On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂⁿ and on domains of finite type in ℂ². Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

Current Trend in Synthesis,Post‐Synthetic Modifications and Biological Applications of Nanometal‐Organic Frameworks (NMOFs)

Since the early reports of MOFs and their interesting properties, research involving these materials has grown wide in scope and applications. Various synthetic approaches have ensued in view of obtaining materials with optimised properties, the extensive scope of application spanning from energy, gas sorption, catalysis biological applications has meant exponentially evolved over the years. The far‐reaching synthetic and PSM approaches and porosity control possibilities have continued to serve as a motivation for research on these materials. With respect to the biological applications, MOFs have shown promise as good candidates in applications involving drug delivery, BioMOFs, sensing, imaging amongst others. Despite being a while away from successful entry into the market, observed results in sensing, drug delivery, and imaging put these materials on the spot light as candidates poised to usher in a revolution in biology. In this regard, this review article focuses current approaches in synthesis, post functionalization and biological applications of these materials with particular attention on drug delivery, imaging, sensing and BioMOFs.     

Investigating the interface of superhydrophobic surfaces in contact with water

Neutron reflectivity (NR) is used to probe the solid, liquid, vapor interface of a porous superhydrophobic (SH) surface submerged in water. A low-temperature, low-pressure technique was used to prepare a rough, highly porous organosilica aerogel-like film. UV/ozone treatments were used to control the surface coverage of hydrophobic organic ligands on the silica framework, allowing the contact angle with water to be continuously varied over the range of 160 degrees (superhydrophobic) to <10 degrees (hydrophilic). NR shows that the superhydrophobic nature of the surface prevents infiltration of water into the porous film. Atomic force microscopy and density functional theory simulations are used in combination to interpret the NR results and help establish the location, width, and nature of the SH film-water interface.     

The reactivity of dimethylaluminum hydride with the aminoarsines Me2AsNMe2, MeAs(NMe2)2, and As(NMe2)3

The reactions of (Me₂AlH)₃ with Me₂AsNMe₂, MeAs(NMe₂)₂, and As(NMe₂)₃ were investigated as a function of time at room temperature and over the temperature range −90 to 24°C by use of ¹H and ¹³C NMR spectroscopy. (Me₂AlH)₃ was found to be very reactive toward the aminoarsines, even at −90°C, and no stable Me₂AlH-aminoarsine adducts were observed. Instead, the initial stages of the reactions involved AS---N bond cleavage with the generation of highly reactive AlN- and AsH-bonded species. The subsequent course of each reaction and the final arsenic-containing product distribution depended upon the original AL:N stoichiometric ratio and the respective aminoarsine. When the Al:N ratio was 1:1, the reactions were straightforward for each aminoarsine. However, in every case, [Me₂AlNMe₂]₂ was the final AlN-containing product. Independent reactions were carried out to verify many of the proposed decomposition pathways that lead to thermodynamically stable products. The results of this study are compared with those of the analogous, previously reported (Me₃Al)₂-aminoarsine systems. Additionally, a new synthetic route to [Me₂AlAsMe₂]₃ has been established from the reaction of (Me₂AlH)₃ with Me₂AsH.     

Layered droplet microstructures in sheared emulsions: finite-size effects

We investigate the influence of confinement on the steady state microstructure of emulsions sheared between parallel plates, in a regime where the average droplet dimension is comparable to the gap width between the confining walls. Utilizing droplet velocimetry, we find that the droplets can organize into discrete layers under the influence of shear. The number of layers decreases from two (at relatively higher shear rates) to one (at lower shear rates), as the drops grow slightly larger due to coalescence. We argue that the layering and overall composition profile may be controlled by the interplay of droplet collisions (which can cause separation of droplet centers in the velocity gradient direction), droplet migration toward the centerline (due to wall effects), and droplet packing constraints. We also study the effects of mixture composition on droplet microstructure, and summarize these results in the form of a morphology diagram in the parameter space of mass fraction and shear rate. We find that formation of strings of the suspended phase (reported earlier by our group in flow-visualization studies on confined emulsions) is observed over a broad composition window. We also find a stable (nontransient) morphology wherein the droplets are arranged in highly ordered pearl-necklace chain structures.     

On the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f₁,₂, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f₁),λ(f₂)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f₁, f₂ each with λ(f_i) ≤ 1.