Lösungspolymerisation von 1,3,5-Trioxan und 1,3,5,7-Tetroxocan. 2. Mitt. Morphologie der so erhaltenen Polyoxymethylen-Kristalle

Ohne Zusammenfassung     

Exact solutions to chaotic and stochastic systems

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems. (c) 2001 American Institute of Physics.     

Relatively weakly open sets in closed balls of Banach spaces,and real <Emphasis Type="Italic">JB</Emphasis><Superscript>*</Superscript>-triples of finite rank

We prove that, given a real JB^*-triple X, there exists a nonempty relatively weakly open subset of the closed unit ball of X with diameter less than 2 (if and) only if the Banach space of X is isomorphic to a Hilbert space. Moreover we give the structure of real JB^*-triples whose Banach spaces are isomorphic to Hilbert spaces. Such real JB^*-triples are also characterized in two different purely algebraic ways.Mathematics Subject Classification (2000): 46B04, 46B22, 46L05, 46L70Partially supported by Junta de Andalucía grant FQM 0199.Revised version: 30 September 2003     

Experimental Investigation of Plant Root Growth Through Granular Substrates

It is well known that granular materials are not homogeneous, i.e. the forces between grains are localized in force chains. However, previous work on plant root growth has neglected this variability in granular soils and reported bulk characteristics or used homogeneous media, such as agar, to grow plant roots. In this paper we report the results of pinto bean root growth through a granular system where photoelastic grains are used to visualize and quantify the local forces in the system. Two issues are addressed: how plant roots respond to different levels of force between grains, and how the growing roots alter the force distribution in a granular system. We find that pinto bean roots are less likely to grow between grains as the force between those grains increases and that roots can exert, on average, 110 mN of force on the granular system. However, both of these observations are time-dependent. Both the inter-grain forces as the roots grow and the forces that the roots impart to the system increase in time without observable concomitant geometric changes in root cross-section.     

Protein-based bioplastics: effect of thermo-mechanical processing

Bioplastics based on glycerol and different proteins (wheat gluten, albumen, rice and albumen/gluten blends) have been manufactured to determine the effect that processing and further thermal treatments exert on different thermo-mechanical properties of the bioplastics obtained. Oscillatory shear, modulated differential scanning calorimetry, dynamic mechanical thermal analysis, thermo-gravimetric analysis and water absorption tests were carried out to study the effect of processing on the physical characteristics of the bioplastics. The protein-based bioplastics studied in this work present a high capacity for thermosetting modification because of protein denaturation that may favour the development of a wide variety of materials. The use of albumen or rice protein allows the reduction in both protein concentration and thermosetting temperature, leading to linear viscoelastic moduli values similar to those of synthetic polymers such as LDPE and HDPE. The hygroscopic characteristics of protein-glycerol bioplastics may lead to a decrease in the values of the linear viscoelasticity functions. However, hygroscopic properties depend on the protein nature and may be used for industrial applications where water absorption is required. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Optimal control of wave-packets: a semiclassical approach

We studied the optimal quantum control of a molecular rotor in tilted laser fields using the time-sliced Herman–Kluk propagator for the evaluation of the optimal pulse and the light–dipole interaction as the control mechanism. The proposed methodology was used to study the effects of an optimal pulse on the evolution of a wave-packet in a double-well potential and in the effective potential of a molecular rotor in a collinear tilted fields setup. The amplitude and frequency of the control pulse were obtained in such a way that the transition probability between two rotational wave-packets was maximised.     

Octahedral norms and convex combination of slices in Banach spaces

We study the relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach space is octahedral if, and only if, every convex combination of w^?$w^{?}$-slices in the dual unit ball has diameter 2, which answers an open question. As a consequence we get that the Banach spaces with the Daugavet property and its dual spaces have octahedral norms. Also, we show that for every separable Banach space containing _?1${?}_1$ and for every ε>0$\epsilon >0$ there is an equivalent norm so that every convex combination of w^?$w^{?}$-slices in the dual unit ball has diameter at least 2−ε$2-\epsilon$.     

Bishop–Phelps–Bollobás property for certain spaces of operators

We characterize the Banach spaces Y   for which certain subspaces of operators from _L1(μ)$L_1(\mu )$ into Y have the Bishop–Phelps–Bollobás property in terms of a geometric property of Y, namely AHSP. This characterization applies to the spaces of compact and weakly compact operators. New examples of Banach spaces Y with AHSP are provided. We also obtain that certain ideals of Asplund operators satisfy the Bishop–Phelps–Bollobás property.     

Hydroalumination of Thioacetylenes: A Versatile Generation and Reactions of α-Aluminate Sulfides Intermediates

Hydroalumination of thioacetylenes using DIBAL-H and lithium di-(isobutyl)-n-(butyl)-aluminate hydride (Zweifel's reagent), followed by addition of water, furnished exclusively the (Z)- and ( E )-vinyl sulfides, respectively. The regio- and stereochemistry of the intermediates generated, (Z)- and ( E )-phenylthio vinyl alanates, were determined by capture with iodine, which afforded the corresponding ( E )- and (Z)-1-iodo-1-phenylthio-2-organoyl ethenes. Reactions of the ( E )-iodo(thio)ketene acetals with n-BuLi followed by addition of hexanal afforded the (Z)-phenylthio allylic alcohol, while the (Z)-iodo(thio)ketene acetals under similar reactions conditions gave the ( E )-phenylthio allylic alcohol exclusively.