A note on strong embeddings of maximal planar graphs on non-orientable sufraces

Abstract. In this paper, it is shown that for every maximal planar graph     

Measurements of the(p,ρ,T) relation of methane and carbon dioxide in the temperature range 240 K to 520 K at pressures up to 30 MPa using a new accurate single-sinker densimeter

Comprehensive (p, ρ, T) measurements on pure methane (159 values) and pure carbon dioxide (118 values) have been carried out in the temperature range 240 K to 520 K at pressures up to 30 MPa. The measurements were performed by means of a single-sinker densimeter that is based on Archimedes’ buoyancy principle. The total relative uncertainty of the measurements in the density ρ was estimated to be⩽ |(1.5 to 2) · 10 ^− 4·ρ | for methane and⩽ |(2 to 3) · 10 ^− 4·ρ | for carbon dioxide. The measurements are compared with previous results of other experimentalists and with values calculated from current equations of state. Moreover, previously unpublished results of (p, ρ, T) measurements on carbon dioxide (29 values) and methane (53 values) are listed in the appendix.     

二{氧合-二[3-二茂铁基丙烯酸二正丁基锡(Ⅳ)]} 配合物的晶体结构及溶液中的 配位互变平衡机理

测定了配合物{[(n-Bu)2Sn(FcCH=CHCO2)]2O}2(Fc=Ferrocenyl)晶体结构,它属三斜晶系,空间群P1,晶胞参数a=1.3943(3)nm,b=1.4635(3)m,c=1.2792(3)nm,α=94.32(3)°,β=116.27(3)°,γ=109.08(3)°,Z=2,V=2.1362(8)nm^3,Dc=1.542g/cm^3,F(000)=1004。最终偏差因子R=0.0401,Rw=0.1076。该分子中存在着内环锡和外环锡配位单元,锡原子均形成具有假六配位的单加帽畸变三角双锥配位构型。Sn2O2中心内环与丙烯酸酯基茂环等共轭体系之间相互未能共平面。配合物中四个羧基配体划分为两类：两个为桥式双齿配位(μ-COO),跨接于一个内环锡和一个外环锡;另两个仅以单齿配位方式各连接一个外环锡。根据核磁共振谱信息表明分子在溶液中存在着配位互变异构体之间的快交换。我们提出振动模式的假说,认为可能是羧酸酯基氧在其平面内快速摇摆建立了动态平衡之故。     

甲烷-空气-H2O模拟光化学反应体系中CH3OO·自身复合反 应的研究

在1.013×10^5Pa,(298±2)K及O2-N2气氛下,研究了羟基自由基·OH引发的甲烷光化学反应体系中过氧甲基自由基CH3OO·自身复合反应。反应物和产物采用长光路Fourier红外光谱(LP-FTIR)和高效液相色谱(HPLC)测定。证实产物中有甲基过氧化氢(CH3OOH,MHP)和过氧甲醚(CH3OOCH3,DMP)存在并首次在该体系中发现了羟甲基过氧化氢(HOCH2OOH,HMHP).HMHP的检出表明,CH3OO·自身复合的可能途径之一生成了Criegee中间体过氧次甲基双自由基·CH2OO·,采用G2,G2(MP2)和G2(ful)方法对一些反应的标准焓变和标准Gibbs自由能变化进行了理论计算。结果表明CH3OO·自身复合生成·CH2OO·及·CH2OO·与H2O反应生成HMHP的途径在热力学上是可能的。     

Large metric perturbations from rescattering

We study numerically evolution of metric perturbations during reheating in a model with two fields and a strong parametric resonance. Our calculation is fully nonlinear and includes gravity but is restricted to spherical symmetry. In this model, super-Hubble metric perturbations can grow during reheating only due to effects nonlinear in fluctuations of the fields. We find that they indeed grow and, soon after the growth begins, dominate variances of the metric functions. Thus, the metric functions become smooth but varying significantly over large scales. Their profiles at late times are interpreted as signaling a gravitational instability and formation of a black hole.     

Propagation characteristics of thermoelastic waves in piezoelectric (6 mm class) rotating plate

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.     

Rh(Ⅱ)-卡宾分子内C－H键插入反应研究进展

综述了Rh(Ⅱ)-卡宾分子内C－H键插入反应的研究进展。     

Analysis of the relationship between neutron dose and Cerenkov photons under neutron irradiation through Monte Carlo method

To theoretically explore the feasibility of neutron dose characterized by Cerenkov photons, the relationship between Cerenkov photons and neutron dose in a water phantom was quantified using the Monte Carlo toolkit Geant4. Results showed that the ratio of the neutron dose deposited by secondary electrons above Cerenkov threshold energy to the total neutron dose is approximately a constant for monoenergetic neutrons from 0.01 eV to 100 eV. With the initial neutron beam energy from 0.01 eV to 100 eV, the number of Cerenkov photons has a good correlation with the total neutron dose along the central axis of the water phantom. The changes of neutron energy spectrum and mechanism analysis also explored at different depths. And the ratio of total neutron dose to the intensity of Cerenkov photons is independent of neutron energy for neutrons from 0.01 eV to 100 eV. These findings indicate that Cerenkov radiation also has potential in the application of neutron dose measurement in some specific fields.     

On energy balance and the structure of radiated waves in kinetics of crystalline defects

Traveling waves, with well-known closed form expressions, in the context of the defects kinetics in crystals are excavated further with respect to their inherent structure of oscillatory components. These are associated with, so called, Frenkel–Kontorova model with a piecewise quadratic substrate potential, corresponding to the symmetric as well as asymmetric energy wells of the substrate, displacive phase transitions in bistable chains, and brittle fracture in triangular lattice strips under mode III conditions. The paper demonstrates that the power expended theorem holds so that the sum of rate of working and the rate of total energy flux into a control strip moving steadily with the defect equals the rate of energy sinking into the defect, in the sense of N.F. Mott. In the conservative case of the Frenkel–Kontorova model with asymmetric energy wells, this leads to an alternative expression for the mobility in terms of the energy flux through radiated lattice waves. An application of the same to the case of martensitic phase boundary and a crack, propagating uniformly in bistable chains and triangular lattice strips, respectively, is also provided and the energy release is expressed in terms of the radiated energy flux directly. The equivalence between the well-known expressions and their alternative is established via an elementary identity, which is stated and proved in the paper as the zero lemma. An intimate connection between the three distinct types of defects is, thus, revealed in the framework of energy balance, via a structural similarity between the corresponding variants of the ‘zero’ lemma containing the information about radiated energy flux. An extension to the dissipative models, in the presence of linear viscous damping, is detailed and analog of the zero lemma is proved. The analysis is relevant to the dynamics of dislocations, brittle cracks, and martensitic phase boundaries, besides possible applications to analogous physical contexts which are marked by macroscopic energy release through emission of waves and possibly linear viscous damping.