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Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from 'If A were true, then C would be true' to 'If A and B were true, then C would be true'), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. [ABSTRACT FROM AUTHOR]

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from 'If A were true, then C would be true' to 'If A and B were true, then C would be true'), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. [ABSTRACT FROM AUTHOR]

Improving student participation and achievement in post-secondary STEM courses continues to be an important concern of many governments and educational institutions since this is one avenue by which the number of STEM professionals can be increased. This paper examines and compares the gendered participation, performance and attrition rate of candidates in two post-secondary mathematics courses over a 5-year period from 2013 to 2017. This study used the Caribbean Advanced Proficiency Examination (CAPE) results from the Caribbean Examinations Council (CXC), which is the main public examination board in the Caribbean, for 15,220 candidates (N = 19,585) from 71 post-secondary educational institutions in Jamaica. 'CAPE' applies to both the course of study and the associated examination. The study found that, on average, approximately one-fifth of the candidates who pursue CAPE courses in Jamaica opt to study a mathematics course and that across the 5 years this remained relatively stable. There was, however, a marked decrease in the number of candidates choosing to enrol in Unit 2 courses on completion of the related Unit 1 course. Another key finding was that, while a higher percentage of males chose to undertake Applied Mathematics Unit 2 and equal proportions of male and female candidates the other three courses, there was a significant difference in the overall performance by gender with females outperforming their male peers. These findings suggest that initiatives are needed which improve student performance and experience in CAPE mathematics Unit 1 subjects which could then reduce student attrition across units. [ABSTRACT FROM AUTHOR]

We can distinguish between two different ways in which mathematics is applied in science: when mathematics is introduced and developed in the context of a particular scientific application; when mathematics is used in the context of a particular scientific application but it has been developed independently from that application. Nevertheless, there might also exist intermediate cases in which mathematics is developed independently from an application but it is nonetheless introduced in the context of that particular application. In this paper I present a case study, that of the Lagrange multipliers, which concerns such type of intermediate application. I offer a reconstruction of how Lagrange developed the method of multipliers and I argue that the philosophical significance of this case-study analysis is twofold. In the context of the applicability debate, my historically-driven considerations pull towards the reasonable effectiveness of mathematics in science. Secondly, I maintain that the practice of applying the same mathematical result in different scientific settings can be regarded as a form of crosschecking that contributes to the objectivity of a mathematical result. [ABSTRACT FROM AUTHOR]

The epilogue, Chapter 7, describes Guccia's death and the decay of the Circolo from the interwar period through the Second World War, when the bombing of Palermo in 1943 destroyed the Palazzo Guccia. Two mathematicians particularly assisted Guccia in improving his mathematical society and the I Rendiconti i : the French Poincaré and the well-known Italian mathematician Vito Volterra (1860-1940). The other important mathematician in Guccia's scientific life was Poincaré, who supported Guccia throughout his career by contributing important papers to the I Rendiconti i . However, the book remains captivating, sheds light on a still little-known story, and contains unpublished documents on the origins of the Guccia family, the role of Guccia's uncle Giulio Fabrizio Tomasi, and the first years of Guccia's life. [Extracted from the article]

In this paper we consider stability in the Ulam-Hyers sense, and in other similar senses, for the five equivalent definitions of one-dimensional dynamical systems. [ABSTRACT FROM AUTHOR]