bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dense gas effects in inviscid homogeneous isotropic turbulence
Authors: Sciacovelli L. , Cinnella P. , Content C. , Grasso F. 
Published: June 2016

A detailed numerical study of the influence of dense gas effects on the large-scale dynamics of decaying homogeneous isotropic turbulence is carried out by using the van der Waals gas model. More specifically, we focus on dense gases of the Bethe–Zel’dovich–Thompson type, which may exhibit non-classical nonlinearities in the transonic and supersonic flow regimes, under suitable thermodynamic conditions. The simulations are based on the inviscid conservation equations, solved by means of a ninth-order numerical scheme. The simulations rely on the numerical viscosity of the scheme to dissipate energy at the finest scales, while leaving the larger scales mostly unaffected. The results are systematically compared with those obtained for a perfect gas. Dense gas effects are found to have a significant influence on the time evolution of the average and root mean square (r.m.s.) of the thermodynamic properties for flows characterized by sufficiently high initial turbulent Mach numbers (above 0.5), whereas the influence on kinematic properties, such as the kinetic energy and the vorticity, are smaller. However, the flow dilatational behaviour is very different, due to the non-classical variation of the speed of sound in flow regions where the dense gas is characterized by a value of the fundamental derivative of the gas dynamics (a measure of the variation of the speed of sound in isentropic compressions) smaller than one or even negative. The most significant differences between the perfect and the dense gas case are found for the repartition of dilatation levels in the flow field. For the perfect gas, strong compressions occupy a much larger volume fraction than expansion regions, leading to probability distributions of the velocity divergence highly skewed toward negative values. For the dense gas, the volume fractions occupied by strong expansion and compression regions are much more balanced; moreover, strong expansion regions are characterized by sheet-like structures, unlike the perfect gas which exhibits tubular structures. In strong compression regions, where compression shocklets may occur, both the dense and the perfect gas exhibit sheet-like structures. This suggests the possibility that expansion eddy shocklets may appear in the dense gas. This hypothesis is also supported by the fact that, in dense gas, vorticity is created with equal probability in strong compression and expansion regions, whereas for a perfect gas, vorticity is more likely to be created in the strong compression ones.
The effect of dietary changes on distinct components of the metabolic syndrome in a young Sri Lankan population at high risk of CVD
Authors: Guess Nicola , Wijesuriya Mahen , Vasantharajah Laksha , Gulliford Martin , Viberti Giancarlo , Gnudi Luigi , Karalliedde Janaka 
Published: June 2016

AbstractSouth Asian populations are predisposed to early onset of the metabolic syndrome. Lifestyle intervention programmes have demonstrated a reduction in the metabolic syndrome and CVD risk; however, the most effective components of the multi-faceted lifestyle interventions are unknown. We studied 2637 Sri Lankan males (n 1237) and females (n 1380), with a mean BMI of 23·9 (sd 4·2) kg/m2, aged 22·5 (sd 10·0) years, who had participated in a 5-year lifestyle-modification programme to examine the effect of dietary changes on distinct components of the metabolic syndrome. The dietary intervention comprised advice to replace polished starches with unpolished starches, high-fat meat and dairy products with low-fat products and high-sugar beverages and snacks with low-sugar varieties. For the purposes of this analysis, data from the control and intensive lifestyle groups were combined. Anthropometric and biochemical data were recorded, and a FFQ was completed annually. Multiple regression was used to determine the effect of the dietary changes on distinct components of the metabolic syndrome. The ratio unpolished:polished rice was inversely related to change in fasting glucose (β=−0·084, P=0·007) and TAG (β=−0·084, P=0·005) and positively associated with change in HDL-cholesterol (β=0·066, P=0·031) at the 5-year follow-up after controlling for relevant confounders. Red meat intake was positively associated with fasting glucose concentrations (β=0·05, P=0·017), whereas low-fat (β=−0·046, P=0·018) but not high-fat dairy products (β=0·003, P=0·853) was inversely related to glucose tolerance at the follow-up visit. Replacement of polished with unpolished rice may be a particularly effective dietary advice in this and similar populations.
Worldwide burden of gastric cancer in 2010 attributable to high sodium intake in 1990 and predicted attributable burden for 2030 based on exposures in 2010
Authors: Peleteiro Bárbara , Barros Susana , Castro Clara , Ferro Ana , Morais Samantha , Lunet Nuno 
Published: June 2016

