Minimal Zero Norm Solutions of Linear Complementarity Problems

In this paper, we study minimal zero norm solutions of the linear complementarity problems, defined as the solutions with smallest cardinality. Minimal zero norm solutions are often desired in some real applications such as bimatrix game and portfolio selection. We first show the uniqueness of the minimal zero norm solution for Z-matrix linear complementarity problems. To find minimal zero norm solutions is equivalent to solve a difficult zero norm minimization problem with linear complementarity constraints. We then propose a p norm regularized minimization model with p in the open interval from zero to one, and show that it can approximate minimal zero norm solutions very well by sequentially decreasing the regularization parameter. We establish a threshold lower bound for any nonzero entry in its local minimizers, that can be used to identify zero entries precisely in computed solutions. We also consider the choice of regularization parameter to get desired sparsity. Based on the theoretical results, we design a sequential smoothing gradient method to solve the model. Numerical results demonstrate that the sequential smoothing gradient method can effectively solve the regularized model and get minimal zero norm solutions of linear complementarity problems.     

Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

In the context of semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically.     

Optical ammonia gas sensor based on a porous silicon rugate filter coated with polymer-supported dye

An ammonia gas sensor chip was prepared by coating an electrochemically-etched porous Si rugate filter with a chitosan film that is crosslinked by glycidoxypropyltrimethoxysilane (GPTMS). The bromothylmol blue (BTB), a pH indicator, was loaded in the film as ammonia-sensing molecules. White light reflected from the porous Si has a narrow bandwidth spectrum with a peak at 610 nm. Monitoring reflective optical intensity at the peak position allows for direct, real-time observation of changes in the concentration of ammonia gas in air samples. The reflective optical intensity decreased linearly with increasing concentrations of ammonia gas over the range of 0–100 ppm. The lowest detection limit was 0.5 ppm for ammonia gas. At optimum conditions, the full response time of the ammonia gas sensor was less than 15 s. The sensor chip also exhibited a good long-term stability over 1 year. Therefore, the simple sensor design has potential application in miniaturized optical measurement for online ammonia gas detection.     

Purification and Partial Characterization of Bacillomycin L Produced by Bacillus amyloliquefaciens K103 from Lemon

Bacillus amyloliquefaciens K103 isolated from a lemon sample was used as a biocontrol agent to suppress Rhizoctonia solani Kühn and other fungal plant pathogens. Two antifungal compounds were purified from the culture broth using acid precipitation, gel permeation chromatography, and reversed-phase high-performance liquid chromatography. Matrix-assisted laser desorption ionization-time of flight mass spectrometry analysis indicated that the antifungal compounds were two isomers similar to bacillomycin L. One of the predominant active fractions was subjected to quadrupole time-of-flight mass spectrometry and amino acid analysis to determine its structural characteristics, revealing that the antifungal compound with a molecular mass of 1,034.5464 was identical to bacillomycin L. This is the second report of lemon microflora producing bacillomycin L or any antifungal compound, suppressing the growth of R. solani Kühn. Meanwhile, the study provided insights into the enormous potential of food microbial resources and bacillomycin L antibiotics in biological control and sustainable agriculture.     

Enantioselective phosphorescence behavior of naproxen in β-cyclodextrin supramolecular complex

In the presence of small amount of 1-iodo butane (IBu) (0.1 % (v/v)), Naproxen (Nap) displays strong room temperature phosphorescence (RTP) in β-cyclodextrin (β-CD) solution without deoxygenation because of the formation of ternary complex of β-CD, Nap, and IBu. The results indicate that β-CD shows good enantiodiscrimination for (R)-Nap and (S)-Nap. The RTP intensity of (R)-Nap is larger than that of (S)-Nap, the difference being 29.2 %. Both (R)-Nap and (S)-Nap exhibit single exponential phosphorescence decay with different lifetimes of 2.535 ± 0.056 and 1.798 ± 0.076 ms for (R)-Nap and for (S)-Nap, respectively. The corresponding association constants evaluated for (R)-Nap/β-CD/IBu and (S)-Nap/β-CD/IBu ternary complexes are (8.02 ± 0.15) × 10³ and (2.50 ± 0.06) × 10³ L mol^?1, respectively. Thus, the observation of RTP differences between (R)-Nap and (S)-Nap can be attributed to their different ability to form complexes with chiral β-CD.     

Preparation,Mechanical Properties and Thermal Degradation Kinetics of a Novel Poly(ester-ether-imide) Elastomer Based on N′,N-Bis(2-hydroxyethyl)-Pyromellitimide Unit

A novel poly(ester-ether-imide) (PEEI) based on N′,N-bis(2-hydroxyethyl)-pyromellitimide unit was synthesized via a conventional two-stage procedure with 1,4-butanediol (BD), dimethyl terephthalate (DMT) and poly(tetramethylene glycol) (PTMG1000). The structures of imide dihydric alcohol and PEEI were confirmed by FT-IR and ¹H-NMR spectra, respectively. The thermal properties and mechanical properties were investigated. The results show PEEI possesses good mechanical properties and excellent thermal stability with the 5% weight loss temperature of the PEEI at 367.3°C, and melting temperature of hard segments (T_mh) at 209.7°C. In addition, the kinetic parameters of thermal degradation of the PEEI were studied by thermogravimetric analysis (TGA) at different heating rates. The activation energy of the solid-state process was determined to be 174.83 and 175.83 kJ/mol using Kissinger and Flynn–Wall–Ozawa methods, respectively. The degradation mechanism model of PEEI was determined bythe Coats-Redfern method. Compared with the values obtained from the Kissinger and Flynn–Wall–Ozawa methods, the actual reaction mechanism of the novel PEEI is a F₁ type (Random nucleation with one nucleus on the individual particle nucleation) and growth model with integral g(a)=?ln(1?a)).     

