MR Cygni revisited

New analysis tools and additional unanalyzed observations justify a reanalysis of MR Cygni. The reanalysis applied successively more restrictive physical models, each with an optimization program. The final model assigned separate first and second order limb darkening coefficients, from model atmospheres, to individual grid points. Proper operation of the optimization procedure was tested on simulated observational data, produced by light synthesis with assigned system parameters, and modulated by simulated observational error. The iterative solution converged to a weakly-determined mass ratio of 0.75. Assuming the B3 primary component is on the main sequence, the HR diagram location of the secondary from the light ratio (ordinate) and adjusted T sub eff (abscissa) was calculated. The derived mass ratio, together with a main-sequence mass for the B3 component, implies a main-sequence secondary spectral type of B4. The photometrically-determined secondary radii agree with this spectral type, in marginal disagreement with the B7 type from the HR diagram analysis. The individual masses, derived from the radial velocity curve of the primary component, the photometrically-determined i, and alternative values of derived mass ratio are seriously discrepant with main sequence objects. The imputed physical status of the system is in disagreement with representations that have appeared in the literature

Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model

The Wilson–Devinney model has—over the last 50 years—become the standard in analyzing eclipsing binary observations. To provide orientation for both active binary and non-binary researchers, it is presented here in historical and on-going as well as astrophysical perspectives. Among the important advances that originated with the model are: the representation of star surfaces as equipotentials for circular and eccentric orbits, leading to four morphological types; simultaneous least-squares light and velocity curve analyses; efficient reflection computation, including multiple reflection; disk theory and disk modeling. Solutions in physical units allowed for the accurate estimation of parameters such as stellar masses and photometric distances; inclusion of types of observables, properly weighted

Aspects and Views on Mathematical Optimization in Logistics in the Chemical Industry

Abstract. In large chemical companies, traffic logistics and supply chain logistics contain many decision problems which are suitable to be solved by mathematical optimization. The objectives are to exploit resources (traffic infrastructure such as roads and rail lines, production equipment) in a cost optimal way and to maximize profit. We present two cases: optimal sequences of rail cars in trains visiting various plants in a large company complex, and production and distribution planning. Finally, we discuss the importance of data structure and the consequences of differences between the "booking world" view of systems such as SAP and the "physical world" mapped into mathematical optimization models

Aspects and Views on Mathematical Optimization in Logistics in the Chemical Process Industry

In large chemical companies, traffic logistics and supply chain logistics contain many decision problems which are suitable to be solved by mathematical optimization. The objectives are to exploit resources (traffic infrastructure such as roads and rail lines, production equipment) in a cost optimal way and to maximize profit. We present two cases: optimal sequences of rail cars in trains visiting various plants in a large company complex, and production and distribution planning. Finally, we discuss the importance of data structure and the consequences of differences between the "booking world" view of systems such as SAP and the "physical world" mapped into mathematical optimization models

Eclipsing binary stars: modeling and analysis

This book focuses on the formulation of mathematical models for the light curves of eclipsing binary stars, and on the algorithms for generating such models Since information gained from binary systems provides much of what we know of the masses, luminosities, and radii of stars, such models are acquiring increasing importance in studies of stellar structure and evolution As in other areas of science, the computer revolution has given many astronomers tools that previously only specialists could use; anyone with access to a set of data can now expect to be able to model it This book will provide astronomers, both amateur and professional, with a guide for - specifying an astrophysical model for a set of observations - selecting an algorithm to determine the parameters of the model - estimating the errors of the parameters It is written for readers with knowledge of basic calculus and linear algebra; appendices cover mathematical details on such matters as optimization, coordinate systems, and specific models While emphasizing the physical and mathematical framework, the discussion remains close to the problems if actual implementation It begins with an overview of the problem and a discussion of the observational data that form the basis of any model The treatment then turns to the direct problem (computing the light curve and other observables from the a given set of parameters) and then to the indirect problem (determining a best-fit set of parameters from the data) The book concludes with chapters on specific models and approaches and the authors' views on the structure of future light- curve program

Eclipsing Binary Stars: Modeling and Analysis

Eclipsing Binary Stars focuses on the mathematical formulation of astrophysical models for the light curves of eclipsing binaries stars, and on the algorithms for evaluating and exploiting such models. Since information gained from binary systems provides much of what we know of the masses, luminosities, and radii of stars, such modeling is acquiring increasing importance in studies of stellar structure and evolution. As in other areas of science, the computer revolution has given many astronomers tools that previously only specialists could use; anyone with access to a set of data can now expect to be able to model it. This book will provide astronomers, both amateurs and professionals, with a guide for • specifying an astrophysical model for a set of observations • selecting an algorithm to determine the parameters of the model • estimating the errors of the parameters Eclipsing Binary Stars is written for readers familiar with basic calculus and linear algebra; appendices cover mathematical details on such matters as optimization, coordinate systems, and specific models. This 2nd edition includes new physics in light curve models and distance fitting and implications on T1. Other improvements include, new features in the WD program, new applications in astronomy and astrophysics, new literature cases, Milone's papers and new software developments in the eclipsing binary community

Operations Research in BASF's Supply Chain Operations

In this paper, we highlight the application of operations research (OR) at BASF in the area of supply chain management (SCM) by using selected examples with annual cost savings ranging between several hundred thousand and several million euros. We address special characteristics of the process industry that should be dealt with and identify future research needs. The examples cover strategic, tactical, and operational topics encountered at BASF. We share our lessons learned, based on our experience from past OR projects in SCM, about challenges as well as benefits of standard and tailor-made OR solutions. In general, we find that the special characteristics often call for a modification or enhancement of standard OR models. Providing appropriate solutions therefore requires a joint effort of SCM, IT, and OR experts