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Abstract: Is a mathematical problem a cultural invariant, which would invariably give rise to the same practices, independent of the social groups considered? This paper discusses evidence found in the oldest Chinese mathematical text handed down by the written tradition, the canonical work The Nine Chapters on Mathematical Procedures and its commentaries, to answer this question in the negative. The Canon and its commentaries bear witness to the fact that, in the tradition for which they provide evidence, mathematical problems not only were questions to be solved, but also played a key part in conducting proofs of the correctness of algorithms. [Copyright &y& Elsevier]

This paper applies an innovative approach to monitoring social effects occurring before and during construction of two hydroelectric dams in Canada. The two studied dams, Site C and Keeyask, are under construction in Canada and underwent community-based impact assessment (CBIA). News coverage and the CBIA documents were analyzed to understand and compare how those two groups perceive social effects induced by the two projects. CBIAs contain concerns expressed by affected people, whereas news coverage can include quotes from both affected people and decisionmakers involved in the assessment process. By contrasting these datasets, we found that the documents are complementary: while CBIAs are comprehensive in assessing community concerns, news outlets can reveal how those concerns evolved throughout different phases of the projects' implementation. This approach fills a gap in SIA around monitoring of key social effects around local conflicts and disputes, psychosocial effects, socioeconomic effects, and cumulative effects on a daily life. Furthermore, by contrasting the views identified within the impact assessments and the media, the study demonstrates how specific concerns diverged: affected people focus on local social effects while decisionmakers' interests lie in a broader political perspective grounded in local sacrifices 'for the good of the whole province'. Our analysis emphasizes the role of political power over decision making that can inhibit CBIA and social impact assessment practice from contributing to socially sustainable projects. • News outlets can be used to monitor social effects from infrastructure projects. • Community assessments tend to address more chronic effects while news media coverage focuses on episodes of conflicts. • Pollical power over decision-making might inhibit more sustainable projects. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of stochastic wave equations with nonlinear multiplicative noise. We first show that these stochastic wave equations generate random dynamical systems (or stochastic flows) by transforming the stochastic wave equations to random wave equations through a stationary random homeomorphism. Then, we establish the existence of random invariant manifolds for the random wave equations. Due to the temperedness of the nonlinearity, we obtain only local invariant manifolds no matter how large the spectral gap is unlike the deterministic cases. Based on these random dynamical systems, we prove the existence of random invariant manifolds in a tempered neighborhood of an equilibrium. Finally, we show that the images of these invariant manifolds under the inverse stationary transformation give invariant manifolds for the stochastic wave equations. [Copyright &y& Elsevier]

Abstract: Traditional proofs of the Pontryagin Maximum Principle (PMP) require the continuous differentiability of the dynamics with respect to the state variable on a neighborhood of the minimizing state trajectory, when arbitrary values of control variable are inserted into the dynamic equations. Sussmann has drawn attention to the fact that the PMP remains valid when the dynamics are differentiable with respect to the state variable, merely when the minimizing control is inserted into the dynamic equations. This weakening of earlier hypotheses has been referred to as the Lojasiewicz refinement. Arutyunov and Vinter showed that these extensions of early versions of the PMP can be simply proved by finite-dimensional approximations, application of a Lagrange multiplier rule in finite dimensions and passage to the limit. This paper generalizes the finite-dimensional approximation technique to a problem with state constraints, where the use of needle variations of the optimal control had not been successful. Moreover, the cost function and endpoint constraints are not assumed to be differentiable, but merely locally Lipschitz continuous. The Maximum Principle is expressed in terms of Michel–Penot subdifferential. [Copyright &y& Elsevier]

Abstract: This paper continues the study of Mao et al. investigating two aspects of the equation The first of these is to slightly improve results in [X. Mao, S. Sabais, E. Renshaw, Asymptotic behavior of stochastic Lotka–Volterra model, J. Math. Anal. 287 (2003) 141–156] concerning with the upper-growth rate of the total quantity of species by weakening hypotheses posed on the coefficients of the equation. The second aspect is to investigate the lower-growth rate of the positive solutions. By using Lyapunov function technique and using a changing time method, we prove that the total quantity always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower-growth rate. [Copyright &y& Elsevier]

