Estimates of trigonometric sums by the third derivative

The well-known Van der Corput estimate of a trigonometric sum by the third derivative is sharpened. Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 383–389, September, 1996. This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-00002.     

Deposition behaviors and patterning of TiO2 thin films on different SAMs surfaces from titanium sulfate aqueous solution

Patterning of TiO₂ thin films was successfully obtained on different self-assembled monolayers (SAMs) in aqueous solution by micro-contact printing (μCP) method. The substrates were immersed in an aqueous solution containing titanium sulfate (Ti(SO₄)₂) and hydrogen peroxide for deposition at 80 °C. The growth rates on various surfaces were as follows: sulfonic (–SO₃H) > amino (–NH₂) > methyl (–CH₃) > hydroxyl (–OH). According to the XPS results, SAMs with the terminal groups of –SO₃H and –NH₂ were favorable for the deposition. The TiO₂ film deposited on the SAM with the terminal group of –CH₃ could be easily peeled off. Clearly, TiO₂ patterns were obtained on the prepatterned surfaces of –SO₃H/–CH₃ and –NH₂/–CH₃ SAMs. The deposition mechanism might be relevant to electrostatic interaction, Stern layer, lone pair electrons and Van der Vaals forces. The TiO₂ film was anatase after annealing at 500 °C and comprised particles with an average diameter of ca. 10 nm.     

Van der Waals气体Euler方程的Riemann问题及基本波的相互作用

研究了修正的等熵Van der Waals气体动力学Euler方程Riemann问题及其基本波的相互作用.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符,从而守恒律方程组从混合型转化为双曲型.利用广义特征线分析法,构造性地得到了Riemann问题的解是存在的.进一步,得到了基本波相互作用.     

Lp- and Sp,qrB-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases

We study the local discrepancy of a symmetrized version of the well-known van der Corput sequence and of modified two-dimensional Hammersley point sets in arbitrary base $b$. We give upper bounds on the norm of the local discrepancy in Besov spaces of dominating mixed smoothness $S_{p,q}^{r}B\left({[0,1)}^s\right)$, which will also give us bounds on the $L_p$-discrepancy. Our sequence and point sets will achieve the known optimal order for the $L_p$- and $S_{p,q}^{r}B$-discrepancy. The results in this paper generalize several previous results on $L_p$- and $S_{p,q}^{r}B$-discrepancy estimates and provide a sharp upper bound on the $S_{p,q}^{r}B$-discrepancy of one-dimensional sequences for $r>0$. We will use the $b$-adic Haar function system in the proofs.     

Chaos synchronization of a fractional‐order modified Van der Pol–Duffing system via new linear control,backstepping control and Takagi–Sugeno fuzzy approaches

In this article, based on the stability theory of fractional‐order systems, chaos synchronization is achieved in the fractional‐order modified Van der Pol–Duffing system via a new linear control approach. A fractional backstepping controller is also designed to achieve chaos synchronization in the proposed system. Takagi‐Sugeno fuzzy models‐based are also presented to achieve chaos synchronization in the fractional‐order modified Van der Pol–Duffing system via linear control technique. Numerical simulations are used to verify the effectiveness of the synchronization schemes. © 2015 Wiley Periodicals, Inc. Complexity 21: 116–124, 2016     

Crystal structures,antibacterial, antioxidant and nucleic acid interactions of mononuclear,and tetranuclear palladium(II) complexes containing Schiff base ligands

Two new palladium complexes, [Pd(dpbs)Cl] (1) and [Pd₄(dbbs)₄] (2) (where (dpbs)₂ = o,o′-(N,N′-dipicolinyldene)diazadiphenyl disulfide and (dbbs)₂ = N,N′-(1,1′-dithio-bis(phenylene))-bis(salicylideneimine)), have been synthesized and characterized by analytical and spectral (electronic, IR, ¹H, ¹³C spectroscopy) techniques. The structures of 1 and 2 have been solved by single-crystal X-ray diffraction experiments, which indicate distorted square planar coordination geometries around palladium(II) by O, N, and S donors. The metal chelates have been screened for their antibacterial and antioxidant activities, and compared with their respective ligands. The binding properties of the complexes have been studied by electronic absorption, emission spectroscopy, and viscosity measurements. The competitive fluorescence study with ethidium bromide and the effect of iodide concentration on ?uorescence of the complex-DNA system have been investigated. All these experimental results suggest that palladium complexes strongly bind to DNA, presumably via groove binding. The thermodynamic parameters, enthalpy change (ΔH°), and entropy change (ΔS°) were calculated by the Van’t Hoff equation, suggesting hydrogen bonds play a predominant role in the binding of complexes to DNA.     

关于Van Der Corput不等式双参数推广的改进

梳理了有关Van Der Corput不等式的研究成果与方法,并对Van Der Corput不等式的双参数推广作了进一步改进,建立了更强的推广式,它优于现有的相关结论.     

Thermodynamic models for determination of the solubility of dibenzothiophene in (methanol + acetonitrile) binary solvent mixtures

In this paper, we focused on solubility and solution thermodynamics of dibenzothiophene. By the gravimetric method, the solubility of dibenzothiophene was measured in (methanol + acetonitrile) binary solvent mixtures at temperatures from (278.15 to 333.15) K under atmosphere pressure. The solubility data were fitted using a modified Apelblat equation, a variant of the combined nearly ideal binary solvent/Redich–Kister (CNIBS/R–K) model and Jouyban–Acree model. Computational results showed that the modified Apelblat equation was superior to the other two equations. In addition, the thermodynamic properties of the solution process, including the Gibbs free energy, enthalpy, and entropy, were calculated by the van’t Hoff analysis. The experimental results showed that methanol could be used as effective anti-solvents in the crystallization process.