Balinski-Tucker simplex tableaus : dimensions, degeneracy degrees, and interior points of optimal faces

This paper introduces a general, formal treatment of dynamic constraints, i.e., constraints on the state changes that are allowed in a given state space. Such dynamic constraints can be seen as representations of "real world" constraints in a managerial context. The notions of transition, reversible and irreversible transition, and transition relation will be introduced. The link with Kripke models (for modal logics) is also made explicit. Several (subtle) examples of dynamic constraints will be given. Some important classes of dynamic constraints in a database context will be identified, e.g. various forms of cumulativity, non-decreasing values, constraints on initial and final values, life cycles, changing life cycles, and transition and constant dependencies. Several properties of these dependencies will be treated. For instance, it turns out that functional dependencies can be considered as "degenerated" transition dependencies. Also, the distinction between primary keys and alternate keys is reexamined, from a dynamic point of view.

Degeneracy degrees of constraint collections

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

Elastic modulus in the crystalline region of poly(p-phenylene terephthalamide)

Fibres from aromatic polyamides have a much higher Young's modulus than fibres from aliphatic polyamides. In order to contribute to the explanation of this observed difference we looked at one of the ultimate properties, the elastic modulus in the crystalline region in the chain direction (Ecr). We carried out measurements on a bundle of filaments of PRD 49 fibre, which we identified by i.r. and X-ray analyses as poly(p-phenylene terephthalamide). With the X-ray technique we determined the lattice extensions under loading and from these data the Ecr was calculated. The Ecr was found to be 20 × 1011 dyne/cm2 which is in good agreement with the calculated Ecr, but not very different from that of nylon-6,6. The Young's modulus was found to be 11 × 1011 dyne/cm2

The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm

The first purpose of this paper is to make an old (Russian) theoretical results about the structure of local and global maxima of submodular functions, Cherenin’s excluding rules and his Dichotomy Algorithm more accessible for Western community. The second purpose of this paper is to present our main result which can be stated as follows. For any pair of embedded subsets, the difference of their function values is a lower bound for the difference between the unknown(!) optimal values of the corresponding partition defined by these subsets. A simple justification of Cherenin’s rules, the Dichotomy Algorithmand its generalization with the new branching rules from our main result are presented. The usefulness of our new branching rules is illustrated by means of a numerical example.

The data-correcting algorithm for supermodular functions, with applications to quadratic cost partition and simple plant location problems

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

Theoretical and practical aspects of linear optimization

Linear Programming is developed more than fifty years ago and is since then an important tool for solving problems in a variety of fields. An excellent survey of the history of Linear Programming and its applications is given in G.B. Dantzig and M.N. Thapa[9]. In this thesis we will use the expression “Linear Optimization(LO)” instead of Linear Programming, since the meaning of the term is changed over the last fifty years; fifty years ago a program was a schedule or a plan, whereas nowadays a program is mostly associated with a list of instructions for a computer. Linear Optimization is concerned with the maximization or minimization of a linear objective function in a number of variables subject to equality and inequality constraints. In this definition the word inequality means ‘at most’ or ‘at least’, but not ‘not equal’

Crosslinked agarose encapsulated sorbents resistant to steam sterilization. Preparation and mechanical properties

The application of agarose in hemoperfusion is hampered by the lack of a suitable sterilization method. A technique has been developed for the crosslinking of agarose encapsulated sorbents by the reaction with 1,3-dichloro-2-propanol (DCP) under strong alkaline conditions. A twofold molar excess of DCP with respect to agarose and an equimolar amount of sodium hydroxide at a concentration of 0.3 mol/L with a reaction time of 1-4 h at 50°C are found to be the optimal conditions. The compressive strength of crosslinked beads is increased by a factor of 4. Agarose capsules are found to degrade by the influence of Y radiation, but are resistant to steam sterilization at 134°C during at least 30 min when crosslinked