AbstractAssessing the impact that patterns of Na intake may have on gastric cancer will provide a more comprehensive estimation of Na reduction as a primary prevention approach. We aimed to estimate the proportion of gastric cancer cases that are attributable to Na intake above the recommendation by the WHO (≤2 g/d) throughout the world in 2010, as well as expected values for 2030. Population attributable fractions (PAF) were computed for 187 countries, using Na intakes in 1990 and 2010 and estimates of the association between Na intake and gastric cancer, assuming a time lag of 20 years. Median PAF ranged from 10·1% in low to 22·5 % in very high Human Development Index (HDI) countries in men (P<0·001) and from 7·2 to 16·6 %, respectively, among women (P<0·001). An increase in median PAF until 2030 is expected in most settings, except for countries classified as low HDI, in both sexes. High Na intakes account for a large proportion of gastric cancer cases, and proportions are expected to increase in almost all of the countries. Intensified efforts to diminish Na intake in virtually all populations are needed to further reduce gastric cancer burden.
Age at introduction of solid foods and feeding difficulties in childhood: findings from the Southampton Women’s Survey
Authors: Hollis J. L. , Crozier S. R. , Inskip H. M. , Cooper C. , Godfrey K. M. , Robinson S. M. ,   Southampton Women’s Survey Study Group
Published: June 2016

AbstractThis study aimed to determine whether age at introduction of solid foods was associated with feeding difficulties at 3 years of age. The present study was carried out using data from the Southampton Women’s Survey (SWS). Women enrolled in the SWS who subsequently became pregnant were followed-up during pregnancy and postpartum, and the offspring have been studied through childhood. Maternal socio-demographic and anthropometric data and child anthropometric and feeding data were collected through interviews and self-administered questionnaires. When the children were 3 years of age, mothers/carers rated six potential child feeding difficulty questions on a four-point Likert scale, including one general question and five specific feeding difficulty questions. Age at introduction of solids as a predictor of feeding difficulties was examined in 2389 mother–child pairs, adjusting for child (age last breast fed, sex, gestation) and maternal characteristics (parity, pre-pregnancy BMI, age, education, employment, parenting difficulties, diet quality). The majority of mothers/carers (61 %) reported some feeding difficulties (general feeding difficulty question) at 3 years of age, specifically with their child eating enough food (61 %), eating the right food (66 %) and being choosy with food (74 %). Children who were introduced to solids ≥6 months had a lower risk of feeding difficulties (RR 0·73; 95 % CI 0·59, 0·91, P=0·004) than children who were introduced to solids between 4 and 6 months. No other significant associations were found. There were few associations between feeding difficulties in relation to age at introduction of solid foods. However, general feeding difficulties were less common among infants introduced to solid foods ≥6 months of age.
Divisibility properties for Fibonacci and related numbers
Authors: Sadek Jawad , Euler Russell 
Published: June 2016

Although it is an old one, the fascinating world of Fibonnaci numbers and Lucas numbers continues to provide rich areas of investigation for professional and amateur mathematicians. We revisit divisibility properties for t0hose numbers along with the closely related Pell numbers and Pell-Lucas numbers by providing a unified approach for our investigation.For non-negative integers n, the recurrence relation defined bywith initial conditionscan be used to study the Pell (Pn), Fibonacci (Fn), Lucas (Ln), and Pell-Lucas (Qn) numbers in a unified way. In particular, if a = 0, b = 1 and c = 1, then (1) defines the Fibonacci numbers xn = Fn. If a = 2, b = 1 and c = 1, then xn = Ln. If a = 0, b = 1 and c = 2, then xn = Pn. If a =b = c = 2, then xn = Qn [1].
Fun with Sign
Authors: Zhou Li 
Published: June 2016

