The crank moments weighted by the parity of cranks

In this note, we introduce the 2kth crank moment \(\mu _{2k}(-1,n)\) weighted by the parity of cranks and show that \((-1)^n \mu _{2k}(-1,n)>0\) for \(n\ge k \ge 0\). When \(k=0\), the inequality \((-1)^n \mu _{2k}(-1,n)>0\) reduces to Andrews and Lewis’s inequality \((-1)^n(M_e(n)-M_o(n))>0\) for \(n\ge 0\), where \(M_e(n)\) (resp. \(M_o(n)\)) denotes the number of partitions of n with even (resp. odd) crank. Several generating functions of \(\mu _{2k}(-1,n)\) are also studied in order to show the positivity of \((-1)^n\mu _{2k}(-1,n)\).     

Influence of patterned concave depth and surface curvature on anodization of titania nanotubes and alumina nanopores

Vertically aligned TiO(2) nanotube and Al(2)O(3) nanopore arrays have been obtained by pattern guided anodization with uniform concave depths. There are some studies about the effect of surface curvature on the growth of Al(2)O(3) nanopores. However, the surface curvature influence on the development of TiO(2) nanotubes is seldom studied. Moreover, there is no research about the effect of heterogeneous concave depths of the guiding patterns on the anodized TiO(2) nanotube and Al(2)O(3) nanopore characteristics, such as diameter, growth direction, and termination/bifurcation. In this study, focused ion beam lithography is used to create concave patterns with heterogeneous depths on flat surfaces and with uniform depths on curved surfaces. For the former, bending and bifurcation of nanotubes/nanopores are observed after the anodization. For the latter, bifurcation of a large tube into two smaller tubes occurs on concave surfaces, while termination of existing tubes occurs on convex surfaces. The growth direction of all TiO(2) nanotubes is perpendicular to the local surface and thus is different on different facets of the same Ti foil. At the edge of the Ti foil where two facets meet, the nanotube growth direction is bent, resulting in a large stress release that causes the formation of cracks.     

Moiré pattern nanopore and nanorod arrays by focused ion beam guided anodization and nanoimprint molding

Nanoporous anodic aluminum oxide has been intensively studied as templates in the fabrication of various nanomaterials. Most of the research focuses on highly ordered hexagonal nanopore arrangement with homogeneous area-specific pore density. Anodic aluminum oxide with alternating area-specific nanopore densities has seldom been addressed. In this study, focused ion beam patterned concave arrays created by overlapping two periodic patterns show the exceptional ability of guiding the subsequent anodization and fabricating porous anodic aluminum oxide with Moire? patterns, which have a wide range of interpore distances and area-specific pore densities. The periodicity of the Moire? patterns can be predicted by the interpore distance of the initial patterns and the rotation angle. The depth of the nanopores of these Moire? patterns is around 1 μm. Vertically aligned and high aspect ratio h-PDMS nanorod arrays with Moire? pattern arrangements have been successfully synthesized using the patterned porous anodic aluminum oxide as templates.     

A non-MRA C^r Frame Wavelet with Rapid Decay

A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in . This example has the same multiplicity function as the Journé wavelet, yet has a Fourier transform and can be made to be for any fixed postive integer . L. Baggett and P. Jorgensen were supported by a US–NSF Focused Research Group (FRG) grant.     

Differential proteome analysis of colon carcinoma cell line SW480 after reconstitution of the tumour suppressor Smad4

The tumour suppressor gene Smad4 is frequently inactivated in gastrointestinal carcinomas. Smad4 plays a pivotal role in transducing signals of the transforming growth factor-β (TGF-β) superfamily of proteins. Inactivation of Smad4 seems to occur late during tumour progression when tumours acquire invasive and metastatic properties. Identification of proteins directly or indirectly regulated by Smad4 would, therefore, ease the future design of new diagnostic and therapeutic strategies for gastrointestinal carcinoma. We have used human colon carcinoma cell line SW480 stably transfected with Smad4 as an in-vitro model system to identify Smad4-regulated proteins by applying two-dimensional gel electrophoresis (2DE) then MALDI-PMF/PFF-MS. We identified a total of 47 protein species with a Smad4-dependent expression. From the functions of the candidate proteins we obtained new insights into Smad4’s participation in processes, for example apoptosis, differentiation, and proliferation.     

Complex Inorganic/Organic Core-Shell Particles by an Inverse Emulsion Technique

Two synthetic approaches to modify the surface of inorganic particles are presented. In the first approach the inorganic particles are prepared in-situ in a confined space in inverse emulsions. The used amphiphilic statistical copolymers act not only as emulsifiers, but they also hydrophobize the remaining inorganic particles after the precipitation. This approach represents a versatile method to obtain various inorganic nanoparticles as well as more complex inorganic materials like core-multiple shell and perovskite-based nanoparticles. The second procedure uses preformed inorganic particles, as an aqueous dispersion, to modify them with surface active amphiphilic copolymers in a multicomponent solvent system. This method turns out to be a simple but highly efficient method to modify preformed inorganic nanoparticles. The particles are characterized by SEM, TEM and dynamic light scattering. The modified inorganic nanoparticles are suitable to be homogenously incorporated into a polymer matrix to form transparent nanocomposite materials.     

A unification of two refinements of Euler’s partition theorem

We obtain a unification of two refinements of Euler’s partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt’s insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.     

Investigation of the structure of detonation waves in a non-premixed hydrogen–air rotating detonation engine using mid-infrared imaging

The structure of detonation waves propagating through the annular channel of an optically accessible non-premixed rotating detonation engine (RDE) are investigated using mid-infrared imaging. The RDE is operated on hydrogen–air mixtures for a range of air mass flow rates and equivalence ratios. Instantaneous images of the radiation intensity from water vapor are acquired using a mid-infrared camera and a band-pass filter (2.890?±?0.033?µm). The instantaneous mid-infrared images reveal the stochastic nature of the detonation wave structure, position and angle of oblique and reflected shock waves, presence of shear layer separating products from the previous and current cycles, and extent of mixing between the reactants and products in the reactant fill zone in front of the detonation wave. The images show negligible signal directly in front of the detonation waves suggesting that there is minimal mixing between the reactants and products from the previous cycle ahead of the detonation wave for most operating conditions. The mid-infrared images provide insights useful for improving fundamental understanding of the detonation structure in RDEs and benchmark data for evaluating modeling and simulation results of RDEs.