无扭算子李代数g(G,M)的子代数

由算子构成的李代数在李代数理论中具有重要的应用,因而研究算子李代数及其子代数的代数结构就显得尤为重要.首先构造了无扭算子李代数g(G,M)的子代数L_1,L_2,g1,g2,然后给出了这些子代数的代数结构及一些重要应用.     

Tits-Kantor-Koecher李代数的Wakimoto表示

每一个Jordan代数都对应了一个Tits-Kantor-Koecher李代数.在扩张仿射李代数的分类中[1],A1型李代数的分类依赖于欧氏空间上半格给出的Tits-Kantor-Koecher李代数.另外在相似的意义下,二维欧氏空间R2中只有两个半格.设S是R2上的任一半格,Τ(S)为半格S对应的Jordan代数,(g)(Τ(S))为相应的Tits.Kantor-Koecher李代数.利用Wakimoto自由场的方法给出李代数(g)(Τ(S))的一类顶点表示.     

一类深度1的可迁模Lie超代数

建立了满足如下条件的可迁$\mathbb{Z}$-分次模Lie超代数$\frak{g}=\oplus_{-1\leq i\leq r}\frak{g}_{i}$的嵌入定理:(i) $\frak{g}_{0}\simeq \widetilde{\mathrm{p}}(\frak{g}_{-1}) $ 并且$\frak{g}_{0}$-模 $\frak{g}_{-1}$ 同构于$\widetilde{\mathrm{p}}(\frak{g}_{-1})$的自然模;(ii) $\dim \frak{g}_1=\frac 23 n(2n^2+1),$ 其中 $n=\frac{1}{2} \dim \frak{g}_{-1}.$特别地, 证明了满足上述条件的有限维单模Lie超代数同构于奇Hamilton模Lie超代数.对局限Lie超代数也做了相应的讨论.     

有限维非退化可解李代数的顶点算子代数

构造相应于非退化可解李代数g的顶点算子代数分两步进行,首先构造顶点代数.本文是在已经得到的相应于非退化可解李代数g的顶点代数(Vg(l,0),Y(V,1)上构造顶点算子代数.定义了非退化可解李代数g的Casimir算子Ω,给出了在伴随表示下Ω作用在g上是0及相关性质,并应用Ω定义出Vg(l,0)中元素ω,证明了Vg(l,0)关于ω的顶点算子YV(ω,x)的系数构成一个Virasoro代数-模,还证明了ω满足顶点算子代数定义中Virasoro-向量的所有公理.从而证得(Vg(l,0),Yv,1,ω)是一个顶点算子代数.     

有限维单李代数的2-局部导子

设F是特征为零的代数封闭域,g为F上有限维单李代数.g上的一个映射φ称为2-局部导子,如果对任意的x,y∈g,存在导子D_(x,y):g→g,使φ(x)=D_(x,y)(x),φ(y)=D_(x,y)(y).本文证明g上的所有2-局部导子一定是内导子.     

实半单纯Lie代数的拟内自同构

<正> 1.在[1]中作者组出了决定一个实单纯 Lie 代数的自同构群的方法,特別决定自同构群 Aut g 和内自同构群 Ad g 的商群 Aut g/Ad g.在实 Lie 代数的理论中,特別关于子代数的讨论中,拟内自同构群的概念是重要的.当我们已经知道实 Lie 代数 g 的某一个实子代数时,他的复化便是 g 的复化(?)的一个子代数,对于他所定的共轭类还须进一步弄清在实 Lie 代数 g 内的共轭分类.实际问题往往先找出对实 Lie 代数自同构群下的分类,而     

