Finding all pure strategy Nash equilibria in a planar location game

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.     

Selective extraction of triazine herbicides based on a combination of membrane assisted solvent extraction and molecularly imprinted solid phase extraction

A selective extraction technique based on the combination of membrane assisted solvent extraction and molecularly imprinted solid phase extraction for triazine herbicides in food samples was developed. Simazine, atrazine, prometon, terbumeton, terbuthylazine and prometryn were extracted from aqueous food samples into a hydrophobic polypropylene membrane bag containing 1000μL of toluene as the acceptor phase along with 100mg of MIP particles. In the acceptor phase, the compounds were re-extracted onto MIP particles. The extraction technique was optimised for the type of organic acceptor solvent, amount of molecularly imprinted polymers particles in the organic acceptor phase, extraction time and addition of salt. Toluene as the acceptor phase was found to give higher triazine binding onto MIP particles compared to hexane and cyclohexane. Extraction time of 120min and 100mg of MIP were found to be optimum parameters. Addition of salt increased the extraction efficiency for more polar triazines. The selectivity of the technique was demonstrated by extracting spiked cow pea and corn extracts where clean chromatograms were obtained compared to only membrane assisted solvent extraction or only molecularly imprinted solid phase extraction. The study revealed that this combination may be a simple way of selectively extracting compounds in complex samples.     

Synthesis and reactivity of [2]disilaniobocenophanes

The paramagnetic ansa-niobocene [(Me₂Si)₂(η⁵-C₅H₄)₂NbCl₂] (1) was obtained from the reaction of Li₂[(Me₂Si)₂(C₅H₄)₂] with [NbCl₄(thf)₂]. Further treatment with Li[AlH₄] yielded [(Me₂Si)₂(η⁵-C₅H₄)₂NbH₃] (3), which is prone to decomposition within a few days at room temperature both in solution and in the solid-state, thus affording primarily an insoluble black material. However, after heating or irradiation of a solution of 3 small quantities of the dimeric niobium hydride species, [(Me₂Si)₂{μ-(η¹:η⁵-C₅H₃)}(η⁵-C₅H₄)NbH]₂ (4), were isolated and characterized by X-ray diffraction.     

Excitonic effects in two-dimensional vibrational spectra of liquid formamide

The linear and two-dimensional infrared (2DIR) responses of the amide I vibrational mode in liquid formamide are investigated experimentally and theoretically using molecular dynamics simulations. The recent method based on the numerical integration of the Schr?dinger equation is employed to calculate the 2DIR spectra. Special attention is devoted to the interplay of the structural dynamics and the excitonic nature of the amide I modes in determining the optical response of the studied system. In particular, combining experimental data, simulated spectra and analysis of the simulated atomic trajectory in terms of a transition dipole coupling model, we provide a convincing explanation of the peculiar features of the 2DIR spectra, which show a substantial increase of the antidiagonal bandwidth with increasing frequency. We point out that, at variance with liquid water, the 2DIR spectral profile of formamide is determined more by the excitonic nature of the vibrational states than by the fast structural dynamics responsible for the frequency fluctuations.     

A Dynamic Supplier Selection and Inventory Management Model for a Serial Supply Chain with a Novel Supplier Price Break Scheme and Flexible Time Periods

A new supplier price break and discount scheme taking into account order frequency and lead time is introduced and incorporated into an integrated inventory planning model for a serial supply chain that minimizes the overall incurred cost including procurement, inventory holding, production, and transportation. A mixed-integer linear programming (MILP) formulation is presented addressing this multi-period, multi-supplier, and multi-stage problem with predetermined time-varying demand for the case of a single product. Then, the length of the time period is considered as a variable. A new MILP formulation is derived when each period of the model is split into multiple sub-periods, and under certain conditions, it is proved that the optimal solution and objective value of the original model form a feasible solution and an upper bound for the derived model. In a numerical example, three scenarios of the derived model are solved where the number of sub-period is set to 2, 3, and 4. The results further show the decrease of the optimal objective value as the length of the time period is shortened. Sufficient evidence demonstrates that the length of the time period has a significant influence on supplier selection, lot sizing allocation, and inventory planning decisions. This poses the necessity of the selection of appropriate length of a time period, considering the trade-off between model complexity and cost savings.     

Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

This work deals with log‐symmetric regression models, which are particularly useful when the response variable is continuous, strictly positive, and following an asymmetric distribution, with the possibility of modeling atypical observations by means of robust estimation. In these regression models, the distribution of the random errors is a member of the log‐symmetric family, which is composed by the log‐contaminated‐normal, log‐hyperbolic, log‐normal, log‐power‐exponential, log‐slash and log‐Student‐t distributions, among others. One way to select the best family member in log‐symmetric regression models is using information criteria. In this paper, we formulate log‐symmetric regression models and conduct a Monte Carlo simulation study to investigate the accuracy of popular information criteria, as Akaike, Bayesian, and Hannan‐Quinn, and their respective corrected versions to choose adequate log‐symmetric regressions models. As a business application, a movie data set assembled by authors is analyzed to compare and obtain the best possible log‐symmetric regression model for box offices. The results provide relevant information for model selection criteria in log‐symmetric regressions and for the movie industry. Economic implications of our study are discussed after the numerical illustrations.