A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints

In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace.     

The Box counting Dimension of Invariant Sets for Iterated Function Systems

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Ultrasonic-assisted eggshell extract-mediated polymorphic transformation of calcium carbonate

This study aimed to evaluate the combined effects of eggshell extract and ultrasonic irradiation on the polymorphic transformation of calcium carbonate (CaCO₃). In this context, XRD, Raman spectroscopy, SEM, AFM, TGA-FTIR, BET, and zeta potential analysis were used to identify and characterize the different polymorphs of CaCO₃ obtained in the absence and presence of eggshell extract in the media with and without ultrasonic irradiation. The morphology and polymorphic nature of the CaCO₃ crystals were observed to change, which indicated that the eggshell extract and ultrasonication influenced the structure and crystallization of CaCO₃. The structural analysis results indicated that the addition of eggshell extract to the media resulted in the full transformation of calcite to the vaterite polymorph. The results also showed that ultrasonic irradiation had a more significant influence on the BET specific surface area of the crystals compared to the eggshell extract media. Furthermore, a Box–Behnken design with response surface methodology was employed to determine the optimal operating conditions for CaCO₃ crystallization. The effects of stirring rate, extract concentration, and ultrasonic power on the BET surface area were investigated. The results show that the data sufficiently fit the second-order polynomial model. Understanding the eggshell extract-mediated polymorphic transformation with ultrasonic irradiation obtained in this study makes it possible to control the polymorphic formation and modify the product characteristics.     

2-piercings via graph theory

We provide a very simple proof for a Helly-type result given by Danzer and Grünbaum on 2-piercings of box families in d-dimensional Euclidean space.     

Filters,Antichains and Towers in Topological Spaces and the Axiom of Choice

We find some characterizations of the Axiom of Choice (AC) in terms of certain families of open sets in T₁ spaces.     

Influence d'un ou de plusieurs groupements tertiobutyle sur le comportement magnétooptique du doublet libre d'un atome de phosphore tricoordonné

A magnetooptical study of some halogenotertiobutylphosphines is performed in order to improve the so-called regular relationship which seemed to exist between the magnetic rotation, ?dP, of the lone pair and the bond angles in PX₃ compounds. It is clearly shown that, in any case, ?dP is largely lower than the extreme value which was observed in PX₃ molecules for which XPX=100°. Thus, the existence of the previously invoked relationship vanishes and the question remains as to why there exists a maximum of ?dP for XPX of 100°.     

Evaluation of Automated ECG Monitoring: Theoretical Model Based upon Point Process Techniques

The development of practical methods of ECG monitoring using dedicated computers has presented problems in the evaluation and comparison of the relative effectiveness of various ECG monitoring systems. A theoretical model based on the application of point process techniques is discussed in this paper.     

Flavonoids from Tephrosia—IX : The structure of multijugin and multijuginol

The structures of two flavones, multijuginol and multijugin, isolated from Tephrosia multijuga Young, have been established as 5-methoxy-2?,2?-dimethyl-3?-hydroxy-tetrahydrofurano[5?,4?-b]-dihydrofurano[5″,4″-h]flavone and the 3?-O-acetate derivative, respectively by means of spectral evidence and chemical degradation reactions.