Comparative DFT study of Raman spectra of phosphorus-containing dendrimers built from thiophosphoryl,cyclotriphosphazene and phthalocyanine cores

The FT Raman spectra of the zero and first generations of phosphorus-containing dendrimers built from thiophosphoryl, cyclotriphosphazene and phthalocyanine core with terminal oxybenzaldehyde groups have been recorded and analyzed. The structural optimization and normal mode analysis were performed for dendrimers on the basis of the density functional theory (DFT). The calculated geometrical parameters, harmonic vibrational frequencies and Raman scattering activities are predicted in a good agreement with the experimental data. The experimental Raman spectra of dendrimers were interpreted by means of potential energy distribution. Relying on DFT calculations the lines of the cores, repeating units and terminal groups of dendrimers were assigned.The influence of the encirclement on the line frequencies and intensities was studied and due to the predictable, controlled and reproducible structure of dendrimers the information, usually inaccessible is obtained. The strong line at 1600 cm⁻¹ show marked changes of intensity in dependence of aldehyde (CHO) or azomethyne (CHN) substituents in the aromatic ring. The polarizabilities and lipophilicity of dendrimers were estimated.     

Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.     

Addendum to: “Hamilton-laceable bi-powers of locally finite bipartite graphs” [Discrete Math. 345 (2022) 112777]

In this addendum we give a short and easy negative answer to the two questions raised in the original article.     

An eigen-based high-order expansion basis for structured spectral elements

We present an eigen-based high-order expansion basis for the spectral element approach with structured elements. The new basis exhibits a numerical efficiency significantly superior, in terms of the conditioning of coefficient matrices and the number of iterations to convergence for the conjugate gradient solver, to the commonly-used Jacobi polynomial-based expansion basis. This basis results in extremely sparse mass matrices, and it is very amenable to the diagonal preconditioning. Ample numerical experiments demonstrate that with the new basis and a simple diagonal preconditioner the number of conjugate gradient iterations to convergence has essentially no dependence or only a very weak dependence on the element order. The expansion bases are constructed by a tensor product of a set of special one-dimensional (1D) basis functions. The 1D interior modes are constructed such that the interior mass and stiffness matrices are simultaneously diagonal and have identical condition numbers. The 1D vertex modes are constructed to be orthogonal to all the interior modes. The performance of the new basis has been investigated and compared with other expansion bases.     

OBE理念推动化工设备机械基础课程的改革实践*

以应用型人才培养为目标,探索了利用OBE理念推动化工设备机械基础课程及其课程设计的改革实践。以OBE理念为指导,结合CDIO和LBL的教学模式,提出在教学内容、平台在线课程建设、第二课堂教学、课程设计和考核方法等方面的改革方案,增强了课程的应用性和成果产出,不仅提高了学生对理论知识掌握的牢固度,更提高了学生的实践能力、对知识的灵活应用能力和创新能力,与实际应用连接更加紧密,有效地实现了高素质的应用型人才输出。     

VIBRATIONAL SPECTRA AND NORMAL COORDINATE ANALYSIS OF 1,2-BIS(2-FORMYLGLYCINEBENZENESULFENYL) ETHANE Pd(II) DICHLORIDE COMPLEX

The normal coordinate analysis of the title complex, 1,2-bis(2-formylglycinebenzenesulfenyl) ethane Pd(II) dichloride has been carried out by using the Urey-Bradley force field. According to the molecular structure determined by x-ray crystallographic analysis, 182 internal coordinates were established and 112 theoretical vibration frequencies agree well with the observed values with the average difference of 2.53 cm^?1 and the maximum deviation of 16.0 cm^?1.     

Quantitative study of the temperature dependence of normal LWIR apparent emissivity

In a previous work, a method of measurement of apparent emissivity in situ was implemented. This approach has the decisive advantage of being suitable for any commercial infrared systems. It was tested successfully to characterize the normal LWIR apparent emissivity of an aluminium nitride plate in the temperature range [40–550 °C]. Apparent emissivity exhibits a tight temperature dependence. By using the classical model of apparent emissivity and taking into account the spectral emissivity of aluminium nitride ceramic and the spectral response of the IR sensor, we modelled our apparent emissivity measurement with 5% of accuracy and with dispersion better than 1% within the overall temperature range. The effect on the apparent emissivity of both the detection window and the temperature dependence of the spectral emissivity are highlighted.     

Evolutionary Pareto distributions

We consider here i.i.d. variables which are distributed according to a Pareto up to some point x₁ and a Pareto (with a different parameter) after this point. This model constitutes an approximation for estimating extreme tail probabilities, especially for financial or insurance data. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limits of experiments. Especially, the rates of convergence and the limiting law obtained here are the same as in a change point framework. Simulations are giving an illustration of the quality of the procedure.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where