Time representations and mathematical models for process scheduling problems

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented with corresponding strengthened formulations that rely on exploiting the non-overlapping graph structure of these problems through maximum cliques and bicliques. These formulations are compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stopping criterion used. Computational results show that the multi-operation sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.     

The mathematical models of the stripping voltammetry metal deposition/dissolution process

Three mathematical models of electrochemical two-electron deposition/dissolution process have been presented and discussed. The advanced two-plate model with BET adsorption formula equation has been presented and verified by the use of the experimental Cu²⁺/Cu⁺/Cu⁰ system in 0.5 M HCl solution at different scan rates. A change of electrode properties during electrode process was included into applied model and discussed.     

Some mathematical models of milling

Various system approaches to studying milling and mixing processes formalized as components of a physicomechanical system are discussed. Qualitative analysis of the milling processes is performed in the context of the total spectrum of phenomena starting with the atomic-molecular level and ending with production processes. __________ Translated from Novye Ogneupory, No. 8, pp. 46–51, August, 2006.     

Development of a mathematical model for the pultrusion process

A mathematical model has been developed to simulate the pultrusion process, namely the profiles of temperature and the degree of cure in both the axial and radial directions in a pultrusion die of cylindrical shape. For the study, the equations of continuity and energy transport, coupled with a kinetic expression for the curing reaction, were solved numerically, using a finite difference method. For the kinetic expression, we used an empirical expression of the form dα/dt = (k₁ + k₂α^m)(1 ? α)ⁿ to describe the curing behavior of both unsaturated polyester and epoxy resins. Differential scanning calorimetry (DSC) was used to investigate the curing behavior of the following systems: unsaturated polyester resin/glass fiber, epoxy resin/glass fiber, and epoxy resin/carbon fiber. The results of DSC runs were used to determine the kinetic parameters, which enabled us to predict the effects on the pultrusion characteristics of the following variables: (1) the type of initiator; (2) the type of fiber reinforcement; (3) the type of resin; and (4) the pulling speed and hence the residence time.     

Computerized design of lead-crystal glassware

Translated from Steklo i Keramika, No. 4, pp. 25–26, April, 1993.     

边坡稳定性分析的Fuzzy数学模型

用模糊数学（ＦｕｚｚｙＭａｔｈｍａｔｉｃｓ）理论分析裂隙岩质边坡稳定性问题，根据模糊测度原理，针对实际边坡工作问题，建立了具有实际工程意义的模糊测度模型，并给出了具体的数值方法，使该模型可以更方便地用于分析矿山边坡稳定问题。