关于Sylow子群的极大子群的完全条件置换性

群G的子群H称为G中的完全条件置换子群，如果对G的任意子群T，存在元素x∈(H，T），使HT^x=T^xH，利用Sylow子群的极大子群的完全条件置换性得出了下列结果：①G可解且G的每个Sylow子群的极大子群在G中完全条件置换，则G超可解；②设F是包含超可解群系U的饱和群系，N是群G的可解的正规子群且G／N∈F，如果N的每个Sylow子群的极大子群在G中完全条件置换，则G∈F。     

极小子群的完全条件置换性对有限群结构的影响

群G的子群H称为G中完全条件置换子群，如果对G的任意子群丁，存在元素x∈(H，T)，使HT^x=T^xH．利用极小子群的完全条件置换性给出了超可解群的一个充分条件：设G是一个群，如果G的每个极小子群和每个4阶循环子群都是G的完全条件置换子群，则G是一个超可解群．     

有限群为超可解群的充分条件

关于有限群超可解性的研究已有许多结果，本文利用子群的半正规性及商群的超可解性又得到了有限群为超可解群的一些充分条件。     

s-条件置换子群与有限群的超可解性

有限群G的子群H称为G的s-条件置换子群,如果对G的任意Sylow子群P,存在G的某个元素z,使得HPz=PzH.本文利用s-条件置换子群的概念研究了有限群的某些素数幂阶子群,得到了超可解群的一些充分条件.     

有限群的p-超可解性的一些充分条件

有限群G的子群H称为G的条件置换子群,如果对于G的任意子群K,存在G的某个元素x,使得HKx=KxH.本文利用条件置换子群的概念研究了有限群的某些特殊子群的极大子群,得到了p-超可解群的一些充分条件.     

具有c1-可补子群的有限群结构分析

子群H在群G中被称为是c1-可补的(c1-supplemented),如果存在G的子群K使得G=HK且H∩T≤Z∞(G),其中Z∞(G)是G的超中心.本文研究素数幂阶子群的广义可补性对有限群结构的的影响,得到以下主要定理:对于G的任意Sylow p-子群P,如果P有子群D满足1<|D|<|P|且P每一个|D|阶及p|D|阶子群在G中均c1-可补,那么G超可解.该结果推广了一些已知的结果.     

X-可换子群与有限群的超可解性

利用X-可换子群的概念,得到了有限群超可解的2个充分条件：（1）设G是可解群,石是G的子集且包含G的极小子群和极大子群。如果G的每个极大子群和G的sylow子群的每个极大子群在G中X-可换,那么G是超可解群;（2）设足签,X是G的子集且包含G的p-子群。如果每个不包含K的G的极大子群在G中X-可换,那么K是超可解群。     

完全条件置换子群与有限群的超可解性

利用完全条件置换子群的概念研究了有限群的极小子群和4阶循环子群,得到了超可解群的一些充分条件。     

完全C-置换子群

群G的一个子群H称在G中完全条件置换（或完全C-置换）．如果对群G的任意子群K,存在x∈〈H,K〉,满足HK^x=K^xH．利用子群的完全C-置换性给出了群为P-幂零群及超可解群的一些特征．     

有限群可解性的正规指数刻画

有限群G的极大子群M的正规指数是指G的主因子H/K的阶，其中H为M在G中的极小正规补．文中利用正规指数的概念刻画有限群的可解性，给出了有限群可解的几个充分条件．     

关于Lucas数立方与二项式数的卷积公式

对于非负整数l,L_l表示第l个Lucas数;$\left( {array}{l}n\\i{array} \right) = \frac{{n!}}{{i!\left( {n - i} \right)!}}$为二项式系数;对于非负整数l和k以及正整数n,设l(k, 3, n)是数列$\left\{ {\left( {array}{l}n\\i{array} \right)} \right\}_{i = 0}^n$和$\left\{ {L_{k + i}^3} \right\}_{i = 0}^n$的卷积,即l(k, 3, n)=$\left( {array}{l}n\\0{array} \right)L_k^3 + \left( {array}{l}n\\1{array} \right)L_{k + 1}^3 + \cdots + \left( {array}{l}n\\n{array} \right)L_{k + n}^3 = \sum\limits_{i = 0}^n {\left( {array}{l}n\\i{array} \right)L_{k + i}^3} $。文章证明了k≥n时,l(k, 3, n)=2nL_3k+2n+3(－1)k+nL_k－n; 当k < n时,l(k, 3, n)=2nL_3k+2n+3L_n－k成立。     

