Periodic points and normal families

Let be the family of all functions which are holomorphic in some domain and do not have periodic points of some period greater than one there. It is shown that is quasinormal, and the sequences in which do not have convergent subsequences are characterized. The method also yields a new proof of the result that transcendental entire functions have infinitely many periodic points of all periods greater than one.

     

Effective bulk moduli of materials containing stochastically distributed nano-inhomogeneities with surface stresses

In the present contribution, a mathematical model for the investigation of the effective properties of a material with randomly distributed nano-particles is proposed. The surface effect is introduced via Gurtin-Murdoch equations describing properties of the matrix/nano-particle interface. They are added to the system of stochastic differential equations formulated within the framework of linear elasticity. The homogenization problem is reduced to finding a statistically averaged solution of the system of stochastic differential equations. These equations are based on the fundamental equations of linear elasticity, which are coupled with surface/interface elasticity accounting for the presence of surface tension. Using Green's function this system is transformed to a system of statistically non-linear integral equations. It is solved by the method of conditional moments. Closed-form expressions are derived for the effective moduli of a composite consisting of a matrix with randomly distributed spherical inhomogeneities. The radius of the nano-particles is included in the expression for the bulk moduli. As numerical examples, nano-porous aluminum and nano-porous gold are investigated assuming that only the influence of the interface effects on the effective bulk modulus is of interest. The dependence of the normalized bulk moduli of nano-porous aluminum on the pore volume fraction (for certain radii of nano-pores) are compared to and discussed in the context of other theoretical predictions. The effective Young's modulus of nano-porous gold as a function of pore radius (for fixed void volume fraction) and the normalized Young's modulus vs. the pore volume fraction for different pore radii are analyzed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spray coating of cellulose aerogel particles in a miniaturized spouted bed

Cellulose - Aim of this work is to apply protective and homogeneous shellac coating layers on the surface of hydrophilic open-pore cellulose aerogel particles with low...     

Synthesis and Physical Properties of Tunable Aryl Alkyl Ionic Liquids (TAAILs)

Tunable aryl alkyl ionic liquids (TAAILs) based on the imidazolium cation were first reported in 2009. Since then, a series of TAAILs with different properties due to the electron-donating or -withdrawing effect of the substituents at the aryl ring has been developed. Herein, a wide variety of those ionic liquids (ILs) is presented in terms of their cation structure. The authors synthesized ILs containing the bromide or bis(trifluoromethane)sulfonimide anion and 1-aryl-3-alkyl imidazolium cations with various substituents in the ortho and/ or para position of the phenyl ring and alkyl chains of different lengths varying from butyl to dodecyl. The differences of their physical properties (melting point, thermal decomposition, viscosity, electro-chemical window) of these ILs are reported according to their structure.     

Influence of interfaces on effective properties of nanomaterials with stochastically distributed spherical inclusions

The method of conditional moments is generalized to include evaluation of the effective elastic properties of particulate nanomaterials and to investigate the size effect in those materials. Determining the effective constants necessitates finding a stochastically averaged solution to the fundamental equations of linear elasticity coupled with surface/interface conditions (Gurtin–Murdoch model). To obtain such a solution the system of governing stochastic differential equations is first transformed to an equivalent system of stochastic integral equations. Using statistical averaging, the boundary-value problem is then converted to an infinite system of linear algebraic equations. A two-point approximation is considered and the stress fluctuations within the inclusions are neglected in order to obtain a finite system of algebraic equations in terms of component-average strains. Closed-form expressions are derived for the effective moduli of a composite consisting of a matrix and randomly distributed spherical inhomogeneities. As a numerical example a nanoporous material is investigated assuming a model in which the interface effects influence only the bulk modulus of the material. In that model the resulting shear modulus is the same as for the material without surface effects. Dependence of the bulk moduli on the radius of nanopores and on the pore volume fraction is analyzed. The results are compared to, and discussed in the context of other theoretical predictions.     

Photochemical Transformation of Levoglucosan Imides to Anhydrosugar-Annelated Azepanediones and Azocanediones

Summary.  By reaction of O-protected 3-amino-1,6-anhydro-β-D-glucopyranose with succinic, glutaric, and tartaric anhydride, respectively, the corresponding 3-substituted succinimido, glutarimido, and tatarimido derivatives were obtained. Irradiation of the succinimido and glutarimido derivatives at 254 nm gave 1,4-diradical intermediates by γ-hydrogen abstraction (Norrish Type II reaction) which subsequently recombined (Yang cyclization) to form azetidinols. These in turn fragmented and led to azepanedione and azocanedione derivatives. In contrast, irradiation of the tartarimido derivative resulted in elimination and led to both isomeric enolethers. Received September 3, 2001. Accepted October 31, 2001     

Work hardening and recovery in fully lamellar TiAl: relative activity of deformation systems

The relative activity of deformation systems during work hardening and thermal recovery has been investigated in fully lamellar TiAl. This has been done by a combination of a series of deformation/static recovery experiments and numerical simulations based on a defect density-based crystal plasticity model. Firstly, active deformation systems in differently oriented polysynthetically twinned crystals/single lamellar colonies have been studied. Subsequently, numerical experiments on a polycolony microstructure have been used to investigate the inhomogeneous microplasticity (i.e. the typical microyield) in fully lamellar TiAl. From this, it has been possible to analyse how changes in the lamella thickness, domain size and colony size influence the onset of macroscopic yield. Based on static recovery experiments with differently oriented polysynthetically twinned crystals, numerical studies have revealed trends in the recovery of work hardening in both polysynthetically twinned crystals and polycolony microstructures.