bluuebunny/crossref_metadata_2025_split huggingface dataset:
Coordinates & Constraints
Authors: Mann Peter 
Published: August 2018

Abstract
This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
The Stationary Action Principle
Authors: Mann Peter 
Published: August 2018

Abstract
This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.
The Hamiltonian & Phase Space
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter discusses the Hamiltonian and phase space. Hamilton’s equations can be derived in several ways; this chapter follows two pathways to arrive at the same result, thus giving insight into the motivation for forming these equations. The importance of deriving the same result in several ways is that it shows that, in physics, there are often several mathematical avenues to go down and that approaching a problem with, say, the calculus of variations can be entirely as valid as using a differential equation approach. The chapter extends the arenas of classical mechanics to include the cotangent bundle momentum phase space in addition to the tangent bundle and configuration manifold, and discusses conjugate momentum. It also introduces the Hamiltonian as the Legendre transform of the Lagrangian and compares it to the Jacobi energy function.
Hamilton’s Principle in Phase Space
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter derives Hamilton’s equations using the Legendre transform and the definition of the Hamiltonian function. While, in the Newtonian formalism, conservation laws were rather difficult to tease out, the Lagrangian formalism revolutionised the way of looking at them; however, the Hamiltonian formalism is perhaps even simpler than the Lagrangian formalism, making it straightforward to identify conservation laws and the symmetries of the system associated with each conserved property. In this chapter, the Hamiltonian is treated as being explicitly dependent on time, as this form is more general and will lead to an important relation that, although not an equation of motion, is still useful to discuss. The chapter also introduces Routhian mechanics as a symplectic reduction technique, using integrals of the motion.
Canonical & Gauge Transformations
Authors: Mann Peter 
Published: August 2018

Abstract
In this chapter, the Hamilton–Jacobi formulation is discussed in two parts: from a generating function perspective and as a variational principle. The Poincaré–Cartan 1-form is derived and solutions to the Hamilton–Jacobi equations are discussed. The canonical action is examined in a fashion similar to that used for analysis in previous chapters. The Hamilton–Jacobi equation is then shown to parallel the eikonal equation of wave mechanics. The chapter discusses Hamilton’s principal function, the time-independent Hamilton–Jacobi equation, Hamilton’s characteristic function, the rectification theorem, the Maupertius action principle and the Hamilton–Jacobi variational problem. The chapter also discusses integral surfaces, complete integral hypersurfaces, completely separable solutions, the Arnold–Liouville integrability theorem, general integrals, the Cauchy problem and de Broglie–Bohm mechanics. In addition, an interdisciplinary example of medical imaging is detailed.
Near-Integrable Systems
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter extends the now familiar Lagrangian formulation to a field theory and covers elementary material in this new setting. The motion of systems with a very large number of degrees of freedom makes it necessary to specify an almost infinite number of discrete coordinates. It is possible to simplify the situation by taking the continuum limit, which replaces the individual coordinates with a continuous function that describes a displacement field, which assigns a displacement vector to each position the system could occupy relative to an equilibrium configuration. The field thus takes a point in the spacetime manifold and assigns it a value corresponding to whatever the field represents. In this chapter, many interdisciplinary examples are solved and pedagogical models are discussed. The chapter also discusses Lagrange density, the Lagrange field equation, instantons, the Klein–Gordon equation, Fourier transforms and the Korteweg–de Vries equation.
Classical Electromagnetism
Authors: Mann Peter 
Published: August 2018

