Mathematical Papers Research Articles

Zygmund’s Type Inequality to the Polar Derivative of a Polynomial

In this paper we improve a result recently proved by Irshad et al. [On the Inequalities Concerning to the Polar Derivative of a Polynomial with Restricted Zeroes, Thai Journal of Mathematics, 2014 (Article in Press)] and also extend Zygmund's inequality to the polar derivative of a polynomial.

TheA-Stokes approximation for non-stationary problems

Journal Article The A-Stokes approximation for non-stationary problems Get access Dominic Breit Dominic Breit † School of Mathematical and Computer Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK †E-mail: d.breit@hw.ac.uk Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Mathematics, Volume 67, Issue 2, June 2016, Pages 201–231, https://doi.org/10.1093/qmath/haw008 Published: 30 April 2016 Article history Received: 25 September 2014 Revision received: 14 March 2016 Published: 30 April 2016

Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function

In the paper, the authors find integral representations, complete monotonicity, limits, and other properties of remainders of the Binet and Stirling formulas for the gamma function and their derivatives. These properties strengthen almost all results in three papers published in the Journal of Computational and Applied Mathematics, Applied Mathematics Letters, and Applied Mathematics and Computation in the years 2006, 2011, and 2014 by seven mathematicians. The proofs in the paper unify and are simpler than those in the three papers.

Introduction to the Special Issue on Science, Technology, Engineering, and Mathematics (STEM) Education

This special issue of the Canadian Journal of Science, Mathematics and Technology Education is focusing on STEM education, an acronym that conjures up a variety of meanings, depending on how it is ...

A note on a conjecture for the distance Laplacian matrix

In this note, the graphs of order n having the largest distance Laplacian eigenvalue of multiplicity n −2 are characterized. In particular, it is shown that if the largest eigenvalue of the distance Laplacian matrix of a connected graph G of order n has multiplicity n − 2, then G = S_n or G = K_(p,p), where n = 2p. This resolves a conjecture proposed by M. Aouchiche and P. Hansen in [M. Aouchiche and P. Hansen. A Laplacian for the distance matrix of a graph. Czechoslovak Mathematical Journal, 64(3):751–761, 2014.]. Moreover, it is proved that if G has P_5 as an induced subgraph then the multiplicity of the largest eigenvalue of the distance Laplacian matrix of G is less than n − 3.

On the fine spectrum of generalized upper triangular double-band matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$

The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices
uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics, 234(2010) 1387-1394].

Weak-Shock Interactions with Transonic Laminar Mixing Layers of Fuels for High-Speed Propulsion

This paper extends to transonic mixing layers an analysis of Lighthill (“Reflection at a Laminar Boundary Layer of a Weak Steady Disturbance to a Supersonic Stream, Neglecting Viscosity and Heat Conduction,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 54, No. 3, 1950, pp. 303–325.) on the interaction between weak shocks and laminar boundary layers. As in that work, the analysis is carried out under linear-inviscid assumptions for the perturbation field, with streamwise changes of the base flow neglected, as is appropriate given the slenderness of the mixing-layer flow. The steady-disturbance profile is determined by taking a Fourier transform along the longitudinal coordinate. Closed-form analytical functions for the pressure field are derived in the small- and large-wave-number limits, and vorticity disturbances are obtained as functions of the pressure perturbations. The analysis is particularized to ethylene–air and hydrogen–air mixing layers, for which the dynamics are of current interest for hypersonic propulsion. The results provide, in particular, the effective distance of upstream influence of the pressure perturbation in the subsonic stream. The resulting value, which scales with the thickness of the subsonic layer, is much smaller than the upstream influence distances encountered in boundary layers. This study may serve as a basis to understand shock-induced autoignition and flameholding phenomena in simplified versions of non-premixed supersonic-combustion problems.

A Question of Method Concerning Adab, Governance, Health & Wellbeing, Morality, Science & Tawhid

This essay addresses the need for knowledge synthesis from the perspectives of Sir Isaac Newton, Johann Wolfgang Von Goethe, and Prof. Syed Muhammad Naquib Al-Attas. It is a robust criticism of materialist reductionism and represents an Islamized revision of an unpublished paper submitted to the Mathematics Dept., University of S. Dakota (1982), which Prof. Dan Kennelly (Dept. Head) wished to publish in S. Dakota’s Journal of Mathematics but did not as it would have cost him his chair (under advisement from the Philosophy Chair who endorsed the original essay).

