Geometric properties of basic hypergeometric functions

In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, some useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in a q-close-to-convex family.     

Nuclear Magnetic Resonance Metabolomics with Double Pulsed-Field-Gradient Echo and Automatized Solvent Suppression Spectroscopy for Multivariate Data Matrix Applied in Novel Wine and Juice Discriminant Analysis

The quality of foods has led researchers to use various analytical methods to determine the amounts of principal food constituents; some of them are the NMR techniques with a multivariate statistical analysis (NMR-MSA). The present work introduces a set of NMR-MSA novelties. First, the use of a double pulsed-field-gradient echo (DPFGE) experiment with a refocusing band-selective uniform response pure-phase selective pulse for the selective excitation of a 5–10-ppm range of wine samples reveals novel broad ¹H resonances. Second, an NMR-MSA foodomics approach to discriminate between wine samples produced from the same Cabernet Sauvignon variety fermented with different yeast strains proposed for large-scale alcohol reductions. Third a comparative study between a nonsupervised Principal Component Analysis (PCA), supervised standard partial (PLS-DA), and sparse (sPLS-DA) least squares discriminant analysis, as well as orthogonal projections to a latent structures discriminant analysis (OPLS-DA), for obtaining holistic fingerprints. The MSA discriminated between different Cabernet Sauvignon fermentation schemes and juice varieties (apple, apricot, and orange) or juice authentications (puree, nectar, concentrated, and commercial juice fruit drinks). The new pulse sequence DPFGE demonstrated an enhanced sensitivity in the aromatic zone of wine samples, allowing a better application of different unsupervised and supervised multivariate statistical analysis approaches.     

Geometric Variational Inference

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.     

Plastic shear deformation of a thin strain-hardening disc: variational principles

An analytical solution is derived for the problem of shearing of a thin disc of incompressible rigid, plastic strain-hardening material. The solution is obtained by a methodology introduced by the author in previous publications, relying fundamentally on continuity of the rotation-rate vector field. A variational theorem is derived which shows that the velocity vector field is unique if the boundary values are properly prescribed. The derived solution is compared to experiments, with which it shows good agreement.     

InGaAs近红外相机电路设计与实现

随着国外0.9～1.7μm InGaAs近红外相机的迅速发展,目前已被大量应用于工业和军事领域。探讨了InGaAs近红外相机在不同领域的应用,分析了InGaAs材料的优势及探测器选型。结合相应的探测器阵列,从相机偏置电压产生、时序驱动设计与制冷控制等方面给出了InGaAs近红外相机的硬件电路设计方案,解决了研制过程中的部分重难点,并针对后期图像处理进行了仿真验证,达到应用要求。     

The Generator of the Transition Semigroup Corresponding to a Stochastic Variational Inequality

One proves that the generator of the transition semigroup of a stochastic differential equation with boundary reflection on a convex set K is the realization of a second order elliptic operator on K with zero oblique derivative boundary conditions. Several implications to parabolic problems with oblique derivative are also derived.     

A numeric–analytic method for time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative

In this paper, the fractional variational iteration method (FVIM) was applied to obtain the approximate solutions of time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. Numerical results showed the FVIM is powerful, reliable and effective method when applied strongly nonlinear equations with modified Riemann–Liouville derivative.     

Strategic response to pollution taxes in supply chain networks: Dynamic,spatial, and organizational dimensions

This paper presents a model of the strategic behavior of firms operating in a spatial supply chain network. The manufacturing and retailing firms engage in an oligopolistic, noncooperative game by sharing customer demand such that a firm’s decisions impact the product prices, which in turn result in changes in all other firms’ decisions. Each firm’s payoff is to maximize its own profit and we show that, in response to such changes in prices and to exogenous environmental taxes, the manufacturing firms may strategically alter a variety of choices such as ’make-buy’ decisions with respect to intermediate inputs, spatial distribution of production, product shipment patterns and inventory management, environmental tax payment vs recycling decisions, and timing of all such choices to sustainably manage the profit and the environmental regulations. An important implication is that effects of a tax depends on the oligopolistic game structure. With respect to methods, we show that this dynamic game can be represented as a set of differential variational inequalities (DVIs) that motivate a computationally efficient nonlinear complementarity (NCP) approach that enables the full exploitation of above-mentioned salient features. We also provide a numerical example that confirms the utility of our proposed framework and shows substantial strategic reaction can be expected to a tax on pollution stocks.     

Multiple solutions of a quasilinear elliptic system involving the nonlinear boundary conditions on exterior domain

In this paper, we consider the multiplicity results of nontrivial nonnegative solutions of the quasilinear p‐Laplacian system with the nonlinear boundary conditions: (0.1) where Ω is a smooth exterior domain in is the outward normal derivative on the boundary Γ = ?Ω, and . By the Nehari manifold and variational methods, we prove that the problem (0.1) has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of . Copyright © 2012 John Wiley & Sons, Ltd.