Abstract
In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, spacetime variations), resulting in the Noether condition. Quasisymmetries and spontaneous symmetry breaking are discussed, as well as local symmetry and global symmetry. Following these definitions, Noether’s first theorem and Noether’s second theorem are developed. The classical Schrödinger field is investigated and the key equations of classical mechanics are summarised into a single Lagrangian. Symmetry properties of the field action and equations of motion are then compared. The chapter discusses the energy–momentum tensor, the Klein–Utiyama theorem, the Liouville equation and the Hamilton–Jacobi equation. It also discusses material science, special orthogonal groups and complex scalar fields.
Matrices
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter looks at the calculus of a function of two or more variables, which is the subject of partial differentiation. The partial derivative of a function is the rate of change of the function with respect to the distance in the direction of a particular coordinate axis and is symbolised with the sign ∂. The chapter spends time on the implicit function theorem, since it is relied upon heavily elsewhere in the text. Lagrange multipliers are used to solve constrained optimisation problems. Topics include critical points, the product rule, the chain rule, directional derivatives, hypersurfaces and Taylor’s theorem. In addition, the chapter discusses Jacobian matrices, the inverse function theorem, gradients, level sets and Hessian matrices.
Legendre Transforms
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter introduces vector calculus to the reader from the very basics to a level appropriate for studying classical mechanics. However, it provides only the necessary vector calculus required to understand some of the operations perform in the text and perhaps support self-learning in more advanced topics, so the analysis is not be definitive. The chapter begins by examining the axioms of vector algebra, vector multiplication and vector differentiation, and then tackles the gradient, divergence and curl and other elements of vector integration. Topics discussed include contour integrals, the continuity equation, the Kronecker delta and the Levi-Civita symbol. Particular care is taken to explain every mathematical relation used in the main text, leaving no stone unturned!
Calculus of Variations
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter presents an introduction to linear algebra. Classical mechanics is best understood in the language of differential geometry, which itself requires a working knowledge of the key concepts in linear algebra. This chapter walks through the required knowledge from this broad discipline and guides the reader towards the goal of the next chapter, differential geometry. Topics discussed include vector spaces, linear maps, basis sets, cobases, inner products, tensors, wedge products and exterior algebra, as well as the axioms of vector space geometry. The chapter concludes with a brief discussion of Grassmann variables, which tend to crop up when classical fermionic fields are defined.
Galilean Relativity
Authors: Wittman David M. 
Published: August 2018

Abstract
Galilean relativity is a useful description of nature at low speed. Galileo found that the vertical component of a projectile’s velocity evolves independently of its horizontal component. In a frame that moves horizontally along with the projectile, for example, the projectile appears to go straight up and down exactly as if it had been launched vertically. The laws of motion in one dimension are independent of any motion in the other dimensions. This leads to the idea that the laws of motion (and all other laws of physics) are equally valid in any inertial frame: the principle of relativity. This principle implies that no inertial frame can be considered “really stationary” or “really moving.” There is no absolute standard of velocity (contrast this with acceleration where Newton’s first law provides an absolute standard). We discuss some apparent counterexamples in everyday experience, and show how everyday experience can be misleading.
Late engine activity of GRB 161017A revealed by early optical observations
Authors: Tachibana Yutaro , Arimoto Makoto , Asano Katsuaki , Harita Shohei , Fujiwara Taichi , Yoshii Taketoshi , Itoh Ryosuke , Murata Katsuhiro L , Yatsu Yoichi , Morita Kotaro , Kawai Nobuyuki 
Published: August 2018

Abstract
The long gamma-ray burst GRB 161017A was detected by Fermi and Swift, and its afterglow was observed by the MITSuME 50 cm optical telescope promptly, about 50 s after the burst. Early optical observations revealed that the optical light curve exhibits a plateau and rebrightening in the early afterglow phase about 500 and 5000 s after the trigger, respectively. By investigating the behavior of the spectral and temporal flux variation, it was found that the plateau and rebrightening cannot be explained in the context of the simple standard afterglow model. These observational features can be explained with two independent refreshed shocks, which indicate the long-acting central engine. We evaluated the physical parameters of the subsequent shells, and we then determined the kinetic energy ratios of the two colliding shells to the leading shell to be roughly 1 and 8, respectively. In addition, two prominent X-ray flares about 200 s after the trigger may be signatures of delayed ejections of the energetic jets responsible for the refreshed shocks. Such late activity of the central engine and X-ray flares play a crucial role in understanding the mechanisms for jet formation and photon emission.
Discovery and state transitions of the new Galactic black hole candidate MAXI J1535−571
Authors: Nakahira Satoshi , Shidatsu Megumi , Makishima Kazuo , Ueda Yoshihiro , Yamaoka Kazutaka , Mihara Tatehiro , Negoro Hitoshi , Kawase Tomofumi , Kawai Nobuyuki , Morita Kotaro 
Published: August 2018

