“蜡烛火焰划分”实验的局限成因分析及改进研究

人教版初中化学首个探究性实验"蜡烛及其燃烧"明确指出火焰的划分方法，但在实际教学中肉眼观察法和火柴梗燃烧法对蜡烛火焰的划分存在一定的局限性。采用文献研究法和实验验证法分析其局限性的成因——燃料的析炭能力强弱、材料结构的不同等，并提出相应的改进建议。     

Synthesis and Properties of Polycarbosilanes Having Lactose‐Derived Structures

A polycarbosilane having lactose‐derived structures was synthesized, and its thermal property, cytotoxicity, chemical crosslinking, and protein adsorption properties were investigated. The polycarbosilane (PSB‐Lac) was prepared by a thiol‐ene reaction between precursor poly(1‐(3‐butenyl)‐1‐methylsilacyclubane) (PSB) and heptaacetyl lactose that carried a thiol group at the anomeric position, and the successive deprotection of the acetyl groups. The lactose introduction efficiency determined by ¹H NMR measurement was 75%. TGA and DSC revealed that the polymer had a 5 wt% decomposition temperature of 260 °C and glass transition temperature (T_g) of 84 °C, which indicated that PSB‐Lac was a thermally stable polymer. PSB‐Lac had no significant cytotoxicity, which was evaluated by human liver cancer cell line HepG2 cultivation on the polystyrene dishes coated with the polymer. Urethane‐crosslinked PSB‐Lac films were prepared by casting solutions of PSB‐Lac and hexamethylene diisocyanate and heating at 120 °C after evaporation of the solvent. The crosslinked PSB‐Lac showed higher adsorption of bovine serum albumin than the similarly crosslinked polycarbosilane that had a glucose structure (PSB‐Glc). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2420–2425     

The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Regular characters of classical groups over complete discrete valuation rings

Let $\mathfrak{o}$ be a complete discrete valuation ring with finite residue field $\mathsf{k}$ of odd characteristic, and let G be a symplectic or special orthogonal group scheme over $\mathfrak{o}$. For any $?\in \mathbb{N}$ let $G^{?}$ denote the ?-th principal congruence subgroup of $\mathbf{G}(\mathfrak{o})$. An irreducible character of the group $\mathbf{G}(\mathfrak{o})$ is said to be regular if it is trivial on a subgroup $G^{?+1}$ for some ?, and if its restriction to $G^{?}/G^{?+1}?\mathrm{Lie}(\mathbf{G})(\mathsf{k})$ consists of characters of minimal $\mathbf{G}({\mathsf{k}}^{\mathrm{alg}})$-stabilizer dimension. In the present paper we consider the regular characters of such classical groups over $\mathfrak{o}$, and construct and enumerate all regular characters of $\mathbf{G}(\mathfrak{o})$, when the characteristic of $\mathsf{k}$ is greater than two. As a result, we compute the regular part of their representation zeta function.     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.