Mathematical Work Research Articles

Catherine Walsh's Algebra

In this article I seek to demonstrate the ways in which the contemporary Irish poet Catherine Walsh's Optic Verve (2010) performs algebraic operations in poetry on the page, and thereby highlights Islamic contributions to sciences and culture. Deepening Claire Bracken's work on Walsh's poetry and its relationship to the Celtic Tiger, I suggest that this algebraic poetry obliquely indexes Ireland's own entanglements with not just Islamic culture but also the Iraq War. Optic Verve's mix of registers and styles abruptly cuts memoir into mathematics into news-commentary into autobiography into scholarly commentary. Insofar as the book is or contains commentary, it is commentary on an unknown, the ubiquitous 'x' of algebra. Therefore, we can appropriately describe Walsh's book as a form of algebra, and the text asks to be read as such. I contextualize this claim with the work of contemporary mathematician and philosopher Fernando Zalamea.

On more general inequalities for weighted generalized proportional Hadamard fractional integral operator with applications

<abstract> Fractional calculus has been the target of the work of many mathematicians for more than a century. Some of these investigations are of inequalities and fractional integral operators. In this article, a novel fractional operator which is known as weighted generalized proportional Hadamard fractional operator with unknown attribute weight is proposed. First, a fractional formulation is constructed, which covers a subjective list of operators. With the aid of the above mentioned operators, numerous notable versions of Pólya-Szegö, Chebyshev and certain related variants are established. Meanwhile, new outcomes are introduced and new theorems are exhibited. Taking into account the novel generalizations, our consequences have a potential association with the previous results. Furthermore, we demonstrate the applications of new operator with numerous integral inequalities by inducing assumptions on weight function $ \varpi $ and proportionality index $ \varphi. $ It is hoped that this research demonstrates that the suggested technique is efficient, computationally, very user-friendly and accurate. </abstract>

A Bibliometric study on computer and engineering

Computers & Engineering could be a leading round the world that concentrate on primarily all the sphere of science. thanks to the recent advances of various associated with careful finding out or deep thinking ways that of doing things applied so as to face with provide chain connected issues, the aim of this work is to check with attention on the availability chain employing a bibliometric approach that may establish the leading general ways that things moving into this space by analysing the foremost vital analysis establishments and countries. The work additionally develops a graphical mapping of the associated with a listing of references material by victimisation the seeing in your mind of things that virtually an equivalent as alternative things, (VOS) viewer software package. With this software package, the study analyses associated with a listing of references coupling, co-event of individuals UN agency work to seek out data and establishments and the way they're connected with each other mathematical relationship-related works through co-citation analysis. The results purpose show that Computers and industrial management has the fourth highest variety of analysis, during this space among leading establishments and individual employees in provide Chain, and China and Asian country the leading countries whereas Taiwan and Singapore have the best per person. that the bibliometric study of contemporary generation in laptop and engineering, to understand the standard of being terribly getting ready to the reality or true variety of round the world required and it's abundantly necessary for each individuals

WITHDRAWN: Design, simulation analysis of universal battery management system for EV applications

Abstract Now a days, Electric Vehicles (EVs) are familiar with abundant types of battery chemistries with different specifications. Battery Management System (BMS) is an essential and important device of an EV for smooth operation and long life. In present scenario, a separate BMS has been used for the particular battery. So, there is a need of a common BMS for all type of EVs. This paper proposes a simulation design of common BMS for four different batteries namely Nickel-Metal-Hydride, Nickel-Cadmium, Lithium-Ion and Lead-Acid. A common simulation and mathematical modelling of aforementioned four types of battery is executed here. The proposed system is designed to manipulate and control the instantaneous values of the battery parameters like Battery voltage, Current, Power consumption and State of Charge (SoC). This proposed BMS continuously monitors the battery parameters with high accuracy, especially in SoC measurement. The working of BMS is controlled and monitored by using Extended Kalman Filter (EKF). The entire mathematical modelling and simulation work of BMS is analysed by using MATLAB/Simulink.

Teaching Fractions in the Primary Education: A Cross-Sectional Study with Brazilian Polyvalents Teachers

