推广的Volterra方程的极限环问题

在生物数学中,基本研究对象之一是系统 其中,b>0,c>0,d>0,a(x)为x的至少二阶可微函数。 系统(1)是描述捕食者——食饵相互作用的一种近似数学模型,是对Lotka—Volterra数学模型的推广。这里,x是指食饵种群的密度,y是指捕食者种群的密度,函数a(x)则描述了食饵种群在脱离捕食者情况下的增殖过程。     

EFFECTS OF FREE-STREAM VELOCITY ON TURBULENT NATURAL-CONVECTION FLOW ALONG A VERTICAL PLATE

A detailed measurement of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection adjacent to an isothermal vertical flat plate are reported. A cold-wire anemometer and laser Doppler velocimeter were used, respectively, to measure simultaneously the time-mean turbulent temperature and velocity distributions and their turbulent fluctuations. In this experimental study, measurements of the flow and thermal fields were carried out at one streamwise location, x     

Superconductivity in ordered LiBe alloy under high pressure: A first-principles study

The electronic, vibrational, and superconducting properties of LiBe alloy in the P2₁/m structure under pressure have been investigated using first-principles calculations. The calculated electron–phonon coupling (EPC) of LiBe with both linear response theory and the rigid muffin-tin approximation suggested that pairing electrons are mainly mediated by the Li low-lying phonon vibrations, and the increase of the Li EPC matrix element $〈I_i^2〉$ with pressure is responsible for the increased EPC parameter $\lambda$. The application of the Allen–Dynes modified McMillan equation reveals high superconducting critical temperatures of 15.2 K at 80 GPa and 18.4 K at 100 GPa for P2₁/m LiBe.     

The negative electromagnetic attractive forces arising from kinetic energy of conduction electrons in double-layer metallic nanowire arrays

The coupled-nanowire plasmatic resonances and very strong negative electromagnetic force between the double-layer metallic nanowire arrays is investigated theoretically. The negative electromagnetic force indicates attractive interaction between the metallic nanowires with the air-gap cavity local resonance effect. Plasmon resonances lead to extremely large localized ?eld, thereby resulting in large mutual coupling forces between the double-layer metallic nanowire arrays. The light coupling into metallic microcavity can stimulate collective electron oscillations of plasmatic resonance, and cause the contraction of the negative pressure in metallic cavity wall. The electromagnetic field of the plasmatic resonance mode is mainly localized inside the air-gap region between the two wires.     

Monochromatic soft X-ray-induced reactions of CCl2F2 adsorbed on Si(111)-7 × 7 near the Si(2p) edge

Continuous-time photoelectron spectroscopy (PES) and continuous-time core-level photon-stimulated desorption (PSD) spectroscopy were used to study the monochromatic soft X-ray-induced reactions of CCl₂F₂ molecules adsorbed on Si(111)-7 × 7 at 30 K (CCl₂F₂ dose = 2.0 × 10¹⁴ molecules/cm², ~ 0.75 monolayer) near the Si(2p) core level. Evolution of adsorbed CCl₂F₂ molecules was monitored by using continuous-time photoelectron spectroscopy at two photon energies of 98 and 120 eV to deduce the photolysis cross section as a function of energy. It was found that the photolysis cross sections for 98 and 120 eV photons are _~1.4 × 10^? 18 and ~ 8.0 × 10^? 18 cm², respectively. Sequential F⁺ PSD spectra obtained by using continuous-time core-level photon-stimulated desorption spectroscopy in the photon energy range of 98–110 eV show the variation of their shapes with photon exposure and depict the formation of surface SiF species. The dissociation of CCl₂F₂ molecules adsorbed on Si(111)-7 × 7, irradiated by monochromatic soft X-ray in the photon energy range of 98–110 eV, is mainly due to dissociative electron attachment and indirect dipolar dissociation induced by photoelectrons emitted from the silicon surface.     

Effect of Eu3+ concentration on microstructure and photoluminescence of Sr2SiO4:Eu3+ phosphors prepared by microwave assisted sintering

In this paper, effect of Eu³⁺ doping concentrations on microstructure and photoluminescence of Sr₂SiO₄ phosphors was investigated. The Sr_2?xSiO₄:xEu³⁺ phosphors with x=0.05, 0.1, 0.2, 0.3 were synthesized by microwave assisted sintering at 1200 °C for 60 min in air. X-ray powder diffraction analysis confirmed the formation of pure Sr₂SiO₄ phase without second phase or phases of starting materials irrespective of the adding amount of Eu³⁺. From scanning electron microscopy image, it is found that with more Eu³⁺ ions introduced to Sr₂SiO₄, the shape of the particles is not much different from each other, but the particle size decreases significantly from 1 to 2 μm (when x=0.05) to less than 500 nm (when x=0.3). The emission spectrum was located obviously at 617 nm as the excitation spectrum at λ_ex=395 nm, and it had best emission intensity when x=0.1.     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

Large-scale synthesis and growth habit of 3-D flower-like crystal of PbTe

In this paper, 3-D flower-like crystal of PbTe was successfully synthesized using Pb(CH₃COO)₂·3H₂O and Na₂TeO₃ as precursors under hydrothermal conditions, and characterized by means of scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction pattern (XRD). The reaction parameters that influenced the evolution of PbTe synthesis and morphology were investigated. It was shown that the flower-like crystal of PbTe was composed of a nucleus with eight pods. A possible growth mechanism was proposed based on the calculation of the surface energies of PbTe and the SEM observation. Furthermore, the temperature-dependent transport properties of 3-D flower-like crystal of PbTe specimen have been evaluated with an average thermoelectric power of 120 S cm^?1 and electrical conductivity of 220 μV K^?1 at 740 K.     

Hydrostatic pressure sensor based on a gold-coated thin-core fiber modal interferometer and ripple shift measurement

We propose a hydrostatic pressure sensor based on a gold-coated thin-core fiber modal interferometer (TCFMI). A thin-core fiber is spliced to a single mode fiber forming a single-end fiber modal interferometer (FMI) due to the core mismatch and the fiber end reflection. Relative reflection spectra of TCFMIs based on thin-core fibers with different lengths are investigated. The TCFMI is gold-coated to enhance the optical reflectivity, which also results in the ripple of the relative reflection spectra of TCFMI. A high hydrostatic pressure sensor test system is proposed and the performance of the pressure sensor has been experimentally investigated. A pure-ripple-shift measurement method is used to achieve the demodulation of the sensor. The proposed pressure sensor has a sensing range up to 40 MPa and a sensitivity of 44.8 pm/MPa.     

Effect of SnI2 on the thermal and optical properties of Ge–Se–Te glasses

A systematic series of (Ge₂₀Se₁₅Te₆₅)_1?x–(SnI₂)_x (x = 0, 0.05, 0.1, 0.15) chalcogenide glasses have been prepared. The amorphous nature can be confirmed by XRD and SEM. With the SnI₂ content increasing, the indirect optical band gaps are decreased from 0.662 to 0.622 eV according to Tauc laws. The introduction of SnI₂ makes the glasses much easier to prepare and more stable against crystallization, making them drawable as optical fibers. The highest ΔT (130 °C) value for (Ge₂₀Se₁₅Te₆₅)_0.9–(SnI₂)_0.1 glass composition can be obtained. A slight red-shifting of the long-wavelength cutting-off edge from 18.4 to 19.4 μm was shown and it seems that SnI₂ in these glasses offers the improvement in the far-infrared properties.