弱斜配对双代数和弱相关Long双代数

该文在弱双代数$H$上给出了扭曲积$(H^\sigma,\cdot_\sigma)$成为弱双代数的充分必要条件.设$[B, H, \tau]$是一个弱斜配对, 并且$\tau$可逆,则在某个条件下弱双交叉积$B\bowtie_\tau H$是一个弱双代数. 如果$(B,H, \sigma)$是弱相关Long双代数, 并且$\sigma$可逆,则弱双交叉积$B^{OP}\bowtie_\sigma H$可以被构造. 它的乘法是:$(x\otimes h)(y\otimes g)=\Sigma\sigma(y_1, h_1)y_2x\otimes h_2g\sigma^{-1}(y_3, h_3),$ 特别地, 如果$(B, H,\sigma)$是相关Long双代数, 则$(B^{OP \bowtie_\sigma H,\beta)$是Long双代数当且仅当对任意$b, d\in B^{OP}; g, \ell\in H$,$\Sigma\sigma^{-1}(b, g_2\ell)\sigma(d, g_1)=\Sigma\sigma^{-1}(b,\ell g_1)\sigma(d, g_2),$ 其中$B$为$H$的子Hopf代数,$\beta$定义为$\beta(b\bowtie_\sigma h\otimes c\bowtie_\sigma g)=\varepsilon_H(h)\varepsilon_{B^{OP}}(c)\sigma^{-1}(b, g).$ 对于Sweedler 4维Hopf代数$H$, 作者给出一个例子说明:此弱双交叉积$(B^{OP}\bowtie_\sigma H, \beta)$不仅是一个Long双代数,而且是一个非可换和非余可换的8维Hopf代数. 最后, 设$B,H$都是弱双代数, $\sigma: B\otimes H\rightarrow k$是一个线性映射, 作者给出了$(B,\sigma,\leftharpoonup, \Delta_B)$是弱相关右$(H, B)$ -重模代数的充分必要条件.     

U(g_((+)))的极小生成元和生成关系

设g是有限维单李代数,g是相应于g的无扭仿型Kac-Moody代数的导代数.讨论了g的子代数g(+)的普遍包络代数U(g(+))的极小生成元和生成关系问题,证明了U(g(+))由a t~m,h t~n及1生成,其中m,n∈Z-∪{0}.     

弱量子代数wUq((g))的弱Hopf代数结构

设(g)为有限维半单李代数,参数q不是单位根.定义了一个具有弱Hopf代数结构的弱量子代数wUq((g)),构造了它的类群元素集,并给出了两个不同参数的弱量子代数同构的条件.     

扭平凡扩张与表示维数

设k是代数闭域,∧是k上基本有限维连通Koszul自入射代数.本文首先证明:如果∧满足有限生成(FG)假设,那么存在∧的k-代数自同构σ0使得关于∧-双模D∧~(σ0)的扭平凡扩张T(∧~(σ0))=∧×D∧~(σ0)亦满足FG假设.由此得到,在∧满足FG假设的条件下,(1)T(A~(σ0))的表示维数大于等于∧的复杂度加2;(2)设G是∧的k-代数自同构群Aut_k(∧)的有限子群,且其阶在∧中可逆.如果对于任意的g∈G都有σ0g=gσ0,那么斜群代数∧*G的扭平凡扩张代数T((∧*G)~(σ0))的表示维数大于等于∧的复杂度加2.     

Transverse compression of PPTA fibers

Results of single transverse compression testing of PPTA and PIPD fibers, using a novel test device, are presented and discussed. In the tests, short lengths of single fibers are compressed between two parallel, stiff platens. The fiber elastic deformation is analyzed as a Hertzian contact problem. The inelastic deformation is analyzed by elastic-plastic FE simulation and by laser-scanning confocal microscopy of the compressed fibers ex post facto. The results obtained are compared to those in the literature and to the theoretical predictions of PPTA fiber transverse elasticity based on PPTA crystal elasticity.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).3TEX, Inc. 109, MacKenan Drive, Cary, North Carolina 27511, USA. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 533–544, March–April, 2000.     

