Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Arithmetic properties of overpartition triples

Let p_3(n) be the number of overpartition triples of n. By elementary series manipulations,we establish some congruences for p_3(n) modulo small powers of 2, such as p_3(16 n + 14) ≡ 0(mod 32), p_3(8 n + 7) ≡ 0(mod 64).We also find many arithmetic properties for p_3(n) modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers α≥ 1 and n ≥ 0, we have p_3 (3~(2α+1)(3n + 2))≡ 0(mod 9 · 2~4), p_3(4~(α-1)(56 n + 49)) ≡ 0(mod 7),p_3 (7~(2α+1)(7 n + 3))≡ p_3 (7~(2α+1)(7 n + 5))≡ p_3 (7~(2α+1)(7 n + 6))≡ 0(mod 7),and for r ∈ {1, 2, 3, 4, 5, 6},p_3(11 · 7~(4α-1)(7 n + r)≡ 0(mod 11).     

待定系数法在三角函数积分计算中的应用

运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用.     

|sinx|原函数的直接计算法

利用变限积分函数和周期函数的性质,给出了求|sinx|原函数的一种直接计算法.     

复微分-差分方程组的超越整函数解

利用亚纯函数的Nevanlinna值分布理论, 我们主要研究了一类复微分-差分方程和一类复微分-差分方程组的有限级超越整函数解的存在形式, 得到两个有趣的结论. 将复微分(差分)方程的一些结论推广到复微分-差分方程(组)中.     

Homochiral organic molecular cage RCC3-R-modified silica as a new multimodal and multifunctional stationary phase for high-performance liquid chromatography

In this work, homochiral reduced imine cage was covalently bonded to the surface of the silica to prepare a novel high-performance liquid chromatography stationary phase, which was applied for the multiple separation modes such as normal phase, reversed-phase, ion exchange, and hydrophilic interaction chromatography. The successful preparation of the homochiral reduced imine cage bonded silica stationary phase was confirmed by performing a series of methods including X-ray photoelectron spectroscopy, thermogravimetric analysis, and infrared spectroscopy. From the extracted results of the chiral resolution in normal phase and reversed-phase modes, it was demonstrated that seven chiral compounds were successfully separated, among which the resolution of 1-phenylethanol reached the value of 3.97. Moreover, the multifunctional chromatographic performance of the new molecular cage stationary phase was systematically investigated in the modes of reversed-phase, ion exchange, and hydrophilic interaction chromatography for the separation and analysis of a total of 59 compounds in eight classes. This work demonstrated that the homochiral reduced imine cage not only achieved multiseparation modes and multiseparation functions performance with high stability, but also expanded the application of the organic molecular cage in the field of liquid chromatography.     

LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

Synthesis and Assessment of Two Malonyl Dihydrazide Derivatives as Corrosion Inhibitors for Carbon Steel in Acidic Media: Experimental and Theoretical Studies

Despite the extensive use of carbon steel in all industrial sectors, particularly in the petroleum industry, its low corrosion resistance is an ongoing problem for these industries. In the current work, two malonyl dihydrazide derivatives, namely 2,2’-malonylbis (N-phenylhydrazine-1-carbothiamide (MBC) and N’1, N’3-bis(-2-hydroxybenzylidene) malonohydrazide (HBM), were examined as inhibitors for the carbon steel corrosion in 1.0 M HCl. Both MBC and HBM were characterised using thin-layer chromatography, elemental analysis, infrared spectroscopy, and nuclear magnetic resonance techniques. The corrosion tests were performed using mass loss measurements, polarisation curves, and electrochemical impedance spectroscopy. It is obtained from the mass loss studies that the optimal concentration for both inhibitors is 2.0 × 10⁻⁵ mol/L, and the inhibition efficiencies reached up to 90.7% and 84.5% for MBC and HBM, respectively. Electrochemical impedance spectroscopy (EIS) and potentiodynamic polarisation (PDP) indicate an increased impedance in the presence of both MBC and HBM and mixed-type inhibitors, respectively. Both inhibitors can mitigate corrosion in the range of 298–328 K. Values of free energy changes obtained from the Langmuir model suggest that the inhibitors suppress the corrosion process principally by chemisorption. The computational investigations were conducted to identify the factors connected with the anti-corrosive properties of the examined inhibitors.     

Dynamic polarizability of two‐electron ions under Debye screening

The effect of plasma screening on the dynamic dipole polarizability (DPP) of two‐electron ions Be²⁺, B³⁺, and C⁴⁺ has been investigated using highly correlated exponential wave functions within the framework of pseudostate summation technique and Debye screening concept. Plasma‐screening effect on the oscillator strengths (OS) of the ultraviolet and visible series has also been investigated for the systems Li⁺, Be²⁺, B³⁺, C⁴⁺. The DPP are reported as functions of screening parameters. The OS for S‐P transitions are also reported for various screening parameters. The OS and dynamic polarizability show interesting behavior with increasing screening strength and nuclear charge. © 2015 Wiley Periodicals, Inc.