On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.     

基于循环码的常重复合码的构造

研究给出了一类基于循环码的常重复合码的构造,并利用指数和计算其参数.与相关的常重复合码相比,该码具有更多的码字,且渐近性较好.     

Nanoporous polyimide film from poly(ethylene glycol-co-imide) using a one-step heat calcination process

Polyamic acid (PAA) made from 3,3, 4,4-biphenyltetracarboxylic dianhydride and 4,4-diaminodiphenyl ether was synthesized and used as the backbone of nanoporous polyimide. Thermally labile polyethylene glycol (PEG) at 10, 20 or 30 wt% was introduced to the end group of PAA. Self-assembled PAA-b-PEG micelle-like nanoparticles could be formed as a result of amphiphilic characteristics of hydrophobic PAA and hydrophilic PEG. Thermal imidization and degradation of spin-coated amphiphilic PAA-b-PEG film were performed sequentially through one-step heat treatment to obtain polyimide film with nanopores. Pore sizes decreased with increasing amount of PEG block and their dielectric constants decreased from 2.71 ± 0.13 to 2.38 ± 0.11.     

Atmospheric oxidation chemistry of 1–methoxy 2–propyl acetate initiated by OH radicals: kinetics and mechanisms

Kinetics and mechanism of the gas-phase reaction of CH₃C(O)OCH(CH₃)CH₂OCH₃ (MPA) with OH radicals in the presence of O₂ and NO have been investigated theoretically by performing a high and reliable level of theory, viz., CCSD(T)/6-311?+?G(d,p)//BH&HLYP/6-311++G(d,p)?+?0.9335×ZPE. The calculations predict that the H-abstraction from the ?CH₂?O? position of MPA is the most facile channel, which leads to the formation of the corresponding alkoxy radicals CH₃C(O)OCH(CH₃)C(O ?)HOCH₃ under atmospheric conditions. This activated radicals CH₃C(O)OCH(CH₃)C(O ?)HOCH₃ will undergo further rearrangement, fragmentation and oxidative reactions and predominantly leads to the formation of various products (methyl formate HC(O)OCH₃ and acetic anhydride CH₃C(O)OC(O)CH₃). In the presence of water, acetic anhydride can convert into acetic acid CH₃C(O)OH via the hydrolysis reaction. The calculated total rate constants over the temperature range 263–372?K are used to derive a negative activation energy (E_a= ?5.88 kJ/mol) and an pre-exponential factor (A?=?1.78×10^?12 cm³ molecule^?1 s^?1). The obtained Arrhenius parameters presented here are in strong agreement with the experimental values. Moreover, the temperature dependence of the total rate constant over a temperature range of 263?1000?K can be described by k?=?5.60 × 10^?14×(T/298?K)^3.4×exp(1725.7?K/T) cm³ molecule^?1 s^?1.     

A Weighted Trudinger–Moser Inequality on R^N and Its Application to Grushin Operator

Let x=(x',x')with x'∈Rk and x'∈R^N-k andΩbe a x'-symmetric and bounded domain in R^N(N≥2).We show that if 0≤a≤k-2,then there exists a positive constant C>0 such that for all x'-symmetric function u∈C0^∞(Ω)with∫Ω|■u(x)|^N-a|x'|^-adx≤1,the following uniform inequality holds1/∫Ω|x|^-adx∫Ωe^βa|u|N-a/N-a-1|x'|^-adx≤C,whereβa=(N-a)(2πN/2Γ(k-a/2)Γ(k/2)/Γ(k/2)r(N-a/2))1/N-a-1.Furthermore,βa can not be replaced by any greater number.As the application,we obtain some weighted Trudinger–Moser inequalities for x-symmetric function on Grushin space.     

对《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的讨论

本文绘制了一维等距离子晶体的累加法、埃夫琴法和平均值法的各级马德隆常数的曲线.本文推导了二聚化直线离子晶体马德隆常数的求和式,比较了两种解析式的优劣.本文详细地推导了圆环上等距和二聚化离子晶体的马德隆常数的解析式,使读者更易于理解.本文修正了《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的两个笔误,还建议修正二聚化马德隆常数的定义式,使其物理意义更明显.     

Variations of the elastic constants of InSb near the covalent-metallic transition

Abstract

The pulse-echo-overlap method was used to measure the longitudinal and transverse wave velocities in single-crystal (100) and (111) samples of InSb up to 3 GPa at room temperature. The peculiar variations of the elastic constants were observed near the covalent-metallic transition.     

Dependence of the Constant of the Mark‐Houwink Equation under Theta Conditions on the Bulk of Substituents for Hydrocarbon Polymers

The logarithm of the constant K _θ in the Mark‐Houwink equation under theta conditions was found to be proportional to the molar volume of the substituent groups in the case of vinyl‐ and vinylidene‐type hydrocarbon polymers. This simple empirical relation can be used to estimate K _θ for such polymers.     

New biocidal metal complexes of bisphenol-A formaldehyde polymer containing piperazine

The polymeric ligand (BFP) was synthesized by condensation of bisphenol-A, formaldehyde, and piperazine in alkaline medium at 70–80°C. The polymer–metal complexes were synthesized by the reaction of BFP with Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) acetates in 1?:?0.5 (ligand?:?metal) molar ratio. All the synthesized polymers were characterized by elemental, spectral (infrared, ¹H-NMR, and UV-Vis), magnetic moment measurements, and thermal (TGA) analysis. The ligand-field and nephelauxetic parameters have been determined from UV-Vis spectra using ligand-field theory. Elemental analyses indicate the association of water with metal for Mn(II), Co(II), and Ni(II), which is also supported by TGA. The antimicrobial activities of the synthesized polymers were studied by agar well diffusion methods against Bacillus subtilis, Bacillus megaterium, Staphylococcus aureus, Escherichia coli, Salmonella typhi, Pseudomonas aeruginosa, and Shigella boydii. The antimicrobial activity and thermal stability of Cu(II)–polymer were higher than the other polymer–metal complexes due to the higher stability constant of Cu(II).     

A new representation of permittivity versus temperature for alkanols of the same chain length

The alkanols of three carbon length have been studied by dielectric methods during many years and they do not obey any theoretical model. These substances have the same chain length and have one, two or three dipoles per molecule, so their ability to form hydrogen bridges changes from one substance to other, and one can obtain information by comparative studies. In previous works, we have measured the thermal dependence of permittivity of these substances and analysed the results with an empirical modification of the Onsager equation. Now we shall analyse and compare the results using a different representation. In this representation, the data shows straight lines, whose slopes depend on the quantity of dipoles of each molecule encouraging the high quality of the fittings obtained with the three substances, and also that they behave in the same dielectric way with the rise of temperature.