Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

Synthesis of well‐defined,soluble poly(3‐alkyl‐4‐benzamide) by chain‐growth condensation polymerization

Well‐defined poly(3‐alkyl‐4‐benzamide) was synthesized by means of chain‐growth condensation polymerization of phenyl 3‐octyl‐4‐(4‐octyloxybenzyl(OOB)amino)benzoate ( 1c ) from initiator 2 , followed by removal of the OOB groups on amide nitrogen of poly 1c . Polymerization of 1c with phenyl 4‐(trifluoromethyl)benzoate ( 2b ) in the presence of 1,1,1,3,3,3‐hexamethyldisilazide (LiHMDS) and LiCl in THF at ?10 °C gave poly 1c with a narrow molecular weight distribution (M_w/M_n ≤ 1.08) and a well‐defined molecular weight (M_n = 4480–12,700) determined by the feed ratio of monomer to initiator (from 10 to 30). The OOB groups of poly 1c were removed with H₂SO₄ to give the corresponding N‐unsubstituted poly(p‐benzamide) (poly 1c′ ) with low polydispersity. The solublity of poly 1c′ in polar organic solvents was dramatically higher than that of poly(p‐benzamide), demonstrating that introduction of an alkyl group on the aromatic ring is very effective for improving the solubility of poly(p‐benzamide). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 360–365     

Growth and spectral properties of Yb:Ca0.28Ba0.72Nb2O6 disordered crystal

The growth, XRD patterns, spectral properties, and fluorescence decays of Yb:Ca_0.28Ba_0.72Nb₂O₆ (Yb:CBN) with doping concentration of 1 at.% and 5 at.% were studied. The peak absorption cross-section and the emission cross-section were calculated. Larger Stark splitting of Yb:CBN offers the prospect of the quasi-four level laser operation.     

Syntheses,characterization and nonlinear optical properties of sodium–scandium carbonate Na5Sc(CO3)4·2H2O

A novel nonlinear optical (NLO) material Na₅Sc(CO₃)₄·2H₂O has been synthesized under a subcritical hydrothermal condition. The structure is determined by single-crystal X-ray diffraction and further characterized by TG analyses and UV–vis–NIR diffuse reflectance spectrum. It crystallizes in the tetragonal space group P-421c, with a = b = 7.4622(6) Å, C = 11.5928(15) Å. The Second-harmonic generation (SHG) on polycrystalline samples was measured using the Kurtz and Perry technique, which indicated that Na₅Sc(CO₃)₄·2H₂O was a phase-matchable material, and its measured SHG coefficient was about 1.8 times as large as that of d₃₆ (KDP). The results from the UV–vis diffuse reflectance spectroscopy study of the powder samples indicated that the short-wavelength absorption edges of Na₅Sc(CO₃)₄·2H₂O is about 220 nm, suggesting that this crystal is a promising UV nonlinear optical (NLO) materials.     

Extending the Family of V4+ S=${{ 1/2 }}$ Kagome Antiferromagnets

The ionothermal synthesis, structure, and magnetic susceptibility of a novel inorganic–organic hybrid material, imidazolium vanadium(III,IV) oxyfluoride [C₃H₅N₂][V₉O₆F₂₄(H₂O)₂] (ImVOF) are presented. The structure consists of inorganic vanadium oxyfluoride slabs with kagome layers of V⁴⁺ S=${{ 1/2 }}$ ions separated by a mixed valence layer. These inorganic slabs are intercalated with imidazolium cations. Quinuclidinium (Q) and pyrazinium (Pyz) cations can also be incorporated into the hybrid structure type to give QVOF and PyzVOF analogues, respectively. The highly frustrated topology of the inorganic slabs, along with the quantum nature of the magnetism associated with V⁴⁺, means that these materials are excellent candidates to host exotic magnetic ground states, such as the highly sought quantum spin liquid. Magnetic susceptibility measurements of all samples suggest an absence of conventional long‐range magnetic order down to 2 K despite considerable antiferromagnetic exchange.     

