Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions

Image space analysis is a new tool for studying scalar and vector constrained extremum problems as well as generalized systems. In the last decades, the introduction of image space analysis has shown that the image space associated with the given problem provides a natural environment for the Lagrange theory of multipliers and that separation arguments turn out to be a fundamental mathematical tool for explaining, developing and improving such a theory. This work, with its 3 parts, aims at contributing to describe the state-of-the-art of image space analysis for constrained optimization and to stress that it allows us to unify and generalize the several topics of optimization. In this 1st part, after a short introduction of such an analysis, necessary and sufficient optimality conditions are treated. Duality and penalization are the contents of the 2nd part. The 3rd part deals with generalized systems, in particular, variational inequalities and Ky Fan inequalities. Some further developments are discussed in all the parts.     

Consistency requirements and pattern methods in cost sharing problems with technological cooperation

Using the discrete cost sharing model with technological cooperation, we investigate the implications of the requirement that demand manipulations must not affect the agents’ shares. In a context where the enforcing authority cannot prevent agents (who seek to reduce their cost shares) from splitting or merging their demands, the cost sharing methods used must make such artifices unprofitable. The paper introduces a family of rules that are immune to these demand manipulations, the pattern methods. Our main result is the characterization of these methods using the above requirement. For each one of these methods, the associated pattern indicates how to combine the technologies in order to meet the agents’ demands. Within this family, two rules stand out: the public Aumann–Shapley rule, which never rewards technological cooperation; and the private Aumann–Shapley rule, which always rewards technology providers. Fairness requirements imposing natural bounds (for the technological rent) allow to further differentiate these two rules.     

Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.     

Isometric embeddings into Heisenberg groups

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples.     

High-throughput lipidomics analysis to discover lipid biomarkers and profiles as potential targets for evaluating efficacy of Kai-Xin-San against APP/PS1 transgenic mice based on UPLC–Q/TOF–MS

Lipid metabolism has a significant function in the central nervous system and Alzheimer's disease (AD) is an age-related senile disease characterized by central nerve degeneration. The pathological development of AD is closely related to lipid metabolism disorders. To reveal the influence of Kai-Xin-San (KXS) on lipid metabolism in APP/PSI transgenic mice and potential therapeutic targets for treating AD, brain tissue samples were collected and analyzed by high-throughput lipidomics based on UPLC–Q/TOF-MS. The collected raw data were processed by multivariate data analysis to discover the potential biomarkers and lipid metabolic profiles. Compared with the control wild-type mouse group, nine potential lipid biomarkers were found in the AD model group, of which seven were up-regulated and two were down-regulated. Orally administrated KXS can reverse the changes in these potential biomarkers. Compared with the model group, a total of six differential metabolites showed a recovery trend and may be potential targets for KXS to treat AD. This study showed that high-throughput lipidomics can be used to discover the perturbed pathways and lipid biomarkers as potential targets to reveal the therapeutic effects of KXS.     

旋涂法制备掺杂BiOX薄膜及光催化性能研究

采用旋涂的方法在基底材料表面原位生长BiOX(X=C1、Br、I)薄膜材料.样品的晶体结构和光学性质等通过X射线粉末衍射(XRD)、透射电子显微镜(TEM)、紫外可见漫反射光谱(UV-Vis)进行了表征.结果表明旋涂法制备的BiOX薄膜是纯净的,无其他杂质,均匀性好.通过对BiOX薄膜材料的光催化性能和瞬态表面光电压技术(TPV)进行了研究,发现卤素掺杂的BiOBr0.48I052具有较好的光催化性能.其结果表明催化性能提高的原因可能是BiOBr0.48I0.52薄膜在光照下可以产生更强的光生载流子并具有更长的光生载流子寿命.     

On structure-preserving connections

In this paper we find the formula of connections under which an almost complex structure is covariantly constant. These types of connections on anti-Kähler–Codazzi manifolds are described. Also, twin metric-preserving connections are analyzed for quasi-Kähler manifolds. Finally, anti-Hermitian Chern connections are investigated.     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.