Free-form lens design for wide-angle imaging with an equidistance projection scheme

An algorithm of free-form lens design is presented that can realize wide-angle imaging in conjunction with conventional imaging devices. The wide-angle image obtained through the free-form lens and the camera is not affected by distortions. The formula for the free-form lens surfaces is derived. The surface profile of the free-form lens can be generated through solving a differential equation expressing the camera-viewing angle as a function of the angle of incidence on the free-form lens surface. The surfaces preserve a linear relationship between the angle of incidence of light onto the surface and the angle of refraction into the imaging device.     

Superhydrophobic elastomer surfaces with nanostructured micronails

New approaches to the fabrication of microstructures of special shape were developed for polymers. Unusual superhydrophobic surface structures were achieved with the use of flexible polymers and hierarchical molds.Flexible polyurethane?acrylate coatings were patterned with microstructures with use of microstructured aluminum mold in a controlled UV-curing process. Electron microscope images of the UV-cured coatings on polymethylmethacrylate (PMMA) substrates revealed micropillars that were significantly higher than the corresponding depressions of the mold (even 47 vs. 35 μm). The elongation was achieved by detaching the mold from the flexible, partially cured acrylate surface and then further curing the separated microstructure. The modified acrylate surface is superhydrophobic with a water contact angle of 156° and sliding angle of < 10°.Acrylic thermoplastic elastomers (TPE) were patterned with micro?nanostructured aluminum oxide molds through injection molding. The hierarchical surface of the elastomer showed elongated micropillars (57 μm) with nail-head tops covered with nanograss. Comparison with a reference microstructure of the same material (35 μm) indicated that the nanopores of the micro?nanomold assisted the formation of the nail-shaped micropillars. The elasticity of the TPE materials evidently plays a role in the elongation because similar elongation has not been found in hierarchically structured thermoplastic surfaces. The hierarchical micronail structure supports a high water contact angle (164°), representing an increase of 88° relative to the smooth TPE surface. The sliding angle was close to zero degrees, indicating the Cassie–Baxter state.     

Beyond abstract elementary classes: On the model theory of geometric lattices

Based on Crapo's theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory. One of them, $({\mathbf{K}}^3,?)$, is ω-stable, it has a monster model and an independence calculus that satisfies all the usual properties of non-forking. On the other hand, these classes are rather unusual, e.g. in $({\mathbf{K}}^3,?)$ the Smoothness Axiom fails, and so $({\mathbf{K}}^3,?)$ is not an AEC.     

Graphene from electrochemical exfoliation and its direct applications in enhanced energy storage devices

Graphite was electrochemically exfoliated in mixtures of room temperature ionic liquids and deionized water containing lithium salts to produce functionalized graphenes and such an electrochemical exfoliation technique can be directly used in making primary battery electrodes with significantly enhanced specific energy capacity.     

Novel coordination of a hydroxamic acid : Crystal structures of bis(glycinohydroxamoto)nickel(II) and tris(glycinohydroxamoto)cobalt(III)

The structures of two glycinohydroxamoto (GHA) complexes of Ni(II) and Co(III) have been determined by single-crystal X-ray diffraction methods. The crystals of Ni(GHA)₂ are monoclinic with a = 5.360(1), b = 7.315(4), c = 10.194(4) Å, β = 96.57(3), Z = 2, and space group P2₁/c. The crystals of Co(GHA)₃•1/2 H₂O are monoclinic with a = 22.467(19), b = 8.041(4), c = 13.700(11) Å, β = 116.01(7), Z = 8, and space group C2/c. The values of the final residuals R for Ni(GHA)₂ and Co(GHA)₃•1/2 H₂O are 0.0275 and 0.032, respectvely. The molecular structures of Ni(GHA)₂ and Co(GHA)₃ consist of a square planar and an octahedral coordination, respectively, with the glycinohydroxamato (NH₂CH₂CONOH⁻) ligands coordinating to the metal ion via the N (amino) and the N (NOH⁻). These two complexes are the first well-established cases of coordination of the NHO⁻ group of a hydroxamic acid to a transition metal via the nitrogen atom.     

Categoricity in homogeneous complete metric spaces

We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which we call the perturbation property. We also assume that the Löwenheim-Skolem number, which in this setting refers to the density character of the set instead of the cardinality, is ${\aleph_0}$ . In these settings we prove an analogue of Morley’s categoricity transfer theorem. We also give concrete examples of homogeneous MAECs.     

Forcing a Boolean algebra with predesigned automorphism group

For suitable groups we will show that one can add a Boolean algebra by forcing in such a way that is almost isomorphic to . In particular, we will give a positive answer to the following question due to J. Roitman: Is a possible number of automorphisms of a rich Boolean algebra?

     

Assembly of the Au-diphosphine helical cage molecules via alkynyl-μ4-methylydine ligand transformation

The assembly of the gold(I)-diphosphine cages occurs via unprecedented transformation of the alkynyls into the μ(4)-methylydine ligands under basic conditions. These compounds demonstrate the equilibrium between the P?M helical isomers and serve as hosts to accommodate small molecules (CH(2)Cl(2) and CS(2)).     

Indirect evidence of supramolecular changes within cellulose microfibrils of chemical pulp fibers upon drying

Dried and never-dried chemical pulps were subjected to strong sulfuric acid hydrolysis and the dimensions of the resulting cellulose nanocrystals (CNCs) were characterized by AFM image analysis. Although the average length of CNCs was fairly similar in all samples (55–65 nm), the length distribution histograms revealed that a higher number of longer crystals and a lower number of shorter crystals were present in the CNC suspensions prepared from never-dried pulps. The distinction was hypothetically ascribed to tensions building in individual cellulose microfibrils upon drying, resulting in irreversible supramolecular changes in the amorphous regions. The amorphous regions shaped by tensions were deemed as more susceptible to acid hydrolysis.