One-Point Extensions of t-Koszul Algebras

We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to be t-Koszul is given. We also consider the conditions such that the category of t-Koszul modules and the category of quadratic modules coincide.     

激光电源中基于EXB841的IGBT驱动电路设计

根据IGBT对驱动电路的各项要求,在采用专用驱动模块EXB841及带有过流保护功能的驱动电路的基础上,设计了简化的IGBT驱动电路,并提出了构建实际驱动电路的注意事项。通过对PWM信号、IGBT动态驱动信号、IGBT开通时驱动信号上升沿、IGBT关断时驱动信号下降沿等波形的实际观测,表明此驱动电路工作正常。该驱动电路已用于某型脉冲固体激光电源中,运行良好,可靠性较高。     

Breather molecules and localized interaction solutions in the (2+1)-dimensional BLMP equation

The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations.     

基于TPM的家庭基站安全架构

针对基于SIM卡安全机制的家庭基站平台完整性无法保护,容易产生通过家庭基站的恶意攻击等安全威胁,提出了基于TPM的家庭基站保护机制,采用TPM的安全计算、安全存储和认证机制,实现了核心网对家庭基站的设备认证、家庭基站软硬件完整性验证、家庭基站身份认证、家庭基站位置认证与锁定、用户接入家庭基站的认证.     

基于中国邮递员问题的可信平台模块测试序列生成优化研究

现今国内外已经有不少对可信平台模块进行测试的研究成果,但是对测试效率分析不足.本文基于自动机理论和中国邮递员问题,提出了可信平台模块改进的有限状态机模型与相应的优化测试方案,通过寻找一条遍历有限状态机模型中每一条转移至少一次的最短路径的方法,从而生成费用优化的测试序列.测试结果表明,测试方案能够简化有限状态机状态的测试.     

ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS

A useful reduction is presented to determine the finiteness of △-good module category F(△)of a quasi-heredltary algebra. As an application of the reduction, the f(△)-finitenetess of quasi-hereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(△)-finite M-twisted double incidence algebras is given in case the posets are linearly ordered.     

Contraction of Exterior Powers in Characteristic 2 and the Spin Module

Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers ^k V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies ² = 0 and ( ^k V) ^k–1 V We prove that ( ^k V)= ker ^k–1 V except when k=m+2. In the exceptional case, ( ^m+2 V) has codimension 2^m in ker ^m V and we show that the quotient module ker ^m V/ ^m+2 V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in ^m V and multiplicity 0 in all other components of V.     

Crossed Modules and Quantum Groups in Braided Categories

Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.     

一类弱整体维数为2的局部环上的Bass-Quillen问题Ⅱ

设R是U2环,即(R,m)是局部GCD整环,且存在u∈m-m2,使得R/(u)是赋值环,且Ru是Bézout整环.本文证明了若R是带有正规元素为u的U2环,且dim(R/(u))=1,则每个有限生成投射R[X1,...,Xn]模是自由模.由此得到了若R是广义伞环,则每个有限生成投射R[X1,...,Xn]模是自由模.     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.