Minimax Results and Finite-Dimensional Separation

In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.     

Composition and thermal stability of SiO2-based hybrid materials TEOS-MTEOS system

Hybrid materials with different amounts of organics permanently bound on the inorganic network obtained in the TEOS-MTEOS (tetraethoxysilan-methyltriethoxysilan) system are used for obtaining coatings with different optical and mechanical properties. To study the thermal stability of the mentioned materials, compositions with different molar ratios of the precursors were prepared. The influence of the solvent and water amounts on the gelation process was also investigated. The gels obtained were characterised by IR spectrometry and their decomposition temperatures were determined by DTA/TG. Thermal stability of the gels is rather influenced by their composition than the conditions of the gelation process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radiation dose contribution from coal-slags used as structural building material

A significant dose contribution on the population could be derived from coal slags used as isolation material. Extremely high natural activities are measured in the coal slag, derived from the region of the settlement Ajka, Hungary. In some buildings monitored, the elevated -doses were nearly 5–10 times higher than the world average ones. The annual average indoor radon concentrations from the slag exceeded 400 Bq/m³ and in some cases up to 1200 Bq/m³. Due to the elevated exposure and the radon concentrations in the dwellings the annual dose was estimated to 8–24 mSv/y more than 5–10 times of the world average one.     

CIRCULAR DICHROISM SPECTRA OF SYSTEM I PARTICLES FROM NORMAL CHLOROPLASTS AND CAROTENOID-DEFICIENT MUTANTS OF MAIZE

Abstract— Circular dichroism (CD) spectra were studied in System I particles prepared by digitonin fragmentation of chloroplasts of normal maize and carotenoid-deficient mutants. CD bands of pigment molecules were found to be higher in particles than in solutions. This phenomenon was most pronounced for the particles containing the carotenoid composition of normal chloroplast lamellae. The CD signal of chlorophylls bound to particles of carotenoid-deficient chloroplasts was closer to that found in solutions. This indicates that aggregation and/or binding of chlorophylls in carotenoid-deficient mutants may be less extensive than in normal chloroplasts.     

A Duality Theory for a Class of Generalized Fractional Programs

In generalized fractional programming, one seeks to minimize the maximum of a finite number of ratios. Such programs are, in general, nonconvex and consequently are difficult to solve. Here, we consider a particular case in which the ratio is the quotient of a quadratic form and a positive concave function. The dual of such a problem is constructed and a numerical example is given.     

On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory

In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions for strong duality for a general class of optimization problems. The authors like to thank the comments of the anonymous referees for their remarks, which greatly improved the presentation of this paper.     

Differentiable Distance Spaces

The distance function \({\varrho(p, q) ({\rm or} d(p, q))}\) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over \({\mathbb{R}^n}\), whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are not Finsler spaces (which are special distance spaces). They are situated between general metric spaces (distance spaces) and Finsler spaces. We will investigate such curves of differentiable distance spaces, which possess the same properties as geodesics do in Finsler spaces. So these curves can be considered as forerunners of Finsler geodesics. They are in greater plenitude than Finsler geodesics, but they become geodesics in a Finsler space. We show some properties of these curves, as well as some relations between differentiable distance spaces and Finsler spaces. We arrive to these curves and to our results by using distance spheres, and using no variational calculus. We often apply direct geometric considerations.