Math Education in Brazil has undergone important changes in the last two decades. Among these, we can highlight those that refer to methods and ways of developing the pedagogical work of Mathematics with children aged 6 to 9 years. Until the end of the 20th century, Brazilian Mathematics Education was directed towards a more technicist teaching, focusing on the development of operational contents and without much meaning for students. With some political changes and the growing need for internal investments, Brazil starts to operate within the international standards established by the World Bank and International Monetary Fund, which establish as a priority for the granting of loans, the increase of educational levels, and the eradication of illiteracy. In view of this scenario, and allied to the evolution of curricular discussions, Brazilian basic education, mainly in the primary (6 to 10 years), started to incorporate more and important elements related to the teaching methodologies of Mathematics in its discussions, which knowledge teacher occupies the central point. In this sense, the present paper seeks to understand how polyvalent teachers, pedagogues who work in the teaching of Mathematics in the early years, teach the content of fractions and what the essential aspects regarding the methods chosen for this purpose are. Therefore, the research information sources were obtained in a continuing education course with teachers working in public education systems. Such sources were characterized by records of responses to a problem-situation. Data were obtained from the ipsis litteris transcription of these responses, followed by the Content Analysis (CA), assuming the registration units as the initial parameter. As a result, the research evidenced three categories in which the contents discussed by the professors are classified: technicist, undifferentiated method and non-technicist. In addition, the study evidenced the difficulties of teachers in the focus group in differentiating methods from concepts, thus assuming different meanings for the fractions.

Existence theorems of solution of fractional differential equations with nonlocal conditions

This paper establishes a study on some important latest innovations in the existence of mild solution of semilinear for differential and fractional differential equations subject to nonlocal initial conditions. To apply this, the study uses Hausdorff measure of non-compactness and fixed point theorems. A wider applicability of these techniques are based on their reliability and reduction in the size of the mathematical work.

SIR Model and HIV/AIDS in Khartoum

The Human Immunodeficiency Virus (HIV) epidemic in Khartoum constitutes the most serious health problem in the region and one that we do not fully understand. Recent approaches aiming to understand the situation have attempted to model the Human Immunodeficiency Virus (HIV) epidemic using deterministic compartmental models. Our work has reviewed the formal mathematical work on deterministic models of this nature and considers the relevance of the modelling approach to the HIV in Khartoum. This model is built on SIR and population models. Evaluation of the basic reproduction number, R0, will be carried out using the SIR model for an optimal value of α and γ where α and γ are the inflow and the outflow of infectious individuals per infectious capita respectively (R0 = α γ ). The population will be divided into compartments, in- and out-flows from compartments leading to a corresponding differential equation. A numerical solver in MATLAB is then used to compute the solutions. Our model will be fitted to the data from Khartoum state, which is the capital of the Sudan and it has very good data related to HIV. Our results demonstrated that Khartoum was endemic for HIV when the epidemic began in the year 2002 until the year 2005 (R0 is 1.02). The value of R0 decreases and remains stable for ten years from the year 2006-2016 (R0 is 0.98). The most affected Sudanese population in Khartoum with AIDS was the male (Teenager) 10 - 19 age group. Also the treatment (ART) is recommended for everyone who had HIV.

Stability and applications

We give a brief overview of Bridgeland's theory of stability conditions, focusing on applications to algebraic geometry. We sketch the basic ideas in Bayer's proof of the Brill--Noether Theorem and in the authors' proof of a theorem by Gruson--Peskine and Harris on the genus of space curves. This note originated from the lecture of the first author at the conference From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford, held at the Center of Mathematical Sciences and Applications, Harvard University, August 18-20, 2018.

Mathematical Works of K. Marx: A Century-­Long History of Search, Deciphering and Analysis

Mathematical Works of K. Marx: A Century-­Long History of Search, Deciphering and Analysis

L’infini entre deux bouts. Dualités, univers algébriques, esquisses, diagrammes

The article affixes a resolutely structuralist view to Alain Badiou’s proposals on the infinite, around the theory of sets. Structuralism is not what is often criticized, to administer mathematical theories, imitating rather more or less philosophical problems. It is rather an attitude in mathematical thinking proper, consisting in solving mathematical problems by structuring data, despite the questions as to foundation. It is the mathematical theory of categories that supports this attitude, thus focusing on the functioning of mathematical work. From this perspective, the thought of infinity will be grasped as that of mathematical work itself, which consists in the deployment of dualities, where it begins the question of the discrete and the continuous, Zeno’s paradoxes. It is, in our opinion, in the interval of each duality ― “between two ends”, as our title states ― that infinity is at work. This is confronted with the idea that mathematics produces theories of infinity, infinitesimal calculus or set theory, which is also true. But these theories only give us a grasp of the question of infinity if we put ourselves into them, if we practice them; then it is indeed mathematical activity itself that represents infinity, which presents it to thought. We show that tools such as algebraic universes, sketches, and diagrams, allow, on the one hand, to dispense with the “calculations” together with cardinals and ordinals, and on the other hand, to describe at leisure the structures and their manipulations thereof, the indefinite work of pasting or glueing data, work that constitutes an object the actual infinity of which the theory of structures is a calculation. Through these technical details it is therefore proposed that Badiou envisages ontology by returning to the phenomenology of his “logic of worlds”, by shifting the question of Being towards the worlds where truths are produced, and hence where the subsequent question of infinity arises.

From Plato to Weil and beyond: Genericity through the history of mathematics

At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague linguistic phenomenon and became a precise and fruitful mathematical concept.