Complexation Thermodynamics of p-tert-Butylcalix[4]arene Derivatives with Light Lanthanoid Nitrates in Acetonitrile

Abstract

Calorimetric titrations have been performed for the first time in anhydrous acetonitrile at 25°C to give the complex stability constant (K _S) and thermodynamic quantities for the complexation of light lanthanoid(III) nitrates (La-Gd) with 5,11,17,23-tetra-tert-butyl-26,28-bis(cyanomethoxy)-25,27-dihydroxy-calix[4]arene (1) and 5,11,17,23-tetra-tert-butyl-26, 28-bis(2-aminoethoxy)-25,27-dihydroxycalix[4]arene (2). X-ray crystallographic structures of 1 and 2 were also determined and compared. Possessing the cyanomethoxy and aminoethyl substituents, 1 and 2 displayed strikingly different cation binding abilities and selectivity profiles with much higher K _S values for La³⁺ and Ce³⁺, which may be related to the original structures in the solid state. Thus, the binding profile for 2 showed a rapid decrease in K _S with decreasing ionic diameter from La³⁺ to Pr³⁺ and then became flat up to Gd³⁺, while 1 gave a very flat profile which is superimposable with that for 2 between Pr³⁺-Gd³⁺. Thermodynamically, the complexation is driven absolutely by enthalpy which compensates the entropic loss arising from the structural freezing of the calix[4]arene derivatives upon simultaneous binding of lanthanoid ion by the phenolic oxygen and acetonitrile molecule in the cavity. The general validity and the meaning of the compensative enthalpy-entropy relationship observed are discussed.     

Dextran-coated CdSe quantum dots for the optical detection of monosaccharides by resonance light-scattering technique

A resonance light-scattering (RLS) detection method for saccharides was developed using dextran-coated CdSe quantum dots (dextran-CdSe-QDs) optical probes. The dextran-CdSe-QDs can be aggregated with concanavalin A (Con A), and the change in RLS intensity is used to monitor the extent of aggregation. The presence of glucose competitively binds with Con A, dissociating the Con A/dextran-CdSe-QDs complexes, affording the RLS intensity change and hence determining glucose concentrations in the range from a few to about 90 mM. Transmission electron microscopy was used to investigate the competitive interaction between glucose and dextran-CdSe-QDs with Con A. The competitive strategy could also be used to detect similar types of saccharides and the affinities of various monosaccharides for Con A increased in the order galactose?glucose < fructose < mannose. The proposed method was successfully applied to determine glucose in the human serum.

A resonance light-scattering (RLS) detection method for saccharides was developed using dextran-coated CdSe quantum dots (dextran-CdSe-QDs) optical probes. The dextran-CdSe-QDs were coupled to concanavalin A (Con A) to facilitate the aggregation of nanoparticles. The presence of glucose competitively binds with Con A, dissociating the Con A/dextran-CdSe-QDs complexes affording the RLS intensity change and hence determining glucose in the range from a few millimolar to about 90 mM. The proposed method was applied to the determination of glucose in human serum samples with satisfactory results.

     

A ytterbium polymer incorporating ethyl-4,5-imidazole-dicarboxylate and formate coligand: Structure, luminescent, and magnetic properties

A new lanthanide-organic coordination polymer incorporating both substituted imdazole dicarboxylate and formate auxiliary ligand, namely {[Yb₃(HEimda)₄(μ₂-HCOO) · 4H₂O] · 2H₂O} _n (I) (H₃Eimda = 1H-2-ethyl-4,5-imidazole-dicarboxylic acid), has been prepared and was structurally characterized by elemental analysis, IR and X-ray diffraction. It crystallizes in the monoclinic system, space group of C2/c. The polymer I is built from two dimensional (2D) double decker networks based on the Ln₄HEimda₄ tetranuclear basic carboxylate as secondary building unit. The extensive hydrogen bonds extend the 2D lamellar network into a 3D supramolecular aggregate. The emission spectrum of polymer I exhibits ligand-to-metal charge-transfer luminescence. Variable-temperature magnetic susceptibility measurement reveals that the end to end bridging fashion of formate group results in the depopulation of the stark levels for a single Yb³⁺ ion and/or possible antiferromagntic interactions between Yb³⁺ ions within the carboxylato bridged dinuclear unit.     

Synthesis and Properties of Polypyrrole/Chitosan Composite Hydrogels

Conducting polymer hydrogels consisting of polypyrrole (PPy) and chitosan (CS) are prepared by static polymerization of pyrrole using methyl orange (MO) as the dopant and Fe₂(SO₄)₃ as the oxidant in the CS aqueous solution. PPy/CS composite hydrogels not only have good electrical conductivities, but also exhibit excellent swelling/deswelling behaviors due to the participation of one-dimensional conducting PPy blocks in the hydrogel network. The effects of the amount of the oxidant and ionic strength on the physical properties of PPy/CS composite hydrogels are studied in detail. The results show that PPy/CS composite hydrogels have improved water absorbencies in saline solutions compared with the conventional polyelectrolyte hydrogel.