course a gifted mathematician, one of the earliest workers on the Langlands Program, but much more. He wrote papers, textbooks, supervised students, and served for many years with great distinction as an editor for the Pacific Journal of Mathematics.

Welcome to Journal of Advanced Mathematics and Applications, JAMA, Vol. 3, No. 1

Welcome to Journal of Advanced Mathematics and Applications, JAMA, Vol. 3, No. 1

Introduction to the Special Issue on Graduate Student Innovations in Science, Mathematics, and Technology Education Research

Putting together a Special Issue for the Canadian Journal of Science, Mathematics and Technology Education featuring the innovative work of graduate students from around the world proved to be an e...

Modified iterative method for augmented system

The successive overrelaxation-like (SOR-like) method with the real parameters ω is considered for solving the augmented system. The new method is called the modified SOR-like (MSOR-like) method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like (Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel & Scientific Computations, 7(4), 453–462 (1999)) and the modified symmetric SOR-like (MSSOR-like) methods (Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational andApplied Mathematics, 228(4), 424–433 (2009)).