Asymptotic expansions and fast computation of oscillatory Hilbert transforms

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$\begin{aligned} H^{+}(f(t)e^{i\omega t})(x)=-\!\!\!\!\!\!\int \nolimits _{\!\!\!0}^{\infty }e^{i\omega t}\frac{f(t)}{t-x}\,dt,\quad \omega >0,\quad x\ge 0, \end{aligned}$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$ , the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of $\omega $ are derived for each fixed $x\ge 0$ , which clarify the large $\omega $ behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of $x$ , we classify our discussion into three regimes, namely, $x=\mathcal O (1)$ or $x\gg 1$ , $0<x\ll 1$ and $x=0$ . Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency $\omega $ increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.     

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

决策依赖不确定条件下基于复合实物期权估值的工程系统投资决策研究

不确定性是复杂工程系统的内在属性,在决策依赖不确定条件下对工程系统的投资决策需考虑不确定性与决策过程之间的交互作用,使得投资决策问题的求解非常困难.提出了决策依赖不确定条件下复合实物期权估值的最小二乘模拟算法,方法较好地解决了在决策依赖不确定条件下由于不同期权价值相互耦合所带来的计算复杂性,进一步拓展了最小二乘模拟算法在期权估值中的应用,基于该方法,可以比较方便地解决决策依赖不确定条件下工程系统投资决策问题.     

A high-pressure study of PbCO3 by XRD and Raman spectroscopy

The pressure-induced phase transitions of PbCO3 are studied using synchrotron radiation in a diamond anvil cell at room temperature. The XRD measurement indicates that PbCO3 with an initial phase of aragonite-type structure undergoes two phase transitions at ～7.8GPa and ～15.7GPa respectively. The higher-pressure phase appearing at ～ 15.7GPa is stable up to 51.8GPa. The two phase transitions are further confirmed by Raman scattering up to 23.3GPa. During the decompression process, the high-pressure phases of PbCO3 are gradually recovered to the starting aragonite-type structure, but exhibit some hysteresis. The bulk modulus B0 of the aragonite-type structure is obtained to be 63±(3) GPa by fitting the volume-pressure data to the Birch-Murnaghan equation of states with B0 fixed to 4.     

A statistical thermodynamic model for oxygen segregation during Czochralski growth of silicon single crystals

A thermodynamic model derived from atomic scale statistics is formulated for the crystal–melt interface where oxygen segregation occurs during silicon crystal growth by the Czochralski method. The model shows that the segregation coefficient is close to but less than unity. Approaches for controlling oxygen concentration in the resulted crystal are discussed.     

Zeolite micro fuel cell

Microfabricated HZSM-5 micromembranes were successfully employed as a proton-exchange membrane in a micro fuel cell and the energy generation is strongly dependent on the Al-content of the HZSM-5.     

Sensitive chemiluminescence method for the determination of glutathione, l-cysteine and 6-mercaptopurine

Glutathione (GSH), l-cysteine (l-Cys) and 6-mercaptopurine (6-MP) inhibit the CL reaction of luminol–H₂O₂ catalyzed by gold colloids. In order to explore this, GSH, l-Cys and 6-MP were injected into the chemiluminescence system of luminol and H₂O₂ catalyzed by gold colloids. The results showed that gold colloids interact with GSH, l-Cys and 6-MP and decrease the CL emission. Based on this phenomenon, a simple, sensitive and convenient flow injection CL method was developed for the determination of GSH, l-Cys and 6-MP. This method provides a novel, and effective CL assay for GSH, l-Cys and 6-MP that has been applied to the determination of GSH in human serum.     

Synergistic Porosity and Charge Effects in a Supramolecular Porphyrin Cage Promote Efficient Photocatalytic CO2 Reduction**

We present a supramolecular approach to catalyzing photochemical CO₂ reduction through second-sphere porosity and charge effects. An iron porphyrin box ( PB ) bearing 24 cationic groups, FePB-2(P) , was made via post-synthetic modification of an alkyne-functionalized supramolecular synthon. FePB-2(P) promotes the photochemical CO₂ reduction reaction (CO₂RR) with 97 % selectivity for CO product, achieving turnover numbers (TON) exceeding 7000 and initial turnover frequencies (TOF_max) reaching 1400 min⁻¹. The cooperativity between porosity and charge results in a 41-fold increase in activity relative to the parent Fe tetraphenylporphyrin ( FeTPP ) catalyst, which is far greater than analogs that augment catalysis through porosity ( FePB-3(N ), 4-fold increase) or charge (Fe p-tetramethylanilinium porphyrin ( Fe-p-TMA ), 6-fold increase) alone. This work establishes that synergistic pendants in the secondary coordination sphere can be leveraged as a design element to augment catalysis at primary active sites within confined spaces.