Abstract
We report on the detection and subsequent X-ray monitoring of the new Galactic black hole candidate MAXI J1535−571 with the Gas Slit Camera onboard Monitor of All-sky X-ray Image (MAXI/GSC). After the discovery on 2017 September 2, made independently with MAXI and the Swift/BAT, the source brightened gradually, and in a few weeks reached the peak intensity of ∼5 Crab, or ∼1.6 × 10−7 erg cm−2 s−1 in terms of the 2–20 keV flux. On the initial outburst rise, the 2–20 keV MAXI/GSC spectrum was described by a power-law model with a photon index of ≲ 2, while after a hard-to-soft transition, which occurred on September 18, the spectrum required a disk blackbody component in addition. At around the flux peak, the 2–8 keV and 15–50 keV light curves showed quasi-periodic and anti-correlated fluctuations with amplitudes of 10%–20%, on a time scale of ∼1 d. Based on these X-ray properties obtained with the MAXI/GSC, with additional information from the Swift/BAT, we discuss the evolution of the spectral state of this source, and give constraints on its system parameters.
ALMA twenty-six arcmin2 survey of GOODS-S at one millimeter (ASAGAO): Source catalog and number counts
Authors: Hatsukade Bunyo , Kohno Kotaro , Yamaguchi Yuki , Umehata Hideki , Ao Yiping , Aretxaga Itziar , Caputi Karina I , Dunlop James S , Egami Eiichi , Espada Daniel , Fujimoto Seiji , Hayatsu Natsuki H , Hughes David H , Ikarashi Soh , Iono Daisuke , Ivison Rob J , Kawabe Ryohei , Kodama Tadayuki , Lee Minju , Matsuda Yuichi , Nakanishi Kouichiro , Ohta Kouji , Ouchi Masami , Rujopakarn Wiphu , Suzuki Tomoko , Tamura Yoichi , Ueda Yoshihiro , Wang Tao , Wang Wei-Hao , Wilson Grant W , Yoshimura Yuki , Yun Min S 
Published: August 2018

Abstract
We present the survey design, data reduction, construction of images, and source catalog of the Atacama Large Millimeter/submillimeter Array (ALMA) twenty-six arcmin2 survey of GOODS-S at one millimeter (ASAGAO). ASAGAO is a deep (1 σ depth ∼ 61 μJy beam−1 for a 250 kλ-tapered map with a synthesized beam size of 0${^{\prime\prime}_{.}}$51 × 0${^{\prime\prime}_{.}}$45) and wide area (26 arcmin2) survey on a contiguous field at 1.2 mm. By combining with ALMA archival data in the GOODS-South field, we obtained a deeper map in the same region (1 σ depth ∼ 30 μJy beam−1 for a deep region with a 250 kλ-taper, and a synthesized beam size of 0${^{\prime\prime}_{.}}$59 × 0${^{\prime\prime}_{.}}$53), providing the largest sample of sources (25 sources at ≥5.0 σ, 45 sources at ≥4.5 σ) among ALMA blank-field surveys to date. The number counts show that $52^{+11}_{-8}$% of the extragalactic background light at 1.2 mm is resolved into discrete sources at S1.2 mm &gt; 135 μJy. We create infrared (IR) luminosity functions (LFs) in the redshift range of $z$ = 1–3 from the ASAGAO sources with Ks-band counterparts, and constrain the faintest luminosity of the LF at 2.0 &lt; $z$ &lt; 3.0. The LFs are consistent with previous results based on other ALMA and SCUBA-2 observations, which suggest a positive luminosity evolution and negative density evolution with increasing redshift. We find that obscured star-formation of sources with IR luminosities of log (LIR/L⊙) ≳ 11.8 account for ≈60%–90% of the $z$ ∼ 2 cosmic star-formation rate density.
Cumulative exposure to air pollution and subsequent mortality among older adults in China
Authors: Zhang Jiaan , McLaughlin Sara J , Li Lydia W 
Published: August 2018

