Poisson brackets,Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.     

并联交错PFC技术在磁体电源中的应用

并联交错功率因数校正(powerfactorcorrection,PFC)具有能减小输入电流纹波,减小电感磁芯尺寸,减小输出电容纹波、功率因数高等优点．针对其优点,考虑将该变换器应用到强磁场中心的超导磁体电源的备用方案中,以弥补现在运行电源体积过大的不足．本文主要介绍了并联交错PFC的工作原理,对其参数进行设计和选型,分析了控制方法,利用SiC器件,搭建了１kW 的实验样机,实验验证了方案的可行性,为下一步超导磁体电源的升级改造提供了理论和工程经验。     

A recollement construction of Gorenstein derived categories

We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.     

Finitely generated relatively universal varieties of Heyting algebras

Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=_g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.     

不同产地啤酒中无机元素的因子分析与聚类分析

啤酒样品经硝酸消解后,用微波等离子体炬原子发射光谱法(MPT-AES)测定其中无机元素的含量。所得结果用SPSS 17.0科学统计软件进行因子分析和聚类分析。因子分析的结果表明:总方差(52.803%)的贡献来自于代表钴、锶、锰元素的因子1和代表锌、铁、铜元素的因子2,所以这些元素是啤酒中的特征元素。聚类分析的结果表明:9种产地的啤酒可以很好地彼此区别,并以此进行啤酒产地的归属辨别。     

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.     

石墨烯分子振动模式因子群分析与密度泛函计算

运用因子群分析法对石墨烯的分子振动模式进行了理论分析,得到石墨烯的分子振动模式,计算出各振动模式的光谱特性.对所建立的石墨烯晶体的布拉维单胞模型采用基于密度泛函理论的第一性原理进行分子振动频率与模式的计算,所得的振动模式数目以及各振动频率的光谱特性同因子群分析方法所得结论一致.结合上述计算结果,通过系统比较石墨与石墨烯之间的红外光谱和拉曼光谱的差别,从理论上解释了具有D6h对称的石墨烯的A2u、E1u红外活性特征振动模式没有在红外光谱中出现的原因.     

Active allocation of systematic risk and control of risk sensitivity in portfolio optimization

Portfolio risk can be decomposed into two parts, the systematic risk and the nonsystematic risk. It is well known that the nonsystematic risk can be eliminated by diversification, while the systematic risk cannot. Thus, the portfolio risk, except for that of undiversified small portfolios, is always dominated by the systematic risk. In this paper, under the mean–variance framework, we propose a model for actively allocating the systematic risk in portfolio optimization, which can also be interpreted as a model of controlling risk sensitivity in portfolio selection. Although the resulting problem is, in general, a notorious non-convex quadratically constrained quadratic program, the problem formulation is of some special structures due to the features of the defined marginal systematic risk contribution and the way to model the systematic risk via a factor model. By exploiting such special problem characteristics, we design an efficient and globally convergent branch-and-bound solution algorithm, based on a second-order cone relaxation. While empirical study demonstrates that the proposed model is a preferred tool for active portfolio risk management, numerical experiments also show that the proposed solution method is more efficient when compared to the commercial software BARON.     

Integrable maps from Galois differential algebras,Borel transforms and number sequences

A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a given differential equation, in particular symmetries and integrability (see Tempesta, 2010 [40]). Our approach is based on the properties of a suitable Galois differential algebra, that we shall call a Rota algebra. A formulation of the procedure in terms of category theory is proposed. In order to render the lattice dynamics confined, a Borel regularization is also adopted. As a byproduct of the theory, a connection between number sequences and integrability is discussed.     

带Neumann 边界条件的$p(x)$-Kirchhoff 型椭圆系统的研究

本文研究一类带Neumann 边界条件的~$p(x)$-Kirchhoff 型系统解的存在性. 借助于Ekeland变分原理和变指数Sobolev空间理论, 我们给出使得该问题存在解的合适条件.由于Poincar\'{e} 不等式在$W^{1,p(x)}(\Omega)$ 中不再成立, 我们将在$W^{1,p(x)}(\Omega)$ 的某个子空间中证明Poincar\'{e}-Wirtinger 不等式.