A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Various previous results have been generalized and recovered by applying this criterion.

Let X be a smooth toric variety over a number field k such that the global sections of X are constant. We show that U(k) is dense in U(𝐀_k)^Br_1 (U) for any open subset U of X such that the codimension of X∖ U in X is at least 2.

A quadratic lattice M over a Dedekind domain R with fraction field F is defined to be a finitely generated torsion-free R-module equipped with a non-degenerate quadratic form on the F-vector space F⊗_RM. Assuming that F⊗_RM is isotropic of dimension ≥ 3 and that 2 is invertible in R, we prove that a quadratic lattice N can be embedded into a quadratic lattice M over R if and only if S⊗_RN can be embedded into S⊗_RM over S, where S is the integral closure of R in a finite extension of odd degree of F. As a key step in the proof, we establish several versions of the norm principle for integral spinor norms, which may be of independent interest.

An integral quadratic lattice is called indefinite k-universal if it represents all integral quadratic lattices of rank k for a given positive integer k. For k≥ 3 , we prove that the indefinite k-universal property satisfies the local–global principle over number fields. For k=2 , we show that a number field F admits an integral quadratic lattice which is locally 2-universal but not indefinite 2-universal if and only if the class number of F is even. Moreover, there are only finitely many classes of such lattices over F. For k=1 , we prove that F admits a classic integral lattice which is locally classic 1-universal but not classic indefinite 1-universal if and only if F has a quadratic unramified extension where all dyadic primes of F split completely. In this case, there are infinitely many classes of such lattices over F. All quadratic fields with this property are determined.

We study an asymptotic formula for counting integral points over an equation defined by a non-degenerate indefinite integral ternary quadratic form f representing a non-zero integer a such that $-a\cdot det(\,f)$ is square over a number field. In particular, we prove that the leading coefficient of this asymptotic formula is given by the product of local densities normalized by $1-p^{-1}$ over all finite primes p.

A number field $k$ admits a binary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is bigger than one. In this case, there are only finitely many classes of such binary integral quadratic forms over $k$. A number field $k$ admits a ternary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is even. In this case, there are infinitely many classes of such ternary integral quadratic forms over $k$. An integral quadratic form over a number field $k$ with more than one variables represents all integers of $k$ over the ring of integers of a finite extension of $k$ if and only if this quadratic form represents $1$ over the ring of integers of a finite extension of $k$.

Approximately 80% of ASD children struggle with age-appropriate motor skills. Numerous studies in this population have examined the effects of motor intervention on social communication and interaction, executive function, and mental health issues. Whereas heterogeneity in publication prevents researchers from revealing the structure and evolution of this topic. The objective of this study was to conduct a bibliometric analysis of current publications in order to identify prevalent trends and topics concerning motor intervention for children with autism spectrum disorder. Following a systematic search in the Web of Science Core Collection, we used a new research synthesis framework (systematic mapping and bibliometrics) to (1) analyse literature information (productivity and citations) through performance analysis; and (2) perform network analysis of co-cited references and co-occurring keywords to identify research hotspots, frontiers, and emerging trends. There were a total of 2,341 scientific publications included. ASD symptoms, intervention strategies, and treatment modalities were recognised as research hotspots. Physical activity, validation, and machine learning were identified as research frontiers. Motor impairments may be considered a core symptom in children with ASD in the future. Serious games and Exergames are low-cost and potentially effective interventions and treatments. Machine learning has recently emerged as a promising technology for earlier identification of ASD children. However, the validity of diagnostic and evaluation tools, as well as the dosage and clinical efficacy of emerging technological interventions (e.g., serious games and Exergame), remain debatable. Furthermore, while the development and application of new technologies will become an important emerging trend, low-risk treatment with behavioural or psychological treatments is the preferred treatment for children with ASD.

Acute mountain sickness (AMS) is a common syndrome characterized by headache, dizziness, loss of appetite, weakness, and nausea. As a major public health issue, obesity has increased in high altitude urban residents and intermittent commuters to high altitudes. The present study investigated acute hypoxic exposure and hypoxic exercise on hypoxemia severity and AMS symptoms in a physically active obese man. In this case analysis, peripheral oxygen saturation (SpO2) was used to evaluate hypoxemia, heart rate (HR) and blood pressure (BP) were used to reflect the function of autonomic nervous system (ANS), and Lake Louise scoring (LLS) was used to assess AMS. The results showed that acute hypoxic exposure led to severe hypoxemia (SpO2 = 72%) and tachycardia (HRrest = 97 bpm), and acute hypoxic exercise exacerbated severe hypoxemia (SpO2 = 59%) and ANS dysfunction (HRpeak = 167 bpm, SBP/DBP = 210/97 mmHg). At the end of the 6-h acute hypoxic exposure, the case developed severe AMS (LLS = 10) symptoms of headache, gastrointestinal distress, cyanosis, vomiting, poor appetite, and fatigue. The findings of the case study suggest that high physical activity level appears did not show a reliable protective effect against severe hypoxemia, ANS dysfunction, and severe AMS symptoms in acute hypoxia exposure and hypoxia exercise.