AbstractBackgroundResearch on the health effects of exposure to air pollution is growing. However, relatively little attention has been paid to the effects of long-term and cumulative exposure to air pollutants. Individual-level studies on the health consequences of air pollution in China are especially scarce. The purpose of this study is to examine the effect of cumulative exposure to sulfur dioxide (SO2), an air pollutant of particular concern in China, on all-cause mortality in older Chinese adults.MethodsUsing a nationally representative sample of older adults in China (N = 11 199), we tracked mortality over an 11-year period (2000–11). Air pollution data were linked to respondents using provincial identifiers. To examine the effect of cumulative SO2 exposure on mortality, we employed multilevel multinomial logistic regression models that account for within subject clustering of observations over time and clustering at the province level.ResultsWe found that every 10-μg/m3 increase in cumulative exposure to SO2 increased the odds of death by nearly 1% (OR = 1.008; 95% CI: 1.002–1.014), controlling for province- and individual-level social and economic characteristics.ConclusionsOur analysis shows that air pollution is a risk factor for morality in older Chinese adults. Findings suggest that stronger SO2 regulations may enhance longevity.
Migrants, Ancestors, and Foreign Investments
Authors: Burchardi Konrad B , Chaney Thomas , Hassan Tarek A 
Published: August 2018

Abstract
We use 130 years of data on historical migrations to the U.S. to show a causal effect of the ancestry composition of U.S. counties on foreign direct investment (FDI) sent and received by local firms. To isolate the causal effect of ancestry on FDI, we build a simple reduced-form model of migrations: Migrations from a foreign country to a U.S. county at a given time depend on (1) a push factor, causing emigration from that foreign country to the entire U.S., and (2) a pull factor, causing immigration from all origins into that U.S. county. The interaction between time-series variation in origin-specific push factors and destination-specific pull factors generates quasi-random variation in the allocation of migrants across U.S. counties. We find that doubling the number of residents with ancestry from a given foreign country relative to the mean increases the probability that at least one local firm engages in FDI with that country by 4 percentage points. We present evidence that this effect is primarily driven by a reduction in information frictions, and not by better contract enforcement, taste similarities, or a convergence in factor endowments.
ESTIMATION OF EFFECTIVE DOSE OF DENTAL X-RAY DEVICES
Authors: Qiang Wang , Qiang Fu , Lin Lin 
Published: August 2018

Abstract
This study aims to estimate the effective doses of dental X-ray devices under common scanning protocols. After putting TLDs in the Alderson Radiation Therapy Phantom, we exposed the phantom under common scanning protocols of three dental X-ray devices, namely CBCT, dental panoramic machine and intraoral round cone device. Then effective doses were calculated using the measured absorbed doses of organs and tissues. Tissue weighting factors recommended by the ICRP were adopted in the calculation. Effective doses under common scanning protocols of three Dental X-ray devices were obtained. The effective dose of dental CT was 0.20 mSv, and that of dental panoramic machine and intraoral radiography were 0.013 and 0.0050 mSv, respectively. The tissue absorbed doses of dental CT scan were 0.63 mGy of brain, 7.7 mGy of salivary glands, 8.7 mGy of thyroid and 4.0 mGy of the lens of the eye. The tissue absorbed doses from dental panoramic machine are 0.62 mGy of salivary glands and 0.25 mGy of thyroid. And finally the tissue absorbed dose of intraoral radiography was 0.80 mGy of salivary gland. Among the three dental X-ray devices studied, dental CBCT scan can cause much higher effective dose than the other two. Brain, salivary glands, thyroid and the lens of the eye are tissues receiving relatively higher absorbed doses.
Association Between Hospital Volume and Mortality in Status Epilepticus: A National Cohort Study
Authors: Goulden Robert , Whitehouse Tony , Murphy Nick , Hayton Tom , Khan Zahid , Snelson Catherine , Bion Julian , Veenith Tonny 
Published: August 2018