Similar Structural Dynamics for the Degradation of CH3NH3PbI3 in Air and in Vacuum

We investigate the degradation path of MAPbI₃ (MA=methylammonium) films over flat TiO₂ substrates at room temperature by means of X‐ray diffraction, spectroscopic ellipsometry, X‐ray photoelectron spectroscopy, and high‐resolution transmission electron microscopy. The degradation dynamics is found to be similar in air and under vacuum conditions, which leads to the conclusion that the occurrence of intrinsic thermodynamic mechanisms is not necessarily linked to humidity. The process has an early stage, which drives the starting tetragonal lattice in the direction of a cubic atomic arrangement. This early stage is followed by a phase change towards PbI₂. We describe how this degradation product is structurally coupled with the original MAPbI₃ lattice through the orientation of its constituent PbI₆ octahedra. Our results suggest a slight octahedral rearrangement after volatilization of HI+CH₃NH₂ or MAI, with a relatively low energy cost. Our experiments also clarify why reducing the interfaces and internal defects in the perovskite lattice enhances the stability of the material.     

Synthesis and antifungal activity of chalcone derivatives

In the present study, using chalcone as a lead compound, a series of its derivatives (compounds 1–30) were designed and synthesised. Their activity of anti-pathogenic fungi of plants has been evaluated. It is found that these compounds have good antifungal activity against Sclerotinia sclerotiorum, Helminthosprium maydis, Botrytis cinerea, Rhizoctonia solani and Gibberella zeae. Among them, the inhibition of growth for compound 30 against S. sclerotiorum showed 89.9%, with the median effective concentrations (EC₅₀) of 15.4 μg mL^? 1. The inhibition of growth for compounds 28, 29 and 30 at a concentration of 100 μg mL^? 1 against H. maydis is 90.3%, 90.7% and 91.1%, with EC₅₀ of 15.1, 18.3 and 18.1μg mL^? 1, respectively.     

Screening anti‐tumor compounds from Ligusticum wallichii using cell membrane chromatography combined with high‐performance liquid chromatography and mass spectrometry

Tyrosine 367 Cysteine‐fibroblast growth factor receptor 4 cell membrane chromatography combined with high‐performance liquid chromatography and mass spectrometry was developed. Tyrosine 367 Cysteine‐HEK293 cells were used as the cell membrane stationary phase. The specificity and reproducibility of the cell membrane chromatography was evaluated using 1‐tert‐butyl‐3‐{2‐[4‐(diethylamino)butylamino]‐6‐(3,5‐dimethoxyphenyl)pyrido[2,3‐d]pyrimidin‐7‐yl}urea, nimodipine and dexamethasone acetate. Then, anti‐tumor components acting on Tyrosine 367 Cysteine‐fibroblast growth factor receptor 4 were screened and identified from extracts of Ligusticum wallichii. Components from the extract were retained on the cell membrane chromatographic column. The retained fraction was directly eluted into high‐performance liquid chromatography with mass spectrometry system for separation and identification. Finally, Levistolide A was identified as an active component from Ligusticum wallichii extracts. The 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyl‐tetrazolium bromide‐formazan colorimetric assay revealed that Levistolide A inhibits proliferation of overexpressing the mutated receptor cells with dose‐dependent manner. Phosphorylation of fibroblast growth factor receptor 4 was also decrease under Levistolide A treatment. Flex dock simulation verified that Levistolide A could bind with the tyrosine kinase domain of fibroblast growth factor receptor 4. Therefore, Levistolide A screened by the cell membrane chromatography combined with high‐performance liquid chromatography and mass spectrometry can arrest cell growth. In conclusion, the two‐dimensional high‐performance liquid chromatography method can screen and identify potential anti‐tumor ingredients that specifically act on the tyrosine kinase domain of the mutated fibroblast growth factor receptor 4.     

Existence of μ−pseudo almost periodic solutions to some evolution equations

In this article, a new approach for pseudo almost periodic solution under the measure theory, under Acquistpace‐Terreni conditions. We make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of μ‐pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. For illustration, we propose some application to a nonautonomous heat equation. Copyright © 2017 John Wiley & Sons, Ltd.     

The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations

We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd.