Ordered *-Algebras with an Order Unit

We develop a theory of ordered *-algebras with an order unit. These are complex algebras equipped with a conjugate-linear vector space involution whose hermitian elements form an ordered real algebra with an order unit but not necessarily with a multiplicative identity. Our main result is a representation theorem for ordered *-algebras with an order unit. This can be viewed as the complex and the non-unital version of the representation theorem of Stone and Kadison for ordered real algebras containing an order unit which is a multiplicative identity. A key role in our approach is played by certain weighted function algebras.     

Proteomic analysis of cartilage- and bone-associated samples

The skeleton of the human body is built of cartilage and bone, which are tissues that contain extensive amounts of extracellular matrix (ECM). In bone, inorganic mineral hydroxyapatite forms 50-70% of the whole weight of the tissue. Although the organic matrix of bone consists of numerous proteins, 90% of it is composed of type I collagen. In cartilage, ECM forms a major fraction of the tissue, type II collagen and aggrecans being the most abundant macromolecules. It is obvious that the high content of ECM components causes analytical problems in the proteomic analysis of cartilage and bone, analogous to those in the analysis of low-abundance proteins present in serum. The massive contents of carbohydrates present in cartilage proteoglycans, and hydroxyapatite in bone, further complicate the situation. However, the development of proteomic tools makes them more and more tempting also for research of musculoskeletal tissues. Application of proteomic techniques to the research of chondrocytes, osteoblasts, osteocytes, and osteoclasts in cell cultures can immediately benefit from the present knowledge. Here we make an overview to previous proteomic research of cartilage- and bone-associated samples and evaluate the future prospects of applying proteomic techniques to investigate key events, such as cellular signal transduction, in cartilage- and bone-derived cells.     

A note on optimal stopping of diffusions with a two-sided optimal rule

We consider a class of optimal stopping problems of diffusions with a two-sided optimal rule. We propose an approach for finding and characterizing the solution. We establish that the optimal stopping rule can be associated with the unique fixed point of an auxiliary function. The results are illustrated with an explicit example.     

Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm

The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method.According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10^?5 –10^?6). The algorithm converges linearly and its asymptotic error constant is $\text{1}\text{4}$.     

On the impact of infrequent trading on the APT systematic risk components — Evidence from a thin security market

The purpose of this note is to analyze the effects of infrequent trading on the APT systematic risk components using Finnish data. Infrequent trading is reported to influence especially the first systematic risk component produced by factor analysis on stock returns.     

The effect of additives on the speed of the crystallization front of xylitol with various degrees of supercooling

Some liquids can be kept in a supercooled or supersaturated metastable state for substantially long periods. Such liquids can be applied as long-term heat storage where the latent heat can be released when needed. As xylitol possesses a relatively high value of latent heat and as it can be easily supercooled, it has promising properties for this application. However, the speed of the crystallization of xylitol is low, leading to a low release rate of latent heat.Several additives have been experimentally tested for the purpose of accelerating the crystallization speed. The effect of the additives on the latent heat, on the melting temperatures, and on the long-term durability of the supercooled state was also measured.The highest speeds of the crystallization front, at a temperature of 22 °C, were achieved with methanol as an additive leading to speeds 33 times higher in vertical experiments and in 170 times higher in horizontal ones than with pure xylitol. The improved speed of the crystallization front is mostly caused by the methanol flow currents generated as a result of the separation of methanol during crystallization, and to a lesser extent, as a result of the increase in the speed of the growth of the crystals.     

A note on high order schemes for the one dimensional wave equation

We construct in two ways stable schemes of arbitrarily high order for one dimensional wave equation. In both cases the stability limit is independent of the order. The other construction yields also automatically stable schemes for the heterogeneous case. In this case the estimated stability limit decreases slightly with order.     

An experimental 1H NMR study of the structural deformation of benzene and the dipolar CH splitting of methane in various nematic liquid crystals and in smectic HAB

The structure of benzene dissolved in various thermotropic nematic liquid crystals has been studied. ¹³C-methane was used as an internal “deformation reference”. The results indicate that the HH distance ratios obtained front the direct dipole-dipole coupling constants correspond to the hexagon values in cases where benzene is dissolved in mixtures of nematic liquid crystals which produce negligible dipolar CH splittings for methane. The ratio ^rCH/^r CC for benzene is in good accord with the value obtained by other spectroscopic means. The proton structure of benzene in the smectic and nematic phases of p,p′-di-n-heptylazoxybenzene (HAB), however, does not follow the general trend observed in the purely nematic phases. But the dipolar CH splitting of methane also behaves inconsistently.