我国40名青年体育学者以本土情怀和全球视野对我国运动训练学的现状和未来进行思考,达成共识.在梳理"运动训练学"在不同语种中相关概念的基础上,从学科内涵、研究范式、研究问题和面临挑战4个方面介绍世界运动训练学的学科现状,从学科队伍、人才培养、科学研究、实践应用和国际交流等5个方面分析我国运动训练学的学科现状.认为,未来我国运动训练学发展应拓展学科国际视野,调整学科人才培养方式,完善学科研究范式,加强学科成果转化,强化学科价值应用.提出:"运动训练学"可对应国外的"Sports Science"和"Trainingswissenschaft",是以提升运动员竞技表现为目的、整合运用竞技体育相关学科的科学原理和方法的一门体育科学下属学科门类;"科学化"是我国运动训练学未来发展的主要路径和必然趋势,我国运动训练学将从学科诞生50周年这一历史节点开启科学化发展的新时代.

Ghosh and Sarnak have studied integral points on surfaces defined by an equation x^2+y^2+z^2-xyz= m over the integers. For these affine surfaces, we systematically study the Brauer group and the Brauer-Manin obstruction to the integral Hasse principle. We prove that strong approximation for integral points on any such surface, away from any finite set of places, fails, and that, for m\neq 0, 4, the Brauer group does not control strong approximation.

We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative type is given. Such a relation is further refined for torsors under a torus. As an appliaction, we prove that the semi-simple part of a connected linear algebraic group will satisfy strong approximation with Brauer-Manin obstruction if G iteself satisfies strong approximation with Brauer-Manin obstruction.The equivalence between descent obstruction and etale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.

We prove that any open subset U of a semi-simple simply connected quasi-split linear algebraic group G with codim(G \ U, G) >= 2 over a number field satisfies strong approximation by establishing a fibration of G over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given. (C) 2019 Elsevier Masson SAS. All rights reserved.

An integral version of Harpaz-Wittenberg conjecture is proposed. By assuming this conjecture, we show that a variety defined by norm of number fields represented as a polynomial of one variable satisfies strong approximation with Brauer-Manin obstruction under certain unbounded conditions.

We study strong approximation of the equation N_L/k(x) = ∏_i=1^n p_i(t) where L/k is a finite extension of number fields and p_i(t)'s are distinct irreducible polynomials over k. We prove this equation satisfies strong approximation with Brauer-Manin obstruction when L can be imbedded in k[t]/(p_i(t)) over k for all 1≤i≤n. Under Schinzel's hypothesis, we prove that the same result is true without assuming that L can be imbedded in k[t]/(p_i(t)) for all 1≤i≤n when L/k is cyclic.

For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.

The leading term of asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the product of the number of local solutions twisted by the Brauer–Manin obstruction. The similar result is also true for homogeneous spaces of reductive groups with some restriction. As application, we will give the explicit asymptotic formulae of the number of integral points of certain norm equations and prove the leading term of asymptotic formula of the number of integral matrices with a fixed irreducible characteristic polynomial over Z studied by Eskin–Mozes–Shah is equal to the product of the number of local integral solutions over all primes although the density function defined by Borovoi and Rudnick is not trivial in general. We also answer a question raised by Borovoi and Rudnick for comparing the number of integral symmetric matrices with the given determinant with the product of local densities.

The computer forensic discipline was established around 2000 in China, which was further developed along with Chinese judicial appraisal system in 2005. The new criminal and civil procedure laws of the People’s Republic of China was enacted on 1 Jan 2013. The new laws specified electronic data is legal evidence and has great impact on the current practice on handling electronic evidence. This paper introduces the electronic data and electronic evidence examination procedure in mainland China, the general concept of computer forensic legal system, the management of computer judicial experts, the management of computer judicial expertise institutions.

By developing the representation theory of quadratic Diophantine equations, we prove strong approximation with Brauer–Manin obstruction for certain quadratic fibrations where each fiber is compact.

Let \(F\) be a global field. In this work, we show that the Brauer–Manin condition on adelic points for subvarieties of a torus \(T_F\) over \(F\) cuts out exactly the rational points, if either \(F\) is a function field or, if \(F={\mathbb Q}\) and \(T_F\) is split. As an application, we prove a conjecture of Harari–Voloch over global function fields which states, roughly speaking, that on any rational hyperbolic curve, the local integral points with the Brauer–Manin condition are the global integral points. Finally we prove for tori over number fields a theorem of Stoll on adelic points of zero-dimensional subvarieties in abelian varieties.

To examine the joint influences of physical activity (PA) and family history (FH) of diabetes on subsequent type 2 diabetes (T2D), the authors pooled and analyzed data from 2 community-based urban adult prospective cohort studies in 2011 in Nanjing, China. Among 4550 urban participants, the 3-year cumulative incidence of T2D was 5.1%. After adjustment for potential confounders, compared with those with FH+ and insufficient PA, the adjusted odds ratio (95% confidence interval) of developing T2D was 0.42 (0.18, 0.98) for participants with sufficient PA and FH+, 0.32 (0.22, 0.46) for participants with insufficient PA and FH-, and 0.15 (0.08, 0.28) for participants with sufficient PA and FH-. Such significant graduated associations between PA/FH and risk of developing T2D were also identified in either men or women, separately. Sufficient PA and FH- may jointly reduce the risk of developing T2D in urban Chinese adults.