Метафизика Московской математической школы на рубеже XIX–XX веков

В данной работе рассматривается вопрос о формировании религиозных воззрений упредставителей Московской математической школы на рубеже XIX–XX вв. и влиянии ми-росозерцания на их научное творчество. Основное ядро этой группы ученых составлялиН.Д. Брашман, Н.В. Бугаев, П.А. Некрасов, Д.Ф. Егоров, Н.Н. Лузин, П.А. Флоренский.В эволюции идей московских математиков-мыслителей XIX – начала XX века мож-но выделить общую тенденцию: они прошли путь от математики к философии и сно-ва вернулись к математике. Из Московского математического общества (Н.Д. Брашман,Н.В. Бугаев и др.) выросла Московская философско-математическая школа (Н.В. Бугаев,П.А. Некрасов, П.А. Флоренский и др.), а последняя послужила импульсом к образованиюМосковской школы теории функций (Д.Ф. Егоров, Н.Н. Лузин и др.).Впервые выявлены мировоззренческие истоки формирования Московской математиче-ской школы. Философские предпочтения представителей этой школы близки к славяно-фильству (неприятие развития России по западным образцам, учение о цельности духа(отрицающее познание только через разум или чувства без участия духа); учение о собор-ности как получении свободы через растворение личности в церкви, обществе, государстве;православное миропонимание; любовь к Родине). Эти идеи оказали влияние и на характерматематического творчества московских математиков, специфическими чертами которогостали: 1) коллективный характер, генерирование новых направлений в науке и горячее же-лание делиться ими с другими учеными; 2) сосредоточенность на поиске общих методов изакономерностей; 3) склонность к созерцанию, предпочтение теоретических исследований,а не практических (область научных интересов — теория чисел, теория множеств, теорияфункций и пр.).

Antički korijeni Getaldićeva rada na razvoju matematičke analize i sinteze

The diverse opus of Marin Getaldić can methodologically and conceptually be divided into two parts. Getaldić’s early works can be considered as a reinterpretation of selected works from the ancient Greek and Roman tradition with the aim of transmitting ancient knowledge and theories, but also as an effort to further explore and improve these teachings within the framework of ancient Greek mathematical methods. In his more mature works, Getaldić was focused on the problem of the method. For twenty years, in his native Dubrovnik, he was developing the ideas he had encountered on a study trip across Europe, independently and almost completely isolated from the intense developments in the European scientific community in the first decades of the 17th century. He summarized the findings of his research in a seminal, five-volume work De resolutione et compositione mathematica (Rome 1630). Although Getaldić operated in an environment that was permeated by the Renaissance and humanist influences, in his local environment knowledge was transferred more slowly than in Western European countries where modern science emerged during the 16th and 17th centuries. In Dubrovnik isolation, he created new theoretical and practical knowledge, as well as original works that echoed in the European scientific community not only during his lifetime, but also later, during the 17th and 18th centuries. His example shows that the transfer of knowledge did not take place only from European epistemological centers to the periphery, for it shows that the scientific transfers within Europe went in both directions. He worked at a time when the accumulated knowledge about ancient works and the spread of humanistic education outgrew the ancient tradition, and gradually, after the methodological transformation, modern science was founded and shaped. It took almost twenty centuries for the ancient mathematical methodology, complemented by knowledge assimilated from the Arab and Indian mathematical traditions, to be conceptually modified and new methods aiming at achieving new theoretical knowledge and practical solutions to be developed. In building his rich opus, Getaldić relied heavily on the original ancient mathematical methods, which he consistently applied to a variety of problems. His work was largely based on the works of Greek mathematicians, among whom Pappus and Diophantus stand out, and was influenced by Eudoxus’ theory of scale and Archimedes’ application of logical methodology, i.e. arithmetic interpretation of geometry. Getaldić combined different tendencies of ancient Greek mathematics in a unique and fruitful way. After mastering Viète’s symbolic algebra that operated with general quantities, Getaldić systematically explored the possibilities of symbolic algebra in relation to ancient mathematical methods, which played a crucial role in the further development of modern mathematics and gradually lead to another major conceptual change in mathematical history. The change did not only affect mathematics, but also enabled the emergence of new, simpler and more exact interpretations in other sciences as well.

Equations as Unruly Objects

Abstract Specialized notation, complexity, and sheer length contributed to the unruly nature of 18th-century equations, whether in manuscript or printed form. By close examination of early modern material texts, this essay compares constraints and affordances of the pen and the composing stick for setting boundaries and imposing order on algebraic expressions. Drawing on French and British mathematical works, it considers typesetting practices and advice to readers in influential algebra textbooks, compares mathematical manuscripts prepared for print and the printed results, unpacks oversize pages brimming with derivations and multiple cases, and reflects on practices of mise-en-page in the Mémoires of the Paris Academy of Sciences and the Philosophical Transactions. It thus invites attention to the tools, gestures, and traces of amateur, expert, reader, writer, and typesetter in 18th-century algebra.

