Combination of Raman, Infrared, and X-Ray Energy-Dispersion Spectroscopies and X-Ray Diffraction to Study a Fossilization Process

X-ray diffraction was combined with X-ray energy-dispersion, Fourier-transform infrared, and Raman spectroscopies to study the fossilization of a Cretaceous specimen of the plant Brachyphyllum castilhoi, a fossil from the Ipubi Formation, in the Araripe Sedimentary Basin, Northeastern Brazil. Among the possible fossilization processes, which could involve pyrite, silicon oxide, calcium oxide, or other minerals, we were able to single out pyritization as the central mechanism producing the fossil, more than 100 million years ago. In addition to expanding the knowledge of the Ipubi Formation, this study shows that, when combined with other experimental techniques, Raman spectroscopy is a valuable tool at the paleontologist’s disposal.     

Particle-laden viscous thin-film flows on an incline: Experiments compared with a theory based on shear-induced migration and particle settling

Particle settling in driven viscous films is a complex physical process involving different physical effects. A recent analysis by Cook (2008) [10] has identified a balance between hindered settling and shear-induced migration as the dominant large scale physics for particle/liquid separation. However, experimental data for this has been lacking. This paper presents new data including the role of particle size and liquid viscosity showing clear agreement with the theory. We discuss the role of timescales in the dynamics of the experiment and present results from a dynamic model.     

An integrated inventory model with quality improvement and two-part credit policy

Trade credit financing plays a vital role in current business operations. Vendors extend payment dates to encourage sales, and buyers are not required to pay immediately after receiving products. This is equivalent to receiving a price reduction. Besides, buyers reduce their need for capital from bank loans. In addition, a number of defective products are produced during the production process. The number of defective items influences the on-hand inventory levels of buyers, service levels, and frequency of orders. To ensure that the analysis incorporates a realistic production environment, we developed an integrated inventory model with a two-part trade credit and considered an imperfect production process that can be improved by capital investment. The objective was to determine the optimal ordering, shipping, and quality improvement policies to maximize joint total profit. An iterative algorithm was established to determine the optimal strategy. Furthermore, a sensitivity analysis was conducted to examine the effects of changing parameter values on the optimal solution.     

An integer linear programming formulation and heuristics for the minmax relative regret robust shortest path problem

The well-known Shortest Path problem (SP) consists in finding a shortest path from a source to a destination such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path problem (RSP) is a generalization of SP. In the former, the cost of each arc is defined by an interval of possible values for the arc cost. The objective is to minimize the maximum relative regret of the path from the source to the destination. This problem is known as the minmax relative regret RSP and it is NP-Hard. We propose a mixed integer linear programming formulation for this problem. The CPLEX branch-and-bound algorithm based on this formulation is able to find optimal solutions for all instances with 100 nodes, and has an average gap of 17 % on the instances with up to 1,500 nodes. We also develop heuristics with emphasis on providing efficient and scalable methods for solving large instances for the minmax relative regret RSP, based on Pilot method and random-key genetic algorithms. To the best of our knowledge, this is the first work to propose a linear formulation, an exact algorithm and metaheuristics for the minmax relative regret RSP.     

Precise Asymptotic Approximations for Kernels Corresponding to Lévy Processes

By using basic complex analysis techniques, we obtain precise asymptotic approximations for kernels corresponding to symmetric α-stable processes and their fractional derivatives. We use the deep connection between the decay of kernels and singularities of the Mellin transforms. The key point of the method is to transform the multi-dimensional integral to the contour integral representation. We then express the integrand as a combination of gamma functions so that we can easily find all poles of the integrand. We obtain various asymtotics of the kernels by using Cauchys Residue Theorem with shifting contour integration. As a byproduct, exact coefficients are also obtained. We apply this method to general Lévy processes whose characteristic functions are radial and satisfy some regularity and size conditions. Our approach is based on the Fourier analytic point of view.     

On positive solutions for a class of quasilinear elliptic systems

We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.     

Mapped WENO schemes based on a new smoothness indicator for Hamilton–Jacobi equations

In this paper, we introduce an improved version of mapped weighted essentially non-oscillatory (WENO) schemes for solving Hamilton–Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et al. (2005) [31]. The proposed scheme yields fifth-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives. Numerical experiments are provided to demonstrate the performance of the proposed schemes on a variety of one-dimensional and two-dimensional problems.     

Optimizing Multi-stage Production for an Assembly-Type Supply Chain with Unequal Sized Batch Shipments

This paper studies the multi-stage logistics and inventory problem in an?assembly-type supply chain where a uniform lot size is produced uninterruptedly with a single setup at each stage. Partial lots, or sub-batches, can be transported to next stage upon completion. Unequal sub-batch sizes at each stage follow geometric series and the numbers of sub-batches across stages are allowed to be different. Since the mainline and each branch line of an assembly-type supply chain are series-type supply chains, a model of the series-type supply chain is first established and a model of the assembly-type supply chain is subsequently developed. Optimization algorithms that determine the economic lot sizes, the optimal sub-batch sizes and the number of sub-batches for each stage are developed. The polynomial-time algorithms incorporate the optimality properties derived in the paper to find the lower and upper bounds of the solutions by constructing the solution ranges and then the optimal solutions accordingly.     

Parallel mean curvature surfaces in symmetric spaces

We present a reduction-of-codimension theorem for surfaces with parallel mean curvature in symmetric spaces.     

Recent Developments in Robust Portfolios with a Worst-Case Approach

Robust models have a major role in portfolio optimization for resolving the sensitivity issue of the classical mean–variance model. In this paper, we survey developments of worst-case optimization while focusing on approaches for constructing robust portfolios. In addition to the robust formulations for the Markowitz model, we review work on deriving robust counterparts for value-at-risk and conditional value-at-risk problems as well as methods for combining uncertainty in factor models. Recent findings on properties of robust portfolios are introduced, and we conclude by presenting our thoughts on future research directions.