一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析

研究了一个具有Robin自由边界的双曲肿瘤生长数学模型,该模型包含了一个描述营养物浓度变化的椭圆型方程,一个描述肿瘤半径的常微分方程和描述肿瘤细胞生长的两个双曲型偏微分方程.本文通过特征线方法结合Banach不动点定理证明了该模型整体解的存在性和唯一性.最后证明当KR=0时,有(limt→∞)R(t)=∞.     

广义Fibonacci数列和Lucsa数列的关系式

根据广义的Fibonacci数列{u_n}:u_n+1=Au_n+Bu_n-1和广义Lucas数列{v_n}:v_n+1=Av_n+Bv_n-1的定义, 采用初等方法证明了广义的Fibonacci数列和Lucas数列的几个新的关系式$\sum\limits_{i = 0}^n {{u_i}{v_{n - i}} = \left( {n + 1} \right){u_n}} $、 ${2^{n + 1}}{u_{n + 1}}=\sum\limits_{i = 0}^n {{2^i}{v_i}{A^{n - i}}}$、 $\sum\limits_{i = 0}^n {{{\left( { - B} \right)}^i}{v_{n - 2i}} = 2{u_{n + 1}}} $、 ${3^{n + 1}}{u_{n + 1}} = \sum\limits_{i = 0}^n {{3^i}{v_i}{A^{n - i}}} + \sum\limits_{i = 0}^{n + 1} {{3^{i - 1}}{u_i}{A^{n + 1 - i}}} $、 $\sum\limits_{i = 0}^n {{v_i}{v_{n - i}} = \left( {n + 1} \right){v_n}} + 2{u_{n + 1}} = \left( {n + 2} \right){v_n} + A{u_n}$、 $\left( {{A^2} + 4B} \right)\sum\limits_{i = 0}^n {{u_i}{u_{n - i}}} = \left( {n + 1} \right){v_n} - 2{u_{n + 1}} = n{v_n} - A{u_n} $, 将Fibonacci数列和Lucsa数列关系的结论进行了推广。     

加权复合算子从Bloch型空间到圆盘代数的拓扑结构

设A为圆盘代数,u和φ是A上的解析函数,刻画了加权复合算子uCφ从Bloch型空间到圆盘代数的一些范数估计.同时还研究了加权复合算子空间的道路连通性,得知任意2个有界加权复合算子是道路连通的.     

形式幂级数环的表现维数

在阿贝尔范畴中引入了表现维数的概念,并讨论了短正合列中对象间表现维数的关系.进一步地,令R_ab（$\\mathscr{A}$,$\\mathscr{B}$, $\\mathscr{C}$）为阿贝尔范畴粘合,证明了在一定条件下,阿贝尔范畴$\\mathscr{B}$的表现维数有限,当且仅当阿贝尔范畴$\\mathscr{A}$与$\\mathscr{C}$的表现维数有限.

     

A numerical study of counterflow diffusion flames of methane/air at various pressures

A numerical study of the counterflow diffusion flames of methane/air at both subcritical and supercritical pressures,which have very important applications in the air-breathing rocket and advanced gas turbine engines,is conducted to obtain fundamental understanding of the flame characteristics.The analysis is based on a general mathematical formulation and accommodates a unified treatment of general fluids thermodynamics and accurate calculations of thermophysical properties.Results reveal that the maximum flame temperature occurs on the fuel-rich side for low-pressure conditions and shifts toward the stoichiometric position when the pressure increases.The maximum flame temperature increases with an increasing pressure,but decreases with an increasing strain rate.The flame width is inversely proportional to the square root of the product of the pressure and strain rate as■■1 p·a2/1.The total heat release rate varies with the pressure and strain rate in a relationship of Q release ■(p·a)0.518.An increased pressure leads to a slightly more complete combustion process near the stoichiometric position,but its effect on NO production is minor.Under the test conditions,variations of the strain rate have significant impacts on the formation of major pollutants.An increased strain rate leads to the decreased mole fraction of CO in the fuel-rich region and significantly reduced NO near the stoichiometric position.     

