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This special issue of the Journal Mathematical Methods in the Applied Sciences on the topic of Modelling, Analysis, and Applications is devoted to the development of mathematical modelling, analysis, and applications, from theoretical and numerical perspectives, involving different applied sciences and engineering. It collects invited contributions, from selected quality full papers submitted to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC2022). The conference took place in Porto, Portugal in 27–29 June 2022 (https://www.isep.ipp.pt/Page/ViewPage/ICMASC). [ABSTRACT FROM AUTHOR]

Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics and real-life modelling are introduced much earlier than is currently done. Integrating these concepts with philosophical principles of society and ethics would ensure suitable foundations for future modellers and users of technology to build upon. [ABSTRACT FROM AUTHOR]

This article investigates the implementation of inquiry-oriented instruction in 20 undergraduate mathematics classrooms. In contrast to conventional wisdom that active learning is good for all students, we found gendered performance differences between women and men in the inquiry classes that were not present in a noninquiry comparison sample. Through a secondary analysis of classroom videos, we linked these performance inequities to differences in women's participation rates across classes. Thus, we provide empirical evidence that simply implementing active learning is insufficient, and that the nature of inquiry-oriented classrooms is highly consequential for improving gender equity in mathematics. [ABSTRACT FROM AUTHOR]

The unfinished final Contrapunctus from Bach's posthumously-published Kunst der Fuge has received several dozen completions over the past century. Although the majority of these have been published and recorded, none has yet established themselves as the leading solution among performers, and this may have more to do with their perceived 'Bach-ness' than the undoubted contrapuntal skill and ingenuity that they each demonstrate. This study uses an established information-theoretical method drawn from mathematics to explore the extent to which it is possible to 'measure' the similarity of these reconstructions to the original, and so determine which are closest to the musical lines of Bach's existing opening of Contrapunctus XIV. [ABSTRACT FROM AUTHOR]

Bernard Girard's book, Conversations avec Tom Johnson was published in French by Éditions Aedam Musicae in 2011 and is here translated into English for the first time by Christine Lucia. The original book comprised 137 pages of wide-ranging conversations held at various times, covering Johnson's music and career in some detail and organised into categories such as 'The Man Who Counts', 'Minimalisms', 'Mathematics and Music', and 'Opera'. The book also included two short essays on Johnson by musicologist Gilbert Delor and mathematician Franck Jedrzejewski, a brief Worklist and an Index that lists the more than 150 composers, performers, mathematicians and other key figures in Johnson's life discussed in the text. The translated text includes all but the Worklist and Index. The conversations range across six decades of new music and give unique insights into the development of musical minimalism, to which Johnson contributed as a critic in his early career in New York, and since he moved to Paris in 1982, as a composer. Discussions of Johnson and Cage, Feldman, Lucier, La Monte Young, Reich, Rzewski, Niblock and others reveal the diversity of minimalist aesthetics and Johnson's uncompromising vision as a composer and artist. The translated text contributes to the literature in English on musical minimalism, new music and mathematics, computational science and combinatorics, and to our understanding of other relationships between music, science and art. [ABSTRACT FROM AUTHOR]

When Euler began his mathematical career, analysis was not an autonomous and self-founding field of mathematics but only a method for solving geometrical problems. During Euler's activity, analysis emerged as a new field of mathematics whose methods differed from those of geometry. Moreover, Euler changed the architecture of this science and regarded analysis as lying at the heart of mathematics, while geometry and mechanics were considered as a sort of applied analysis. The new structure of mathematical sciences was successful, but this success soon showed the inadequacy of the Eulerian foundations of analysis. [ABSTRACT FROM AUTHOR]

We study the emergence of all references to modern mathematics in Difference and Repetition, and we explain how, using these mathematical approaches, Deleuze constructs an "ideal synthesis of difference" which goes well beyond the usual reductionist perspectives of his commentators. [ABSTRACT FROM AUTHOR]

We examine the extent to which a block operator matrix of Hain-Lüst type can be reconstructed from its Titchmarsh-Weyl coefficients. The detectable subspace of the operator is determined in a variety of cases and the question of unique determination of the coefficients is considered for both first and second order operators. [ABSTRACT FROM AUTHOR]

In 1986, A. Basile and H. Weber proved that every countable family M of σ -additive measures on a σ -complete Boolean ring R admits a dense G δ -set of separating points, with respect to a suitable topology, in the following two cases: either (i) each element of M is s-bounded and, whenever λ , ν ∈ M are distinct, the quotient of R modulo N ( λ − ν ) is infinite, or (ii) each element of M is continuous. In this paper we consider modular measures on lattice-ordered pseudo-effect algebras. Using topological methods, we extend the result of Basile and Weber in a way that allows to unify the above two cases (i) and (ii). This gives a new contribution also in the classical setting of algebras of sets. [ABSTRACT FROM AUTHOR]

