From Agmon–Kannai Expansion to Korteweg–de Vries Hierarchy

We present a new method for computation of the Korteweg–de Vries hierarchy via heat invariants of the one-dimensional Schrödinger operator. As a result, new explicit formulas for the KdV hierarchy are obtained. Our method is based on an asymptotic expansion of resolvent kernels of elliptic operators due to S. Agmon and Y. Kannai.     

Doped Bi2Te3 nano-structured semiconductors obtained by ultrasonically assisted hydrothermal method

Nanocrystalline powders of doped Bi₂Te₃, with Ag (S1 sample), Sb (S2 sample), Sn (S3 sample) ions with different morphology and particle size 30–50 nm were prepared by a ultrasonically assisted hydrothermal method in alkaline aqueous solution with different concentration of NaBH₄ as reducing agent at 200°C for 3 hours and 80% fill degree of autoclave. The influence of dopants and hydrothermal treatment conditions on the formation features, phase composition, particle size, morphology and properties of the products were investigated by X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, atomic force microscopy and electrical measurements. This paper reports a comparative study regarding the dopants influence to the shape and size of nano-structured thermoelectric materials. It was found that hydrothermal processing results in formation of low dimensional dispersion of doped Bi₂Te₃ nanostructures with desired shape and size and high degree of crystallinity with typical semiconductor behavior.      

Unexpected selective enhancement of the thermal stability of aromatic polyimide materials by cerium dioxide nanoparticles

The unusual effect of selective enhancement of the thermal stability of aromatic polyimide materials was established through the introduction of cerium dioxide nanoparticles into these polymers as nanofiller. Depending on the chemical structure of the polymers, a marked increase or a substantial decrease in the thermal stability of the nanocomposite material was registered by thermal analysis, as compared with that of unfilled polymer material. The positive effect was registered only for the composite materials based on the matrix polyimides containing the sulfur atoms located in the sulfonic groups arranged in the elementary units. The results of the thermogravimetric examination are compared with the data obtained during the mechanical tests of the same samples. The possible reasons for the alteration of the thermal stability of polymers by ceria nanoparticles are discussed. The effect above can be of substantial practical interest providing new options for the design of polyimide nanocomposite materials with enhanced thermal stability.     

Chemical modification of nanocrystalline cellulose for improved interfacial compatibility with poly(lactic acid)

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Carbon Nanostructures Derived through Hypergolic Reaction of Conductive Polymers with Fuming Nitric Acid at Ambient Conditions

Hypergolic systems rely on organic fuel and a powerful oxidizer that spontaneously ignites upon contact without any external ignition source. Although their main utilization pertains to rocket fuels and propellants, it is only recently that hypergolics has been established from our group as a new general method for the synthesis of different morphologies of carbon nanostructures depending on the hypergolic pair (organic fuel-oxidizer). In search of new pairs, the hypergolic mixture described here contains polyaniline as the organic source of carbon and fuming nitric acid as strong oxidizer. Specifically, the two reagents react rapidly and spontaneously upon contact at ambient conditions to afford carbon nanosheets. Further liquid-phase exfoliation of the nanosheets in dimethylformamide results in dispersed single layers exhibiting strong Tyndall effect. The method can be extended to other conductive polymers, such as polythiophene and polypyrrole, leading to the formation of different type carbon nanostructures (e.g., photolumincent carbon dots). Apart from being a new synthesis pathway towards carbon nanomaterials and a new type of reaction for conductive polymers, the present hypergolic pairs also provide a novel set of rocket bipropellants based on conductive polymers.     

Modeling of L-lactide Polymerization by Reactive Extrusion

The kinetics of L-lactide ring-opening polymerization initiated by stannous octoate and triphenylphosphine was investigated in a batch apparatus (Haake Rheocord Mixer). Based on the experimental data, a kinetic model is developed, considering a coordination-insertion mechanism. Reactive extrusion experiments were further conducted for the same polymerization process, on a co-rotating twin screw extruder. The melted material flow and mixing was described by using the Ludovic® commercial simulator. Based on the developed kinetic model and simulated flow of L-lactide polymerization mixture, a mathematical model of reactive extrusion process is formulated, describing the evolutions of monomer conversion and average molecular weight along the extruder. The model is predicting with a reasonable good accuracy the experimental data.     

Regularized Traces and Taylor Expansions for the Heat Semigroup

The coefficients in asymptotics of regularized traces and associatedtrace (spectral) distributions for Schrödinger operatorswith short and long range potentials are computed. A kernelexpansion for the Schrödinger semigroup is derived, anda connection with non-commutative Taylor formulas is established.