When I was teaching calculus recently, an exercise in the textbook [1, p. 687, qn. 3] asked students to find the Taylor series of cosx centred at π/4. My students were able to find the seriesbut wondered how to take care of the sign changes, in order to express the series in I.-notation. They were quite puzzled after finding that the answer given in [I] isThe exponent n (n + 1)/2 seemed a rabbit out of the hat! This article is the result of trying to answer their question satisfactorily, and to have some serious fun. Readers are invited to try two teasers first before reading for their solutions.
Sliding in rough convex bowls
Authors: Hennings Mark , Ingram Jon 
Published: June 2016

It is an elementary fact that a particle sliding on a rough horizontal table experiences a deceleration of magnitude μg, where μ is the coefficient of friction between the particle and the table. Thus, if the initial speed u of the particle and the braking distance d are both known, then μ can be determined by the formulaThe idea of using braking distances to determine the coefficient of friction led the second author to ask the following question:A particle slides on the interior surface of a rough hemispherical bowl starting from rest. If the starting point of the particle and the point at which it comes to instantaneous rest after its slide are both known, is it possible to determine the coefficient of friction between the particle and the bowl?
Wind over tide
Authors: Mahony John D. 
Published: June 2016

The article ‘Reflections on the Woolwich Ferry’ [1] brought back some childhood memories. I remember being whisked away with my siblings from the verdant pastures of north-west Kent by bus and tram to Woolwich for a ride on one of the ‘Free Ferry’ paddle steamers; there were four of them and their passing in the mid 1960s was not universally welcomed. It was indeed a real treat that consumed just a little more than a full working day. The depths of a winter school holiday could find us huddled, privileged below the ferry decks on a gantry near the fire hole to receive the welcoming hot blast as its doors opened to accommodate the hand-stoked coke. It was hand-stoked to reduce smoke output, and each steamer could make about eight knots. Presumably health and safety considerations now would not allow for such a luxury of positioning.However, it was not always wine and roses. To borrow a phrase from one of Kipling's poems, it was sometimes a case of ‘not with this wind blowing, and this tide’, for there were rare occasions when journeys were temporarily delayed by exceptionally windy weather. The elements below (river velocity effect) conspired with the elements above (wind velocity effect) to delay ferry movements. The earlier article proposed a velocity model to deal with effects due only to the river flow and it is the purpose of this note to extend that argument by considering also a velocity effect due to the wind, because the superstructure on a ferry can be as susceptible to the wind as is the keel to the tide.
Ordering 15 marbles with a three-way scale
Authors: Audet Charles 
Published: June 2016

Many mathematical puzzles involve using a scale to compare the weights of two objects, or two groups of objects. The present work studies a similar but different type of question involving a scale.We are given a set of marbles, whose weights are all different. The only way to distinguish them is to use a special kind of scale. The scale has three trays and each can accept exactly one marble. The scale then indicates which is the heaviest, the lightest and consequently the middle one of the three marbles.The paper studies the question of ordering 15 different marbles with as few weighings as possible. The problem is taken from the website Enigmes, casse-têtes, curiosités et autres bizarreries [1] and Toppuzzle [2] where the best reported strategy requires 23 weighings. The problem can also be found at the website Trick of Mind [3] where a strategy requiring 22 weighings is proposed. These websites contain many challenging mathematical puzzles, some are classical problems, others are original creations. The author is not aware of any other work on this problem.The present paper describes a strategy that improves on the value of 22 weighings, and is structured as follows. Section 2 introduces some useful definitions and provides strategies to sort up to 9 marbles. Section 3 proves our main result, that 20 weighings is always sufficient to sort 15 marbles.
The tables of John Wallis and the discovery of his product π
Authors: Osler Thomas J. 
Published: June 2016

In the year 1656 John Wallis published his Arithmetica Infinitorum, [1], in which he displayed many ideas that were to lead to the integral calculus of Newton. In this work we find the celebrated infinite product of Wallis which gives π,Earlier in 1593, Vieta [2] found another infinite product which gives πBut, since Wallis does not mention it, we suppose that he was unaware of it. (Remarkably, these two seemingly different products are special cases of a more general formula [3].)
Alteration in the sum of alternating series by simple rearrangement
Authors: Nurcombe J. R. 
Published: June 2016