Influence of Wall Effect on Comprehensive Controllability for Ducted Fan Aircraft

A novel coaxial ducted fan structure aircraft is proposed to enable the aircraft near vertical walls at high altitudes. The state space equation of the system can be obtained by correlation deduction and identification of the whole prototype model. Based on the duct test bench experiment and computational fluid dynamics (CFD) simulation analysis, the expressions between the different distances $d_{\rm{WE}} $ from the rotor center of the prototype to the wall and the thrust, reaction torque, and tilting moment of the system under hovering conditions are obtained. The influence of the wall effect of the prototype is incorporated into the system model to analyze the relationship between distance $d_{\rm{WE}} $ and the comprehensive controllability of the system. The results show that the system comprehensive controllability vector of other channels changes little with the decrease of the distance $d_{\rm{WE}} $, and only the controllability vector of the rolling channel increases significantly. At the same time, the tilting moment also increases significantly, which strengthens the tendency of the prototype to tilt towards the wall.     

Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil

The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model,the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil.The effects of pitching rate on the subcavitating and cavitating response of the pitching hydrofoil are also investigated.In particular,we focus on the interactions between cavity inception,growth,and shedding and the vortex flow structures,and their impacts on the hydrofoil performance.The calculations are 2-D and performed by solving the incompressible,multiphase Unsteady Reynolds Averaged Navier Stokes(URANS)equations via the commercial CFD code CFX.The k-SST(Shear Stress Transport)turbulence model is used along with the transport equation-based cavitation models.The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density.The calculation results are validated with experiments conducted by Ducoin et al.(see Computational and experimental investigation of flow over a transient pitching hydrofoil,Eur J Mech/B Fluids,2009,28:728–743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow,Eur J Mech B/fluids,2012,36:63–74).Results are shown for a NACA66 hydrofoil subject to slow(quasi static,6°/s,*0.18)and fast(dynamic,63°/s,*1.89)pitching motions from=0°to=15°.Both subcavitaing(=8.0)and cavitating(=3.0)flows are considered.For subcavitating flow(=8.0),low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall,and delay of stall is observed with increasing pitching velocity.For cavitating flow(=3.0),small leading edge cavities are observed with the slow pitching case,which significantly modified the vortex dynamics at high angles of attack,leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate.On the other hand,for the fast pitching case at=3.0,large-scale sheet/cloud cavitation is observed,the cavity behavior is unsteady and has a strong impact on the hydrodynamic response,which leads to high amplitude fluctuations of the hydrodynamic coefficients,as well as significant changes in the stall and post-stall behavior.The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region,which significantly modifies the cavity lengths and shedding frequencies,particularly for the fast pitching case.In general,compared with the experimental visualizations,the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.     

Effects and mechanism of titanium modification on structures of cast steel ZG270-500

The influences of titanium modification on the solidification behavior, shrinkage characteristic and primary austenite refinement of cast steel ZG270-500 smelted in intermediate frequency induction furnace were studied. 0.15wt% titanium modification increased the fluidity of the steel liquid, enhanced the feeding capacity of cast steel, changed the dispersed shrinkage porosity to concentrated shrinkage cavity, turned the coarse dendrites into fine equiaxed grain structures and greatly reduced the primary austenite grain size. By scanning electron microscope (SEM) and energy disperse spectroscope (EDS) analysis, it was found that titanium combined with carbon to be solid phase particles TiC, with high melting point, to promote the primary austenite nucleation authentically by non-spontaneous nucleating. The crystal lattice match growing model between γ-Fe and TiC was established. The mechanism of TiC heterogeneous nucleating existed in that the primary austenite grew up by {111}γ-Fe parallel to the closest packed plane {111}TiC in the crystal orientation <110>γ-Fe//<211>TiC. The crystal planes mismatch and the lowest orientation mismatch δ<110>γ-Fe <110>TiC were 8.18%. and 2.25% respectively, almost achieving complete coherent lattice match growing of austenite on TiC.     

对应于Uq(sln)的弱Hopf代数的分类

首先给出A_n型非标准量子群X_q（A_n）的定义,通过替换X_q（A_n）的类群元,得到弱Hopf代数$\\mathfrak{m}{{X}_{q}}$（A_n）,然后探讨$\\mathfrak{m}{{X}_{q}}$（A_n）的结构并给出其Ext箭图.