‘Disturbed’ by Euclid: Thomas Fincke and the reading of Ramist mathematics in sixteenth-century Germany

This article presents evidence of the transmission and reception of Petrus Ramus's mathematical pedagogy, as witnessed in a multi-volume Sammelband constructed and used in late sixteenth-century Germany. It considers how the methodological influence of Ramus was transmitted to students by the mathematical work of Thomas Fincke, before suggesting that idiosyncratic users of the Sammelband tangled with authoritative interpretations of Euclid by incorporating their own reading and notational practices. Whilst Fincke's work was aimed toward students familiar with Ramist teaching, marginalia found within the Sammelband reinterpret these intentions, demonstrating the pedagogical relationships shared between Fincke, his predecessors, and the later readers of the volume.

‘The Curious Ways to Observe Weight in Water’: Thomas Harriot and His Experiments on Specific Gravity

Abstract This paper explores the experiments of the English mathematician Thomas Harriot (1560-1621) on specific gravity in the years 1600-1605, as recorded in a series of manuscript notes in British Library Add. MS 6788. It examines the programme of reading undertaken by Harriot before (or during) these experiments (including works by Jean Bodin, Giovanni Battista della Porta, Gerard de Malynes, Gaston du Clo, and Juan Bautista Villalpando), and describes a series of experiments conducted by him which compared the weight of a wide variety of substances in air and water. Harriot’s work is compared to that of his contemporary Marino Ghetaldi (1568-1626) in Promotus Archimedis (1603), and the work of both mathematicians can be positioned in the context of sixteenth-century mathematical responses to the famous problem posed by Hiero, King of Syracuse to Archimedes (as related by Vitruvius). Harriot’s use of proportional mathematics (especially the “rule of alligation”) in his experimental work and his application of this technique to problems in the alloying of metal and chymical analysis is examined in detail.

Lagrangian Approach to Global Well-Posedness of the Viscous Surface Wave Equations Without Surface Tension

In this paper, we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab, for which the first complete proof was given in Guo–Tice [Anal. PDE 6,1429–1533 (2013)] via a hybrid of Eulerian and Lagrangian schemes. The fluid dynamics are governed by the gravity-driven incompressible Navier–Stokes equations. Even though Lagrangian formulation is most natural to study free boundary value problems for incompressible flows, few mathematical works for global existence are based on such an approach in the absence of surface tension effect, due to breakdown of Beale’s transformation. We develop a mathematical approach to establish global well-posedness based on the Lagrangian framework by analyzing suitable “good unknowns” associated with the problem, which requires no nonlinear compatibility conditions on the initial data.

Gaming for the Greater Good: The North American Scholastic Esports Federation Sets Students on a STEM Trajectory

Broadcom founder Henry Samueli and his wife Susan started the Samueli Foundation with the mission of creating societal value by investing in innovative, entrepreneurial, and sustainable ideas. In exchange for their financial support, they look for forward movement toward the goal of a "vibrant, healthy and well-balanced community." Work in science, technology, engineering, and mathematics (STEM) is the core of philanthropy at the Samueli Foundation, which has a particular focus in growing STEM interest among K-12 students. Recently, the foundation developed and launched the North American Scholastic Esports Federation (NASEF), a free platform and corresponding curriculum that uses e-sports as a sort of Trojan horse to help students grow their 21st century skills in communication, collaboration, creativity, and problem solving, all while creating pathways to STEM careers and building strong relationships between students, teachers, and team coaches.

Data informed leadership: the work of primary mathematics lead teachers in New Zealand

ABSTRACT Increasingly, teachers are considered accountable for continuous improvement in student achievement. They are expected to integrate and analyse data from multiple sources in order to make decisions aimed at positively influencing student outcomes. Given the growing recognition of the importance of data-informed decision making in teaching, it is important to understand how teachers can best be supported in this. Currently, there is little research into how teachers can facilitate data literacy development for their in-school colleagues. This study employed an interpretive qualitative methodology to focus on the experiences of mathematics lead teachers (MLTs) in leading change to support the development of their colleagues. MLTs were found to use a range of tailored strategies, providing ‘on the job’ and ‘just in time’ support, and demonstrating evaluative and adaptive capabilities. They were found to provide leadership in the development of data-informed decision making through their collaborative approach.

Learning to Collaborate While Learning Mathematics

This task structure both engages students in serious, grade-level appropriate mathematical work and allows the teacher to do the intentional and purposeful work of building a collaborative classroom culture. We highlight possibilities for adapting this task structure to teach different mathematics content across grade levels 3–5.