THE MATHEMATICS OF THE TRI–SQUARED TRIANGULATION ALGORITHMIC MODEL

This work provides a mathematical and an epistemological rational for the transformative process of qualitative datainto quantitative outcomes through the Tri–Squared Test. The design of fixed-parameter algorithms for researchengineering can prove to be beneficial to a variety of fields of learning. This novel methodology provides statisticalpower and mathematical elegance to research outcomes. It is a comprehensive approach that has a wide range ofapplicability as it practically addresses important and relevant problems with sample sizes that are small and researcharenas that are rather complex. This research is the continuation of a dynamic mixed methods approach that is atransformative process which changes qualitative data into quantitative outcomes through the Tri–Squared statisticalmeasure first introduced in i-manager's Journal of Mathematics.

American Journal of Mathematics: Founded in 1878 by Johns Hopkins University

American Journal of Mathematics: Founded in 1878 by Johns Hopkins University

Application of Alpha Skew Truncated Cauchy Distribution in Exchange Rate Data

In this article the alpha skew version of truncated Cauchy distribution using the methodology of Elal-Olivero (Alpha–skew–normal distribution. <i>Proyecciones Journal of Mathematics</i>. 29: 224-240, 2010) has been derived. The important distributional properties have been investigated. An application of the distribution in modeling exchange rate data from the field of finance has been presented.

What Is a Canadian Science Education? Towards a Circumpolar Identity in Curriculum

Abstract Despite intermittent episodes of identifiably Canadian influences on science education, the last six decades of science education (and its curriculum) in Canada have been a decidedly American experience. The guiding assumption for this contribution to the 15th anniversary volume of the Canadian Journal of Science, Mathematics and Technology Education is that the systems of science education operating in the provinces and territories in Canada have not had opportunity, historically, to develop curriculum uniquely from Canada that supplies broad and respectful appeal to the context of Canadian society, its demographics, its geographic diversity, and its geopolitical position internationally. The implication of this position, if credible, is that Canada has failed to respond adequately to repeated attempts to reconcile the international commonplaces of science with the unique characteristics of a large and sparsely populated circumpolar nation. Is it time for science education in Canada to make a pl...

Looking Back, Looking Forward: The Past 15 Years of Mathematics Education inCJSMTE

Abstract In this article, we review the publications served by the Canadian Journal of Science, Mathematics and Technology Education in the past 15 years, specific to the field of mathematics education, and make connections with development of the field. In particular, we adopt current Editor-in-Chief John Wallace's (2009) approach of “looking back, looking forward,” to reflect on the journal's development both qualitatively, by recapping significant moments of the journal and highlighting recurrent themes, and quantitatively, by reviewing the number of contributions in terms of country, language, and genre. In looking forward, we inform a discussion of future directions of the journal.

Conversations About Science Education: A Retrospective of Science Education Research inCJSMTE

This review focuses on science education contributions to the Canadian Journal of Science, Mathematics and Technology Education (CJSMTE) from January 2001 through December 2014. Through a combination of content and citation analysis, we examine the journal as a location for conversations around specific themes and broader ideas related to science education. Conversations absent from the journal are also considered. This analysis provides a retrospective of the ways in which the CJSMTE has contributed to the field of science education and makes suggestions for future considerations.

CJSMTEat Fifteen: A Particularly Canadian Approach

This review of the Canadian Journal of Science, Mathematics and Technology Education (CJSMTE) presents descriptive statistics regarding contributions to the journal between January 2001 and December 2014. Data are compared with a brief review from 2009 (Wallace, 2009). Findings suggest that there are areas for improvement with regard to increased representation of contributions in technology education, by French authors, and from non-Western institutions. At the same time, findings also indicate that the journal recognizes both the specificity of the contexts in which education researchers affiliated with Canadian institutions work and the importance of opening up that work to scrutiny and fertility of ideas from other places leading to a healthy tension between the global and the local in CJSMTE.

Happy Anniversary: Fifteen Years of theCanadian Journal of Science, Mathematics and Technology Education/Joyeux anniversaire : laRevue canadienne de l'enseignement des sciences, des mathématiques et des technologiesa quinze ans

When I assumed the role of Editor-in-Chief of the Canadian Journal of Science, Mathematics and Technology Education (CJSMTE) back in 2008, one of the questions in my mind was whether we should cont...