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

This study examined the feasibility and effectiveness of a comprehensive function-based intervention applied across multiple inclusive classroom settings. The participant was a middle school student diagnosed with Asperger Syndrome who exhibited chronic off-task behaviors across all academic environments. This study was conducted across two phases: (a) A descriptive functional behavior assessment (FBA) was conducted across all inclusive classroom environments and (b) a single, comprehensive function-based intervention was developed based on the results of the FBA followed by the implementation of a comprehensive function-based intervention in each inclusive classroom environment using a multiple probe design. The comprehensive function-based intervention markedly improved the participant’s on-task behavior in each classroom setting. Furthermore, social validity ratings by each teacher revealed that the comprehensive, function-based intervention was preferable to the previously used classroom practices. Implications, limitations, and directions for future research are discussed. [ABSTRACT FROM AUTHOR]

We investigate the stability of a fully-implicit, linearly extrapolated Crank-Nicolson (CNLE) time-stepping scheme for finite element spatial discretization of the Navier-Stokes equations. Although presented in 1976 by Baker and applied and analyzed in various contexts since then, all known convergence estimates of CNLE require a time-step restriction. We propose a new linear extrapolation of the convecting velocity for CNLE that ensures energetic stability without introducing an undesirable exponential Gronwall constant. Such a result is unknown for conventional CNLE for inhomogeneous boundary data (usual techniques fail!). Numerical illustrations are provided showing that our new extrapolation clearly improves upon stability and accuracy from conventional CNLE. [ABSTRACT FROM AUTHOR]

The paper analyzes the motion of nonholonomic mechanical systems composed of two particles with imposition of various nonlinear limitations to the velocities of the particles - parallelism of velocities, equality of the intensities of velocities and perpendicularity of velocities. The analysis for such systems includes: equations of constraints, reactions of constraints, i.e. the mode of variations of such constraints, trajectories of the points of the systems, linear integrals for generalized velocities, i.e. cyclical coordinates. It is clearly demonstrated on these models that in the case of nonlinear nonholonomic constraints the Hamiltonian effect, in the general case, has no stationary value. Lastly, the equations of brachistochronic motion of described systems are derived and the brachitochrones of specified points are determined. [ABSTRACT FROM AUTHOR]

Based on the analysis of three cases of mathematical problem solving, this paper shows how we should deal with the circumstances arising during the process of problem solving in order to succeed when we face difficulties, mistakes and failures. [ABSTRACT FROM AUTHOR]

In his Elementorum Myologiae Specimen, Steno geometrizes "the new fabric of muscles" and their movement of contraction, so as to refute the main contemporary hypothesis about the functioning of the muscles. This physiological refutation relies on an abstract representation of the muscular fibre as a parallelepiped of flesh transversally linked to the tendons. Those two features have been comprehensively studied. But the method used by Steno, as well as the way he has chosen to present his physiological results, have so far been neglected. Yet, Steno's work follows a true synthetic order, which he conceives as a tool to separate uncertain anatomical "elements" from the certain ones. We will show that the true understanding of this "more geometrico" order is the only way to avoid frequent misconceptions of the scientific aim pursued by Steno, which is neither to give a mathematical explanation of the functioning of the muscles, nor to reduce the muscles to some mathematical shapes. [ABSTRACT FROM AUTHOR]

Dilated integers form an ordered group of the Cartesian indices into a d-dimensional array represented in the Morton order. Efficient implementations of its operations can be found elsewhere. This paper offers efficient casting (type)conversions to and from an ordinary integer representation. As the Morton order representation for 2D and 3D arrays attracts more users because of its excellent block locality, the efficiency of these conversions becomes important. They are essential for programmers who would use Cartesian indexing there. Two algorithms for each casting conversion are presented here, including to-and-from dilated integers for both d = 2 and d = 3. They fall into two families. One family uses newly compact table lookup, so the cache capacity is better preserved. The other generalizes better to all d, using processor-local arithmetic that is newly presented as abstract d-ary and (d - 1)-ary recurrences. Test results for two and three dimensions generally favor the former. [ABSTRACT FROM AUTHOR]

Abstract: Advanced mathematical tools for metrology and testing have just one primary purpose: to convey confidence for a model of the system that has been measured. Novel tools need to go beyond the creation of confidence and include the communication of the confidence to the end users of the modelled measurements. To reach the widest possible community of users, simplicity is an important criterion in guiding the choice of, and presentation of, any novel advanced mathematical tools. For choosing paths to simplicity, different aspects are presented and discussed with an emphasis on avoiding nuisance parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we present a view of kernels from a fuzzy set theoretical perspective. Indeed, it turns out that kernels which are positive-definite functions have to fulfill a consistency property given by the so-called T-transitivity of a fuzzy T-equivalence relation with respect to the triangular norm T. As a result, we introduce a triangular norm which is characterized as being the greatest one for which all kernels mapping to the unit interval and having constant 1 in its diagonal are -equivalences. Finally, some applied relevant aspects are discussed as a starting point for further research. [Copyright &y& Elsevier]