On free products in varieties of associative algebras

Varieties of associative algebras over a field of characteristic zero are considered. Belov recently proved that, in any variety of this kind, the Hilbert series of a relatively free algebra of finite rank is rational. At the same time, for three important varieties, namely, those of algebras with zero multiplication, of commutative algebras, and of all associative algebras, a stronger assertion holds: for these varieties, formulas that rationally express the Hilbert series of the free product algebra via the Hilbert series of the factors are well known. In the paper, a system of counterexamples is presented which shows that there is no formula of this kind in any other variety, even in the case of two factors one of which is a free algebra. However, if we restrict ourselves to the class of graded PI-algebras generated by their components of degree one, then there exist infinitely many varieties for each of which a similar formula is valid. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 693–702, May, 1999.     

Dynamic properties of composite laminates and panels with highly contrasting directions of anisotropy

An asymptotic analysis of the dynamic stress-strain state of a thin laminar packet of anisotropic layers is presented. The statement is nonclassical, since in layer materials the ratio of elastic moduli in the longitudinal and transverse directions can generate small parameters comparable to the relative half-thickness of the packet, as, for example, in high-strength unidirectional composites. Alternation of strong load-carrying layers and a relatively soft filler with a similar difference in the elastic moduli between the layers is also allowed. The averaged two-dimensional equations and the total stress tensor in the layers are determined. The results are classified with respect to the types of anisotropy and the indices of differences in the elastic moduli. It is shown that first-approximation models lead to kinematic relations similar to those of the theories of high-order shear strains. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 605–614, September–October, 1999.     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

关于药物对小鼠肝脏细胞色素P-450含量的影响实验结果的分析

肝药酶诱导剂苯巴比妥能诱导细胞色素P-450的合成,而肝药酶抑制剂放线菌素D能抑制细胞色素P-450的合成,本实验应用示差光谱法对P-450含量加以测定.本文改进了传统的计算药后诱导组和抑制组P-450含量增加或减少的百分比来评价药物的方法,在M athem atica数学软件环境下,对数据进行方差分析和t检验,提高了数据处理精度和可信度.并对原方法表示怀疑.     

网络优化中一个组合问题的探讨

文[4]提出了网络优化中若干有待解决的组合问题，本文围绕其中之一“减小直径问题”进行了探讨．设P（n，t）表示长为n的路径增加t条边后所得图直径的最小值，C（n，t）表示长为n的圈增加t条边后所得回直径的最小值．本文取得如下进展：1）给出P（n，2），P（n，3）及C（n，2）的精确值，并得出P（n，4）的一更精细的上界及一种更好的加边方式．上述结果均满足小极大度原则．2）在有极大度限制的条件下，分别对t为偶数和奇数给出了P（n，t）的上界．     

Influence of Moisture on the Structure and Properties of the Interphase Layer of a Composite Based on an Epoxy Binder with a Disperse Filler

Properties of a model composite based on an ED-22 epoxy binder, cured with polyprophylene polyamine, and disperse LiF crystals as a filler were investigated by the methods of dilatometry and X-ray diffractometry. It was established that the density of cross-links of the epoxy binder in the interphase layer was lower than in a block specimen. Therefore, the thermal expansion of the composite on heating to 120°C, in terms of that of the binder, grew significantly with the degree of filling ϕ, and the water uptake also increased at the initial stage. The presence of absorbed water led to considerable changes in the structure and properties of the composite interphase: the binder became more cross-linked, its structural ordering decreased, the thermal expansion at heating diminished by a factor of 3. 7 (at ϕ = 50%), and the glass-transition temperature increased. As a result of long-term action of moisture, changes in the internal stresses had an extreme character.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 535–544, July–August, 2005.     

Numerical-experimental investigation of resonance characteristics of a sounding board

The paper presents results of numerical and experimental investigations into the vibrations of thin-walled structures, considering such their features as the complexity of geometry, the laminated structure of walls, the anisotropy of materials, the presence of stiffeners, and the initial stresses. The object of the study is the sounding board of an acoustic guitar, the main structural material of which is a three-layer birch veneer. Based on the finite-element method, a corresponding calculation model is created, and the steady-state regimes of forced vibrations of the sounding board are investigated. A good correspondence between calculation results and experimental data is found to exist. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 399–410, May–June, 2007.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.