It is well known that the sum of an absolutely convergent series is invariant under rearrangement of its terms. On the other hand, a conditionally convergent series, that is one which converges but the sum of whose absolute values is unbounded, can be rearranged to have any sum whatsoever, or diverge in any desired manner (see for example [1, §44]). A simple examplS of a conditionally convergent series is the alternating harmonic series (AHS), . In [2], the following theorem on rearrangement of the AHS was proved:Theorem A: The AHS remains convergent under a simple rearrangement (i.e. the sub-sequence of its positive terms and the sub-sequence of its negative terms are in their original order) when p of its positive terms alternate throughout with q of its negative terms, and the alteration in sum is (p/q).
Folding a triangle
Authors: Jobbings Andrew 
Published: June 2016

The Original problemTake a right-angled triangle ABC, where ∠C = 90°, and fold along UV so that C lies on AB, as shown in Figure 1, where C' is the new position of C.Problem: Where should one fold in order to minimise the area of the folded triangld CUV?This problem was discussed by Hirschhom in [1], where he gives its origins and provides a solution, describing the answer as ‘quite remarkable’. However, he does not relate the answer to the geometry of the configuration. We adopt a more geometrical approach and use some simple folding ideas—there is a close relationship between paper folding and geometry which deserves to be more widely known (see [2] for example).
The gaps between sums of two squares
Authors: Shiu Peter 
Published: June 2016

Problems concerning the setof numbers which are representable as sums of two squares have a long history. There are statements concerning W in the Arithmetic of Diophantus, who seemed to be aware of the famous identitywhich shows that the set W is ‘multiplicatively closed’. Since a square must be congruent to 0 or 1 (mod 4), it follows that members of W cannot be congruent to 3 (mod 4). Also, it is not difficult to show that a number of the form 4k + 3 must have a prime divisor of the same form dividing it an exact odd number of times. However, the definitive statement (see, for example, Chapter V in [1]) concerning members of W, namely that they have the form PQ2, where P is free of prime divisors p ≡ 3 (mod 4), was first given only in 1625 by the Dutch mathematician Albert Girard. It was also given a little later by Fermat, who probably had a proof of it, but the first published proof was by Euler in 1749.
Regarding a generalisation of Ioachimescu's constant
Authors: Sîntămărian Alina 
Published: June 2016

The purpose of this paper is to present some results regarding the limit is of the sequenceIn the problem proposed by A. G. Ioachimescu in 1895 [1], it is asked to be shown that the sequence , defined by , for each , is convergent and its limit lies between -2 and -1.There have been given many generalisations and other results regarding Ioachimescu's problem in the literature (see, for example, [2, problem 3.1, p. 431], [3,4], [5, Theorem 1, parts (a) and (b)], [6, problem P2, parts (i) and (ii)], [7, 8]).
Vieta-like products of nested radicals
Authors: Osler Thomas J. 
Published: June 2016

The beautiful infinite product of radicalsdue to Vieta [1] in 1592, is one of the oldest non-iterative analytical expressions for π, In a previous paper [2] the author proved the following two Vieta-like products:for N even, andfor N odd. Here N is a positive integer, FN and LN are the Fibonacci and Lucas numbers, and is the golden section. (The Fibonacci numbers are F1 = 1, F2 = 1, with the recursion relation , while the Lucas numbers are L1 = 1, L2 = 3 with the same recursion relation )
An elementary, limit-free calculus for polynomials
Authors: McAndrew Alasdair 
Published: June 2016

This work grew out of a simple problem: how could I introduce the basic concepts of calculus to students who were mathematically under-prepared? It has been pointed out by many authors (see [1] and its references) that limits are a major stumbling block for many students beginning their study of calculus. Part of the difficulty with limits is the conceptual confusion between process and value. Some limits can be evaluated by a simple process of substitution, for example,while others cannot, for example,
The ‘stop after k girls or N children’ policy
Authors: Paseau A.C. , Villiers Michael de , Fox Michael 
Published: June 2016

