Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

Molecular deformation mechanisms of isotactic polypropylene in α‐ and β‐crystal forms by FTIR spectroscopy

The orientation behavior of isotactic polypropylene (iPP) in α‐ and β‐crystal form was investigated by rheo‐optical Fourier transformed infrared (FTIR) spectroscopy. This method enabled quantification of the degree of orientation as a feature of structural changes during uniaxial elongation in not only the crystalline phase but also the amorphous one. Molecular orientation mechanisms can be successfully derived from experimental results. Generally, three mechanisms were detected for iPP: (1) interlamellar separation in the amorphous phase, (2) interlamellar slip and lamellar twisting at small elongations, and (3) intralamellar slip at high elongations. The third mechanism was favored by α‐PP, whereas β‐PP favored the second mechanism, which, in fact, was responsible for the different mechanical properties of both materials at the macroscopic level. On the other hand, crystallization conditions may have significantly affected the amorphous orientation. Nevertheless, for both iPP types the chains in the amorphous phase always oriented less than did those in the crystalline phase. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4478–4488, 2004     

Evaluation of Morphology and Deformation Micromechanisms in Multilayered PP/PS Films: An Electron Microscopy Study

Nanostructured polymers and ultra-thin polymer layers are used more and more in technical applications like nanotechnology and microelectronics. Therefore, it is really important to understand the size-scale dependent properties as bulk polymers become thinner and more two-dimensional. Here the morphology as well as the macroscopic and the microscopic deformation behaviour of multilayered films of polypropylene (PP) and polystyrene (PS) have been investigated. For investigation different microscopic techniques and tensile testing were used. The films were prepared by multilayer coextrusion, whereas the composition of PP and PS and the film thickness – and therefore the thickness of each layer – varied. The thinnest calculated thickness of a single layer was about 5 nm. It is shown that the PP/PS films consist usually of homogeneous layers with only few defects. As the composition of PP/PS deviates strongly from 50/50 or the films get thinner the number of defects increases and the layered system turns to irregular lamellar system. In macroscopic tensile tests the small PS layers affect the elongation at break enormously: Most of the samples are brittle. For the films with a composition of PP/PS 90/10 and the film PP/PS 70/30 with a film thickness of 25 µm an elongation at break of 66% and higher could be reached. Transmission electron microscopy on these samples shows that the layers are characterized by plastic yielding in local deformation zones.     

Double Yielding in a Styrene/Butadiene Star Block Copolymer

Summary: The morphology and tensile deformation behaviour of a highly asymmetric styrene/butadiene star block copolymer (polystyrene (PS) content = 74%) containing random PS‐co‐PB (polybutadiene) copolymer as a rubbery phase were investigated. The existence of double yielding, similar to that observed in some semicrystalline polymers, was detected in this nanostructured amorphous polymer. The observed phenomenon may be correlated with two different micromechanical processes taking place at the initial stage of deformation.

The stress‐strain curve of the star block copolymer prepared here (each curve represents a different method). The two yield points are clearly visible (labelled I and II).     

6-Chloro-3-hydroxy-2-(5'-methylfuryl)-4H-chromene-4-one as an analytical reagent for micro determination of molybdenum(VI).

6-Chloro-3-hydroxy-2-(5'-methylfuryl)-4H-chromene-4-one (CHMFC) has been used as an analytical reagent for the spectrophotometric determination of molybdenum. Molybdenum(VI) in the presence of several cations, anions and complexing agents forms a yellow 1:2 complex with CHMFC. The complex is quantitatively extractable into 1,2-dichloroethane from 1 mol dm(-3) acetic acid medium and is stable for more than 6 h. The complex shows an absorption maximum at 438 nm with a molar absorptivity of 5.36 x 10(4) dm3 mol(-1) cm(-1) and Sandell's sensitivity equal to 0.0017 microg Mo cm(-2). The method obeys Beer's law up to 1.9 microg Mo ml(-1). The relative standard deviations are 0.2% for solutions and 0.5-1.5% for solid samples. The method is simple, selective, precise and rapid, and has been satisfactorily applied to the micro determination of molybdenum in various synthetic and standard samples.     

Social media and sensemaking patterns in new product development: demystifying the customer sentiment

Artificial intelligence by principle is developed to assist but also support decision making processes. In our study, we explore how information retrieved from social media can assist decision-making processes for new product development (NPD). We focus on consumers’ emotions that are expressed through social media and analyse the variations of their sentiments in all the stages of NPD. We collect data from Twitter that reveal consumers’ appreciation of aspects of the design of a newly launched model of an innovative automotive company. We adopt the sensemaking approach coupled with the use of fuzzy logic for text mining. This combinatory methodological approach enables us to retrieve consensus from the data and to explore the variations of sentiments of the customers about the product and define the polarity of these emotions for each of the NPD stages. The analysis identifies sensemaking patterns in Twitter data and explains the NPD process and the associated steps where the social interactions from customers can have an iterative role. We conclude the paper by outlining an agenda for future research in the NPD process and the role of the customer opinion through sensemaking mechanisms.