Testing hypotheses by using optimal statistical criteria. I

We propose a method for constructing statistical criteria. It can be used for testing an arbitrary finite set of simple alternative hypotheses. A concept of an optimal statistical criterion is introduced, special cases of which are the Bayesian criterion and the minimax criterion. It is proved that any optimal statistical criterion can be constructed on the basis of the likelihood ratio.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 378–388, April, 1994.     

Study of the mobility,surface area,and sintering behavior of agglomerates in the transition regime by tandem differential mobility analysis

The surface area of nanosized agglomerates is of great importance as the reactivity and health effects of such particles are highly dependent on surface area. Changes in surface area through sintering during nanoparticle synthesis processes are also of interest for precision control of synthesised particles. Unfortunately, information on particle surface area and surface area dynamics is not readily obtainable through traditional particle mobility sizing techniques. In this study, we have experimentally determined the mobility diameter of transition regime agglomerates with 3, 4, and 5 primary particles. Agglomerates were produced by spray drying well-characterised polystyrene latex particles with diameters of 55, 67, 76, and 99 nm. Tandem differential mobility analysis was used to determine agglomerate mobility diameter by selecting monodisperse agglomerates with the same number of primary particles in the first DMA, and subsequently completely sintering the agglomerates in a furnace aerosol reactor. The size distribution of the completely sintered particles was measured by an SMPS system, which allowed for the determination of the number of primary particles in the agglomerates. A simple power law regression was used to express mobility diameter as a function of primary particle size and the number of primary particles, and had an excellent correlation (R² = 0.9971) with the experimental data. A scaling exponent was determined from the experimental data to relate measured mobility diameter to surface area for agglomerates. Using this relationship, the sintering characteristics of agglomerates were also examined for varying furnace temperatures and residence times. The sintering data agreed well with the geometric sintering model (GSM) model proposed by Cho & Biswas (2006a) as well as with the model proposed Koch & Friedlander (1990) for sintering by viscous flow.     

Synthesis and characterization of a series of wholly aromatic copolyesters containing 2‐(α‐phenylisopropyl)hydroquinone moiety

Two series of new wholly aromatic thermotropic copolyesters containing the 2‐(α‐phenylisopropyl)hydroquinone (PIHQ) moiety have been synthesized and their basic properties such as glass transition temperature (T_g), melting temperature (T_m), thermal stability, crystallinity, and liquid crystallinity were studied by differential scanning calorimetry (DSC), thermogravimetry (TG), and wide‐angle X‐ray diffractometry (WAXD) and on a polarizing microscope. The first series was prepared from acetylated PIHQ, terephthalic acid (TPA), and 2,6‐naphthalenedicarboxylic acid (NDA), and the second series from acetylated PIHQ, TPA, and 1,1′‐biphenyl‐4,4′‐dicarboxylic acid (BDA). The T_g values (152–168°C) of the two series are not much different, although the values for the first series appear slightly higher. The T_m values (287–378°C) and the degree of crystallinity of the first series are appreciably greater than those of the second series. Such differences can be explained by the geometric structure of NDA and BDA moieties. All of the present polyesters are thermotropic and nematic. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 881–889, 1999     

Calix[4]arene-based fluorescent probe and the adsorption capacity of its electrospun nanofibrous film for the cesium cation as an adsorbent

Calix[4]arene-based cation receptor 1 has been synthesised by following a multi-step synthetic procedure. The fluorescence properties of 1 upon the addition of various metal ions were investigated by fluorescence spectroscopy. As a result, it was revealed that 1 displayed dramatic quenching effect upon the exposure to Cs⁺. In contrast, no significant quenching effects were observed upon the addition of other metal ions such as Li⁺, Na⁺, K⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ag⁺, Zn²⁺ and Ni²⁺. Compound 1 was also found by Job plot to form a 1:1 complex with Cs⁺. In addition, we also prepared 1-embedded electrospun nanofibrous film (NF-1) as an adsorbent for Cs⁺. NF-1 is proved to adsorb Cs⁺ effectively from an aqueous solution, indicating that it would be usefully utilised as an adsorbent to remove Cs⁺.     

Synthesis of highly ordered mesoporous CeO<Subscript>2</Subscript> and low temperature CO oxidation over Pd/mesoporous CeO<Subscript>2</Subscript>

Highly ordered mesoporous cerium dioxide (meso-CeO₂) was successfully synthesized using a facile solvent-free infiltration method from a mesoporous silica template, KIT-6. The meso-CeO₂ material, thus obtained, exhibited well-defined mesostructure and high surface area (153 m² g⁻¹). The physicochemical properties of meso-CeO₂ material and Pd-supported on meso-CeO₂ (Pd/meso-CeO₂) were characterized by electron microscopy, X-ray diffraction, N₂ adsorption–desorption, and temperature-programmed experiments. The Pd/meso-CeO₂ catalyst exhibited excellent catalytic activity for CO oxidation compared with those of other Pd/CeO₂ catalysts which were prepared using nanocrystalline CeO₂ and bulk-CeO₂ as the supports. Moreover, a hydrogen pretreatment of the Pd/meso-CeO₂ catalyst resulted in a remarkable increase of catalytic activity (T ₁₀₀ = 52 °C).     

Naphthocrown‐Strapped Calix[4]pyrroles: Formation of Self‐Assembled Structures by Ion‐Pair Recognition

A new approach to the construction of self‐assembled structures is reported that is based on ion‐pair recognition. Towards this end, the calix[4]pyrrole naphthocrown‐4 hybrid structures 2 and 3 were prepared. These multitopic receptors contain recognition sites for both anions and cations. On the basis of solution‐phase ¹H NMR spectroscopic analysis and solid‐state single‐crystal X‐ray diffraction structural studies, it was established that receptors 2 and 3 are able to bind specific ion pairs with high selectivity via different binding modes. In the case of CsF and CsCl, the ion‐pair complexes formed from receptors 2 and 3 were found to self‐assemble to produce either linear supramolecular polymeric crystalline solids or nanotube‐like cyclic hexamers depending on the specific choice of ion pairs and crystallization solvents. Proton NMR studies provided evidence for solution‐phase self‐association in organic media.     

Spectroscopic identification of benzyl-type radicals generated by corona discharge of 2-chloro-4-fluorotoluene

By means of a technique of corona excited supersonic expansion coupled with a pinhole-type glass nozzle, we generated vibronically excited but jet-cooled benzyl-type radicals from precursor 2-chloro-4-fluorotoluene seeded in a large amount of inert carrier gas He. From an analysis of the visible vibronic emission spectrum, we found evidence of the formation of the 2-chloro-4-fluorobenzyl and 4-fluorobenzyl radicals. A possible pathway for the formation of these benzyl-type radicals is herein proposed. Also, the electronic energy in the D(1) → D(0) transition and the vibrational mode frequencies of the 2-chloro-4-fluorobenzyl radical in the ground electronic state were accurately determined, for the first time, by comparison with ab initio calculations and the known vibrational data of the precursor.     

A calix[2]phenol[2]pyrrole and a fused pyrrolidine-containing derivative

The hybrid calix[2]phenol[2]pyrrole 4 and the fused pyrrolidine-containing macrocycle 9 were synthesized from two different isomeric starting materials, namely dimethyl 2-hydroxyisophthalate and 5-hydroxyisophthalate, respectively. The fused species 9 is devoid of obvious substrate binding properties. In contrast, the heterocalix system 4 displays the fluoride-induced conformational changes characteristic of the parent system.