Objectives:
In various medical and surgical conditions, research has found that centers with higher patient volumes have better outcomes. This relationship has not previously been explored for status epilepticus. This study sought to examine whether centers that see higher volumes of patients with status epilepticus have lower in-hospital mortality than low-volume centers.

Design:
Cohort study, using 2010–2015 data from the nationwide Case Mix Programme database of the U.K.’s Intensive Care National Audit and Research Centre.

Setting:
Greater than 90% of ICUs in United Kingdom, Wales, and Northern Ireland.

Patients:
Twenty-thousand nine-hundred twenty-two adult critical care admissions with a primary or secondary diagnosis of status epilepticus or prolonged seizure.

Interventions:
Annual hospital status epilepticus admission volume.

Measurements and Main Results:
We used multiple logistic regression to evaluate the association between hospital annual status epilepticus admission volume and in-hospital mortality. Hospital volume was modeled as a nonlinear variable using restricted cubic splines, and generalized estimating equations with robust ses were used to account for clustering by institution. There were 2,462 in-hospital deaths (11.8%). There was no significant association between treatment volume and in-hospital mortality for status epilepticus (p = 0.54). This conclusion was unchanged across a number of subgroup and sensitivity analyses, although we lacked data on seizure duration and medication use. Secondary analyses suggest that many high-risk patients were already transferred from low- to high-volume centers.

Conclusions:
We find no evidence that higher volume centers are associated with lower mortality in status epilepticus overall. It is likely that national guidelines and local pathways in the United Kingdom allow efficient patient transfer from smaller centers like district general hospitals to provide satisfactory patient care in status epilepticus. Future research using more granular data should explore this association for the subgroup of patients with refractory and superrefractory status epilepticus.
Ophthalmic Eosinophilic Granulomatosis With Polyangiitis (Churg–Strauss Syndrome): A Systematic Review of the Literature
Authors: Akella Sruti S. , Schlachter Dianne M. , Black Evan H. , Barmettler Anne 
Published: August 2018

Purpose:
To review and summarize the clinical features, presentations, diagnostic modalities, and management of ophthalmic manifestations of eosinophilic granulomatosis with polyangiitis (EGPA, formerly Churg–Strauss Syndrome).

Methods:
A systematic PubMed search of all English articles on EGPA with ophthalmic involvement was performed. Emphasis was placed on English-language articles, but any article with an abstract translated into English was also included. Only those cases that satisfied the American Rheumatology criteria (1990) for diagnosis were included. Data examined included epidemiology, pathogenesis, presentations, diagnostic modalities, and management.

Results:
There was a wide range in ophthalmic manifestations of EGPA. In order of most frequent presentation to least frequent, these include central retinal artery or vein occlusion, ischemic optic neuropathy, conjunctival nodules, orbital myositis, proptosis, dacryoadenitis, retinal vasculitis/infarcts/edema, cranial nerve palsy, and amaurosis. The 46 qualifying cases were divided into the categories of ischemic vasculitis versus idiopathic orbital inflammation due to prognostic significance. Ischemic vasculitis cases tended to be older patients (p = 0.03), unilateral (p = 0.006), require immunosuppressive therapy beyond steroids (p = 0.015), and were less likely to show improvement on therapy (p = 0.0003).

Conclusions:
Prompt diagnosis of EGPA by the ophthalmologist can decrease patient morbidity and mortality. This requires knowledge of likely ophthalmic EGPA presentations, as well as recommended workups and treatment.