Locking in finite-element approximations to long thin extensible beams

Finite-element approximations to a linearized model of the extensiblebeam problem are examined. For long thin beams, the model maybe viewed as a fourth-order singular perturbation problem. Ifthe mesh size in the finite-element method is not taken to befine enough, the numerical solution may exhibit locking; weexplore the cause of this phenomenon and a possible correction.     

ChemInform Abstract: A Paramagnetic Cl-O Defect Produced by X Irradiation of KBr:ClO- 4.

From IR, Raman, and EPR measurements on KBr:ClO4^- single crystals before and after X-ray irradiation at 77 K it is concluded that irradiation causes the formation of ClO₄^2- (from a parent ClO₄^- ion in Td symmetry) in trigonal symmetry.     

Linear Relationships for Constrained Multiple-item Inventory Systems

Inventory control is a problem common to many businesses andmanufacturing systems. Management spends a fair amount of timetrying to determine appropriate inventory policies. The firstinventory model, which is still used widely today, is the economicorder quantity (EOQ) model of Harris. This model, however, doesnot consider constraints on the problem such as storage capacityor budget Limitations. It is the purpose of this paper to examinethe multiple-item deterministic inventory system with one linearconstraint, and establish linear relationships between the Lagrangemultiplier of the constrgint and artain system characteristics.It is then discussed how the insights from these relationshipscan be used to provide tight hunds to the optimal multiplier.Computational results for these bounds are also included.