Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

A differential oligopoly game with differentiated goods and sticky prices

We investigate a dynamic oligopoly game where goods are differentiated and prices are sticky. We study the open-loop and the closed-loop memoryless Nash equilibrium, and show that the latter equilibrium entails a larger level of steady state production as compared to the former; both equilibria entail a larger level of production in steady state than the static game. We also study the effects of price stickiness and product differentiation upon the steady state equilibrium allocation and profits. The per-firm equilibrium output is increasing in both product differentiation and price stickiness, while profits are increasing in both product differentiation and the speed of price adjustment. The steady state social welfare monotonically increases in the speed of price adjustment, and the overproduction entailed by dynamic competition has beneficial effect from a social standpoint.     

A global rigidity theorem for weakly Landsberg manifolds

In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian.     

Positioning of new brands in an experiment

This paper deals with an experimental investigation of positioning new brands. For this purpose, a management game was carried out with students. The brands introduced in the cause of the game were analysed in respect to their positions in a two-dimensional feature space. We try to find out which of the two strategies, niche policy and imitation, is more frequently used in complex decision situations and if there is a difference in profits. Furthermore, we want to find out, whether differences of prices and advertising exist in our experiment depending on the positioning strategy used.     

多体系统动力学设计灵敏度分析直接微分法

针对受完整约束的多体系统动力学微分／代数方程数学模型动态最优化设计问题，建立了通用的目标函数和约束方程，并以此为基础，用直接微分方法系统地推导出了计算设计灵敏度的通用公式，最后通过平面机械臂模型对理论结果和相应算法进行了验证．     

Pretreating near infrared spectra with fractional order Savitzky–Golay differentiation(FOSGD)

With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation(FOSGD) is calculated and applied to pretreat near infrared(NIR) spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation(IOSGD),FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.     

Self‐Assembled Peptide‐Based Hydrogels as Scaffolds for Proliferation and Multi‐Differentiation of Mesenchymal Stem Cells

Fluorenyl‐9‐methoxycarbonyl (Fmoc)‐diphenylalanine (Fmoc‐FF) and Fmoc‐arginine‐glycine‐­aspartate (Fmoc‐RGD) peptides self‐assemble to form a 3D network of supramolecular hydrogel (Fmoc‐FF/Fmoc‐RGD), which provides a nanofibrous network that uniquely presents bioactive ligands at the fiber surface for cell attachment. In the present study, mesenchymal stem cells (MSCs) in Fmoc‐FF/Fmoc‐RGD hydrogel increase in proliferation and survival compared to those in Fmoc‐FF/Fmoc‐RGE hydrogel. Moreover, MSCs encapsulated in Fmoc‐FF/Fmoc‐RGD hydrogel and induced in each defined induction medium undergo in vitro osteogenic, adipogenic, and chondrogenic differentiation. For in vivo differentiation, MSCs encapsulated in hydrogel are induced in each defined medium for one week, followed by injection into gelatin sponges and transplantation into immunodeficient mice for four weeks. MSCs in Fmoc‐FF/Fmoc‐RGD hydrogel increase in differentiation into osteogenic, adipogenic, and chondrogenic differentiation, compared to those in Fmoc‐FF/Fmoc‐RGE hydrogel. This study concludes that nanofibers formed by the self‐assembly of Fmoc‐FF and Fmoc‐RGD are suitable for the attachment, proliferation, and multi‐differentiation of MSCs, and can be applied in musculoskeletal tissue engineering.

     

A second‐order ensemble method based on a blended backward differentiation formula timestepping scheme for time‐dependent Navier–Stokes equations

We present a second‐order ensemble method based on a blended three‐step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier–Stokes equations. Compared with the only existing second‐order ensemble method that combines the two‐step BDF timestepping scheme and a special explicit second‐order Adams–Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 34–61, 2017     

Assortment planning for vertically differentiated products under a consider-then-choose model

Consider-then-choose models, borne out by empirical literature in marketing and psychology, note that customers follow a two-stage procedure to choose among alternatives. In this paper, we consider the assortment optimization problem of a retailer who manages a category of vertically differentiated products under customers’ consider-then-choose behavior. We characterize some structural results of the optimal assortment and find that the problem can be solved as the shortest path problem. Also, we develop an efficient algorithm to identify an optimal assortment.