Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Analytical chemistry and the cone penetrometer: In situ chemical characterization of the subsurface

The development of novel microanalytical techniques forin situ chemical characterization of the terrestrial subsurface environment has grown significantly over the last decade, particularly those instruments that are interfaced to the cone penetrometer. Cone penetrometer testing (CPT) has emerged as an effective means to introduce samplers and probes forin situ analysis of contaminants in soil and groundwater matrices. A variety ofin situ chemical samplers for CPT have been developed that can be driven into the subsurface to collect soil gas, groundwater, or soil samples at depth, thus providing a means of determining the vertical and horizontal extent of contamination. Cone penetrometer testing is also being explored as a means to deliverin situ subsurface sensor probes, including probes based on laser-induced fluorescence, Raman, and infrared spectroscopies for organics; on laser-induced breakdown and X-ray fluorescence spectroscopies for heavy metals; and on passive gamma-ray spectroscopy for radionuclides. The range of analytical technologies used in CPT for the determination of organic and inorganic species in the subsurface is described.     

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论     

快点火锥壳靶内爆自发光图像数据处理

为研究快点火预压缩过程中导引锥对压缩靶丸芯部辐射对称性的影响,在神光Ⅲ原型上开展了快点火预压缩的自发光测量实验。采集了相同长度黑腔中不同类型靶丸的内爆自发光图像和不同长度黑腔中同类靶丸的内爆自发光图像,利用最小二乘椭圆拟合方法对芯部的自发光半峰值强度等高线进行椭圆拟合,通过椭圆特征来分析靶丸在最强发光时刻的压缩对称性。分析结果表明：导引锥的存在会使发光区域沿着赤道方向拉长,降低了压缩对称性;有锥靶丸在1600 m黑腔内的形变小于在1500 m和1700 m黑腔内的形变,压缩对称性可以通过调整黑腔长度来控制。     

Conformational properties of propargyloxy-calix[4]arene tricarboxamides: NMR and DFT studies on the O-through-the-annulus rotation

The size limit of substituents allowing O-through-the-annulus rotation of substituted calix[4]arenes was further extended to the propargyloxy group in 24-propargyloxy-25,26,27-tris(N,N-dimethylcarbamoylmethoxy)-p-tert-butylcalix[4]arene by demonstrating its free but slow motion affording equilibrium between the partial cone and 1,2-alternate conformers. The effect of solvent and upper rim substituents R¹ on the conformational inversion was investigated by means of ¹H NMR. The rotational isomerisation of the parent (R¹ = H) analogue could not unambiguously be detected. The experimental results were supported by comprehensive density functional theory studies.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Study on properties of flame‐retardant cyanate esters modified with DOPO and triazine compounds

Ternary flame‐retardant modified cyanate ester blends (CEPG and CEPA) are formed by combining triazine compounds (TGIC or TAIC) and 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide with cyanate ester resin. The curing behaviors, thermal and mechanical properties, and the flame‐retardant properties are investigated. The results show that the CEPG and CEPA blends result in lower curing temperatures and glass transition temperatures than those of neat CE. Both of CEPG and CEPA blends significantly improve the flame‐retardant properties of CE resins, and UL‐94V‐0 rate is achieved for CEPG‐1.0 and CEPA‐0.5. The dielectric constant and loss of CEPA blends are lower than those of CEPG blend with the same phosphors content, and both of them are lower than those of neat CE. Therefore, the ternary flame‐retardant modified cyanate ester blends provide 2 ways for composites of producing printed circuit board with high flame‐retardant property and low dielectric constant and loss.     

Density functional study of α-graphyne derivatives: Energetic stability,atomic and electronic structure

The energetic stability, atomic and electronic structures of α-graphyne and its derivatives (α-GYs) with extended carbon chains were investigated by density functional (DF) calculations in this work. The studied α-GYs consist of hexagon carbon rings sharing their edges with carbon atoms N=1–10. The structure and energy analyses show that α-GYs with even-numbered carbon chains have alternating single and triple C–C bonds (polyyne), energetically more stable than those with odd-numbered carbon chains possessing continuous double C–C bonds (polycumulene). The calculated electronic structures indicate that α-GYs can be either metallic (odd N) or semiconductive (even N) depending on the parity of number of atoms on hexagon edges despite the edge length. The semiconducting α-graphyne derivatives are found to possess Dirac cones (DC) with small direct band gaps 2–40 meV and large electron velocities 0.554×10⁶–0.671×10⁶ m/s, 70–80% of that of graphene. Our DF studies suggest that introducing sp carbon atoms into the hexagon edges of graphene opens up an avenue to switch between metallic and DC electronic structures via tuning the parity of the number of hexagon edge atoms.