Abstract: François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète’s major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète’s ‘new algebra’ relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète’s algebraic analysis is not an analysis in the same sense as his cryptanalysis is. In Aristotelian terms, the first is a form of ‘’, while the second is a form of . While the first is a top-down argument from the point of view of the human subject, since it is an argument going from what is not actual to what is actual for such a subject, the second one is a bottom-up argument from this same point of view, since it starts from what is first for us and proceed towards what is first by nature. [Copyright &y& Elsevier]

The aim of the study was to evaluate a new method for automated definition of a center lumen line in vessels in cardiovascular image data. This method, called VAMPIRE, is based on improved detection of vessel-like structures. A multiobserver evaluation study was conducted involving 40 tracings in clinical CTA data of carotid arteries to compare VAMPIRE with an established technique. This comparison showed that VAMPIRE yields considerably more successful tracings and improved handling of stenosis, calcifications, multiple vessels, and nearby bone structures. We conclude that VAMPIRE is highly suitable for automated definition of center lumen lines in vessels in cardiovascular image data. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy homoclinic orbits and commuting fuzzifications are defined and studied. We study sufficient conditions, involving commuting fuzzifications, under which a crisp homoclinic orbit is preserved after fuzzification. We show the usual fuzzification is commuting and therefore preserves homoclinic orbits. Several examples are given regarding fuzzy homoclinic orbits and commuting fuzzifications. [Copyright &y& Elsevier]

This note extends the results in Feng (Fuzzy Sets and Systems 123 (2001) 11) about sums of independent fuzzy random variables by means of a convergence criterion in uniform Hausdorff metric. [Copyright &y& Elsevier]

We compared selected kinematic variables for four different ski turn techniques performed by five experienced and five intermediate male skiers. The four ski turn techniques were the upstem turn, the downstem turn, the parallel turn and the parallel step turn. Each turn was divided into the initiation phase and the first and second steering phases. Most of the statistically significant differences (P < 0.05) between the two groups were found for the initiation phases of the four turns. Both the hip axis-hand axis angle and the edging angle of the uphill ski were significantly different between the two groups for the upstem turn at the beginning of the initiation phase. For the downstem turn, significant differences between the groups were found at the start of the initiation phase for the hip axis-hand axis angle, the shoulder axis-fall line angle, and the edging angle of the uphill ski. The standard deviation of the distance between the tips of the two skis over the second steering phase also differed significantly between the two groups. For the parallel step turn, significant differences were found at the start of the initiation phase for the edging angle of the downhill ski and the downhill ski to movement direction angle. Significant differences were also found for the edging angle of the downhill ski in the middle of the second steering phase and the shoulder axis to movement direction angle at the end of this phase. For the initiation phase of the parallel turn, significant differences were found for the timing of setting the ski pole, the uphill knee angle at the start of this phase and the range of the knee angle of the uphill leg from the start to the end of this phase. For this turn, significant differences between the two groups were also found for the edging angle of the downhill ski in the middle of the second steering phase and the shoulder axis to movement direction angle at the end of this phase. One of the reasons it was possible to identify a few significant differences only for the turns analysed, was the variability within the intermediate group: for most of the variables analysed, the standard deviation was much higher for the intermediate than for the experienced group. [ABSTRACT FROM AUTHOR]

During the prosecution and defence of drink-driving cases, forensic practitioners are often required to engage in various blood-alcohol calculations, such as whether or not the statutory limit was exceeded (e.g. 80mg/100mL, 0.08g/100mL or 0.80g/L). For this purpose, most forensic scientists utilize the Widmark equation, or some modification thereof, to calculate a person's blood alcohol concentration (BAC) based on information about the amount of ethanol consumed and the pattern of drinking. This equation comes in two main forms; one of which incorporates the apparent volume of distribution of ethanol (V) and the other a person's total body water (TBW). In this study, we utilised two independent data sets, one involving the determination of V for ethanol in 173 men and 63 women, and the other TBW determined for 582 men and 884 women. Those subjects included in the TBW group represented various racial groups (Caucasians, African Americans, Hispanics, Asians and Puerto Ricans), with body mass index (BMI) ranging from 17 to 80kg/m2. Both versions of the Widmark equation were evaluated in relation to their accuracy and precision in predicting TBW and/or V using the two most common anthropometric equations; those of Watson et al. and Forrest. Both anthropometric equations exhibited good accuracy (<4.3%) for the prediction of both TBW and V. However, the root mean square error was lower TBW was used for prediction (9.09-12.84%) rather than V (11.72-15.08%). Overall, this study has demonstrated (a) that blood-alcohol calculations are more reliable using TBW rather than V (b) that both equations (Watson et al. and Forrest) are applicable to ethnic groups other than Caucasians and (c) the Forrest equation predicts TBW in men and women with BMI from 17 to 35kg/m2 and that the Watson et al. equation works for those with more extreme BMI; females (17-80kg/m2) and males (17-67kg/m2). [ABSTRACT FROM AUTHOR]