CR singular images of generic submanifolds under holomorphic maps

The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorphism onto its image. We find a necessary (sufficient in dimension 2) condition for the diffeomorphism to extend to a finite holomorphic map. The multiplicity of this map is a biholomorphic invariant that is precisely the Moser invariant of the image, when it is a Bishop surface with vanishing Bishop invariant. In higher dimensions, we study Levi-flat CR singular images and we prove that the set of CR singular points must be large, and in the case of codimension 2, necessarily Levi-flat or complex. We also show that there exist real-analytic CR functions on such images that satisfy the tangential CR conditions at the singular points, yet fail to extend to holomorphic functions in a neighborhood. We provide many examples to illustrate the phenomena that arise.     

The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations

Fuzzy hyperbolic partial differential equation, one kind of uncertain differential equations, is a very important field of study not only in theory but also in application. This paper provides a theoretical foundation of numerical solution methods for fuzzy hyperbolic equations by considering sufficient conditions to ensure the existence and uniqueness of fuzzy solution. New weighted metrics are introduced to investigate the solvability for boundary valued problems of fuzzy hyperbolic equations and an extended result for more general classes of hyperbolic equations is initiated. Moreover, the continuity of the Zadeh’s extension principle is used in some illustrative examples with some numerical simulations for \(\alpha \) -cuts of fuzzy solutions.     

Metal-enhanced fluorescence using silver nanoparticles-embedded polyelectrolyte multilayer films for microarray-based immunoassays

Metal-enhanced fluorescence (MEF) of quantum dots (QDs) and its potential application in microarray-based immunoassays was investigated using silver nanoparticles (AgNPs) prepared by the in situ photoreduction of Ag⁺ inside a multilayer film consisting of poly(ethyleneimine) (PEI) and hyaluronic acid (HA). UV–Vis spectroscopy, X-ray diffraction, atomic force microscopy, scanning electron microscopy, and transmission electron microscopy confirmed the formation of well-dispersed AgNPs within the multilayer films, the thickness and the amount of which depended on the number of HA layers. Using AgNPs-containing hybrid multilayered films, it was possible to observe the MEF effect of adsorbed QDs, which could be tuned by the thickness of interlayer spacer film prepared of the layer-by-layer assembly of PEI and poly(styrene sulfonate). When the MEF-inducing hybrid film was used as a platform for immunoassay, a significant improvement in the fluorescence signal and sensitivity of the biosensing were observed in the presence of AgNPs in comparison with films that did not contain the nanoparticles.     

Desolvation and Dehydrogenation of Solvated Magnesium Salts of Dodecahydrododecaborate: Relationship between Structure and Thermal Decomposition

Attempts to synthesize solvent‐free MgB₁₂H₁₂ by heating various solvated forms (H₂O, NH₃, and CH₃OH) of the salt failed because of the competition between desolvation and dehydrogenation. This competition has been studied by thermogravimetric analysis (TGA) and temperature‐programmed desorption (TPD). Products were characterized by IR, solution‐ and solid‐state NMR spectroscopy, elemental analysis, and single‐crystal or powder X‐ray diffraction analysis. For hydrated salts, thermal decomposition proceeded in three stages, loss of water to form first hexahydrated then trihydrated, and finally loss of water and hydrogen to form polyhydroxylated complexes. For partially ammoniated salts, two stages of thermal decomposition were observed as ammonia and hydrogen were released with weight loss first of 14 % and then 5.5 %. Thermal decomposition of methanolated salts proceeded through a single step with a total weight loss of 32 % with the release of methanol, methane, and hydrogen. All the gaseous products of thermal decomposition were characterized by using mass spectrometry. Residual solid materials were characterized by solid‐state ¹¹B magic ‐ angle spinning (MAS) NMR spectroscopy and X‐ray powder diffraction analysis by which the molecular structures of hexahydrated and trihydrated complexes were solved. Both hydrogen and dihydrogen bonds were observed in structures of [Mg(H₂O)₆B₁₂H₁₂] ? 6 H₂O and [Mg(CH₃OH)₆B₁₂H₁₂] ? 6 CH₃OH, which were determined by single‐crystal X‐ray diffraction analysis. The structural factors influencing thermal decomposition behavior are identified and discussed. The dependence of dehydrogenation on the formation of dihydrogen bonds may be an important consideration in the design of solid‐state hydrogen storage materials.     