Abstract: A key tool in the study of the dynamics of vector fields near an equilibrium point is the theory of normal forms, invented by Poincaré, which gives simple forms to which a vector field can be reduced close to the equilibrium. In the class of formal vector valued vector fields the problem can be easily solved, whereas in the class of analytic vector fields divergence of the power series giving the normalizing transformation generally occurs. Nevertheless the study of the dynamics in a neighborhood of the origin can very often be carried out via a normalization up to finite order. This paper is devoted to the problem of optimal truncation of normal forms for analytic vector fields in . More precisely we prove that for any vector field in admitting the origin as a fixed point with a semi-simple linearization, the order of the normal form can be optimized so that the remainder is exponentially small. We also give several examples of non-semi-simple linearization for which this result is still true. [Copyright &y& Elsevier]

In the paper we study a semiparametric density estimation method based on the model of an elliptical distribution. The method considered here shows a way to overcome problems arising from the curse of dimensionality. The optimal rate of the uniform strong convergence of the estimator under consideration coincides with the optimal rate for the usual one-dimensional kernel density estimator except in a neighbourhood of the mean. Therefore the optimal rate does not depend on the dimension. Moreover, asymptotic normality of the estimator is proved. [Copyright &y& Elsevier]

In this paper we study the existence and qualitative property of standing wave solutions ψ(x,t)=e-iEt/ℎu(x) for the nonlinear Schrödinger equation iℎ∂ψ/∂t+ℎ2/2mΔψ-W(x)ψ+|ψ|p-1ψ=0 with E being a critical frequency in the sense that infx∈RN W(x)=E. We show that if the zero set of W-E has several isolated connected components Zi(i=1,…,m) such that the interior of Zi is not empty and ∂Zi is smooth, then for ℎ>0 small there exists, for any integer k,1⩽k⩽m, a standing wave solution which is trapped in a neighborhood of ⋃j=1k Aj, where {Aj | j=1,…,k} is any given subset of {Zi | i=1,…,m}. Moreover the amplitude of the standing wave is of the level ℎ2/p-1. This extends the result of Byeon and Wang (Arch. Rational Mech. Anal. 165 (2002) 295) and is in striking contrast with the non-critical frequency case infx∈RN W(x)>E, which has been studied extensively in the past 20 years. [Copyright &y& Elsevier]

The neighborhood effect averaging problem (NEAP) is a major methodological problem that might affect the accuracy of assessments of individual exposure to mobility-dependent environmental factors (e.g., air/noise pollution, green/blue spaces, or healthy food environments). Focusing on outdoor ground-level ozone as a major air pollutant, this paper examines the NEAP in the evaluation of sociodemographic disparities in people's air pollution exposures in Los Angeles using one-day activity-travel diary data of 3790 individuals. It addresses two questions: (1) How does the NEAP affect the evaluation of sociodemographic disparities in people's air pollution exposures? (2) Which social groups with high residence-based exposures do not experience neighborhood effect averaging? The results of our spatial regression models indicate that assessments of sociodemographic disparities in people's outdoor ground-level ozone exposures might be erroneous when people's daily mobility is ignored because of the different manifestations of neighborhood effect averaging for different social/racial groups. The results of our spatial autologistic regression model reveal that non-workers (e.g., the unemployed, homemakers, the retired, and students) do not experience downward averaging : they have significantly lower odds of experiencing downward averaging that could have attenuated their high exposures experienced in their residential neighborhoods while traveling to other neighborhoods (thus, being doubly disadvantaged). Therefore, to avoid erroneous conclusions in environmental inequality research and ineffective public policies, it would be critical to take the NEAP into account in future studies of sociodemographic disparities related to mobility-dependent environmental factors. • Ignoring human mobility may lead to the neighborhood effect averaging problem (NEAP). • This study examined how the NEAP affects assessments of sociodemographic disparities in people's ozone exposures. • We found that these assessments might be erroneous when people's daily mobility is ignored. • Non-workers constitute the doubly disadvantaged groups that do not experience downward averaging. • Studies on exposures to mobility-dependent environmental factors should consider the NEAP. [ABSTRACT FROM AUTHOR]