1. IntroductionIn the article [1], a follow-up to my article [2], Christian and Trustrum cite empirical evidence that the probability of a family giving birth to a boy or to a girl may vary from family to family. Letting bi and gi = 1 − bi respectively denote the probability of the ith family giving birth to a boy or to a girl, the suggestion is that bi may be distinct from bj for distinct i and j. As they point out, this has implications for the expected society-wide number of boys and girls. Following my discussion of the ‘stop after k girls’ policy, Christian and Trustrum introduce the related policy ‘stop after k girls or N children’. They argue that the expected number of children under this latter policy is an increasing function of bi (when 0 < k < N). The present article complements their discussion by examining this alternative stopping policy in more detail.
Triangles meeting triangles
Authors: Crilly Tony , Fletcher Colin R. 
Published: June 2016

We consider two connected problems:
•For a given but otherwise arbitrary triangle in the plane, to construct similar triangles which ‘meet’ this triangle.•To find the triangle so formed which has least area.1. Constructing a triangle which meets anotherThese problems beg the question of what is meant by ‘meet’ and we now aim to make this precise:
Definition: A triangle XYZ will meet a given triangle ABC if on the triangle ABC, the vertex X lies on a line through AB, the vertex Y lies on a line through BC, and the vertex Z lies on a line through CA.When triangle XYZ is actually ‘in’ the triangle ABC, ‘meet’ is synonymous with the traditional ‘inscribe’ (such as in case (1) below). For ‘inscribe’ we understand that some of X, Y, Z may coincide with the vertices of ABC (such as case (2) below).More generally we use ‘meet’ to extend these possibilities by allowing XYZ to meet triangle ABC with its sides produced externally (such as case (3) below).
Statistics education: fit for purpose?
Authors: Toller Owen 
Published: June 2016

The Royal Statistical Society and the Institute and Faculty of Actuaries have published a report, written by Roger Porkess [1], which draws urgent attention to the issue of statistical education: is it fit for purpose? Statistics is an ever-present part of real life, and there can be no doubt that for most pupils it is statistics that will be the most directly used part of their mathematical education.The report follows an investigation into the perceived statistical needs of various subject ‘communities’, and is a follow-up to The future of statistics in our schools and colleges [2] by the same author and publishers. It is aimed at a wide readership, from policy-makers through curriculum providers and teachers (fairly low in the pecking order!) to authors and other providers of resources. There is no doubt that all such interested parties should be considering the issues covered by this study, and it should be read widely. The title of the report implies suggestions for cross-curricular work, but it is more essentially a plea to rethink the role of statistical education – a plea articulated more fully in [2]. It is the purpose of this article to further the debate.
Sultan among Dutchmen? Royal dress at court audiences in South India, as portrayed in local works of art and Dutch embassy reports, seventeenth–eighteenth centuries
Authors: BES LENNART 
Published: June 2016

AbstractFrom the fourteenth century CE onwards, South Indian states ruled by Hindu kings were strongly influenced by politico-cultural conventions from Muslim-governed areas. This development was, for instance, manifest in the dress and titles of the rulers of the Vijayanagara empire. As has been argued, they bore the title of sultan and on public occasions they appeared in garments fashioned on Persian and Arab clothing. Both adaptations exemplified efforts to connect to the dominant Indo-Islamic world. From Vijayanagara's fragmentation in the sixteenth and seventeenth centuries, new Hindu-ruled kingdoms arose. We may wonder to what extent those succeeding polities continued practices adopted from Islamic courts. With that question in mind, this article discusses royal dress at court audiences in four Vijayanagara successor states, chiefly on the basis of embassy reports of the Dutch East India Company and South Indian works of art. It appears that kings could wear a variety of clothing styles at audiences and that influences on these styles now came from multiple backgrounds, comprising diverse Islamic and other elements. Further, not all successor states followed the same dress codes, as their dynasties modified earlier conventions in different ways, depending on varying political developments.