Giving Canadian Science, Mathematics, and Technology Education an Independent Voice

It is noted that the Canadian Journal of Science, Mathematics and Technology Education (CJSMTE) was founded with the support of a donation of $1.0 million from the Imperial Oil Charitable Foundation. Four goals were uppermost in the thinking behind the journal: first, it should be bilingual; second, it should be cross-disciplinary; third, it should project a distinctive and independent voice for Canadian educators; fourth, it should celebrate diversity of views and perspectives while upholding values of excellence and equity. Some early teething problems are discussed and questions are raised about what constitutes a successful international journal, including the originality and rigour of published papers and the richness of interactions among authors, editors, and manuscript reviewers.

Decompositions into products of idempotents

The purpose of this note is two-fold: (1) to study when quasi-Euclidean rings, regular rings and regular separative rings have the property (∗) that each right (left) singular element is a product of idempotents, and (2) to consider the question: “when is a singular nonnegative square matrix a product of nonnegative idempotent matrices?” The importance of the class of quasi- Euclidean rings in connection with the property (∗) is given by the first three authors and T.Y. Lam [Journal of Algebra, 406:154–170, 2014], where it is shown that every singular matrix over a right and left quasi-Euclidean domain is a product of idempotents, generalizing the results of J. A Erdos [Glasgow Mathematical Journal, 8: 118–122, 1967] for matrices over fields and that of T. J. Laffey [Linear and Multilinear Algebra, 14:309–314, 1983] for matrices over commutative Euclidean domains. We have shown in this paper that quasi-Euclidean rings appear among many interesting classes of rings and hence they are in abundance. We analyze the properties of triangular matrix rings and upper triangular matrices with respect to the decomposition into product of idempotents and show, in particular, that nonnegative nilpotent matrices are products of nonnegative idempotent matrices. We study as to when each singular matrix is a product of idempotents in special classes of rings. Regarding the second question for nonnegative matrices, bounds are obtained for a rank one nonnegative matrix to be a product of two idempotent matrices. It is shown that every nonnegative matrix of rank one is a product of three nonnegative idempotent matrices. For matrices of higher orders, we show that some power of a group monotone matrix is a product of idempotent matrices.

Spherical folding tessellations by kites and isosceles triangles IV

The classification of the dihedral folding tessellations of the sphere and the plane whose prototiles are a kite and an equilateral triangle were obtained in [C. Avelino and A. Santos, Spherical and planar folding tessellations by kites and equilateral triangles, Australasian Journal of Combinatorics, 53 (2012), 109–125.]. Recently, this classification was extended to isosceles triangles so that the classification of spherical folding tesselations by kites and isosceles triangles in three cases of adjacency was presented in [C. Avelino and A. Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles: a case of adjacency, Mathematical Communications, 19 (2014), 1–28.; C. Avelino and A. Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles II, International Journal of Pure and Applied Mathematics, 85 (2013), 45–67.; C.Avelino and A.Santos, Spherical Folding Tessellations by Kites and Isosceles Triangles III, submitted.]. In this paper we finalize this classification presenting all the dihedral folding tessellations of the sphere by kites and isosceles triangles in the remaining three cases of adjacency, that consists of five sporadic isolated tilings. A list containing these tilings including its combinatorial structure is presented at the end of this paper.

Symmetry detection of rational space curves

We present a novel, deterministic, and efficient method to detect whether a given rational space curve C is symmetric. The method combines two ideas. On one hand in a similar way to [1], [2], if C is symmetric then the symmetry provides a second parametrization of the curve; furthermore, whenever the first parametrization is proper, i.e. injective except for finitely many parameter values, the latter is also proper and both are related by means of a Mobius transformation [3] that completely determines the symmetry. On the other hand, if C is symmetric then the curvature and torsion of C at corresponding points must coincide. By putting together these two ideas we can give an algorithm to directly find the Mobius transformations defining the symmetries of the curve. From here we can compute these symmetries and its characteristic elements (symmetry axes, symmetry planes, etc.) This completes and improves on an earlier method addressing a similar problem [3]. Keywords Symmetry Detection, Space Curves, Rational Curves References [1] Alcazar J.G. (2014), Efficient detection of symmetries of polynomially parametrized curves, Journal of Computational and Applied Mathematics vol. 255, pp. 715–724. [2] Alcazar J.G., Hermoso C., Muntingh G. (2014), Detecting Similarity of Plane Rational Plane Curves, Journal of Computational and Applied Mathematics, Vol. 269, pp. 1–13. [3] Alcazar J.G., Hermoso C., Muntingh G. (2014), Detecting Symmetries of Rational Plane and Space Curves, to appear in Computer Aided Geometric Design.