Complexity and synchronization in stochastic chaotic systems

We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.     

The initial treatment of the concept of function in the selected secondary school mathematics textbooks in the US and China

In order to provide insight into cross-national differences in students’ achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year earlier than the Chinese curriculum and provide strikingly more problems for students to work on. However, the Chinese curriculum emphasizes developing both concepts and procedures and includes more problems that require explanations, visual representations, and problem solving in worked-out examples that may help students formulate multiple solution methods. This result could indicate that instead of the number of problems and early introduction of the concept, the cognitive demands of textbook problems required for student thinking could be one reason for differences in American and Chinese students’ performances in international comparative studies. Implications of these findings for curriculum developers, teachers, and researchers are discussed.     

Compatibility of Thermally Reduced Graphene with Polyesters

The compatibility of thermally reduced graphene (TRG) with multiblock copolyesters, composed of poly(butylene terephthalate) (PBT) segments and poly(tetramethylene ether) glycol segments, was examined in detail. The morphology observed by optical microscopy and scanning electron microscopy showed that the compatibility was enhanced with increasing content of the PBT segment in the polyester. This compatibility behavior was analyzed quantitatively, by using the percolation threshold of electrical conductivity, and then further analyzed by using the Hansen solubility parameters to provide a general quantitative guideline to predict the compatibility of TRG with various polymers. The results suggest that the total solubility parameter, δ_T, value of TRG is larger than 24.0 (MPa)^½, and thus that the compatibility with polymer is enhanced as the δ_T value of a polymer increases toward 24.0 (MPa)^½. However, this prediction does not fit well in the presence of a comonomer such as acrylic acid, which has a high tendency to hydrogen bond with itself.     

Low-temperature synthesis of ultrathin Sb2S5 nanofibers and their application as highly selective Pb-adsorbents in water

Ultrathin Sb(2)S(5) nanofibers were prepared using a wet chemical method at 50 degrees C and applied as selective adsorbents of Pb ions in water.     

Turning on fluorescent emission from C-alkylation on quinoxaline derivatives

Reduction on imine moiety (C=N) of quinoxalines by alkyl-/aryllithiums led to a geometrical change on the quinoxaline ring, thereby perturbing the electronic structure to turn on fluorescence emission. Such a structural change resulted in interrupted cyclic-ring systems with electron-donating amine (sp(3)-type) and electron-accepting imine (sp(2)-type) units bridged by a phenylene unit. Through either alkylation or arylation, a highly polarized electron donor-electron acceptor bipolar system was established in a single molecule with dramatically enhanced PL efficiency (up to 60%).     

Rapid and quantitative DNA analysis of genetic mutations for polycystic kidney disease (PKD) using magnetic/luminescent nanoparticles

Rapid and accurate detection of genetic mutations based on nanotechnology would provide substantial advances in detection of polycystic kidney disease (PKD), a disease whose current methods of detection are cumbersome due to the large size and duplication of the mutated gene. In this study, a nanotechnology-based DNA assay was developed for detection of SNPs (single nucleotide polymorphisms) in a feline autosomal dominant PKD (ADPKD) model which can readily be adapted to diagnosis of human ADPKD type 1. Europium and terbium phosphors were doped into gadolinium crystal hosts with a magnetic core, providing stable luminescence and the possibility of magnetic manipulations in a solution-based assay. A hybridization-in-solution DNA assay was optimized for feline PKD gene SNP detection using genomic DNA extracted from feline kidney tissue and blood. This assay showed a substantial differentiation between PKD and control specimens. The nanotechnology-based DNA assay is attractive from the viewpoint of rapid availability, simple methodology, and cost reduction for clinical use to detect mutations involved in human ADPKD and other genetic diseases. Figure Schematic diagram of PKD (Polycystic Kidney Disease) SNPs detection assay using feline genomic DNA in magnetic/luminescent nanoparticle-based DNA hybridization