A differential game of evasion with delays

A game of evasion (or contact avoidance problem) described by a system of differential equations containing delays in state and control is considered. There is given a sufficient condition for the existence of a strategy which ensures the contact avoidance. A method of constructing such a strategy is presented.     

A Geometric Relationship Between Equivalent Spreads

By Andrè theory, it is well known how to algebraically convert a spread in a projective space to an equivalent spread (representing the same translation plane) in a projective space of different dimension and of different order (corresponding to a subfield of the kernel). The goal of this paper is to establish a geometric connection between any two such equivalent spreads by embedding them as subspaces and subgeometries of an ambient projective spaces. The connection can be viewed as a generalization of a construction due to Hirschfeld and Thas.     

用消光法测定还原糖

本文详细研究了用乙二胺（en）-铜（Cu2＋）络合物（简作EDAC）测定还原糖的分光光度法．结果表明：Cen／CCu2＋≥2．5即可形成稳定的络合物EDAC，其最大吸光度λmax＝547nm；在介质中吸光度稳定，λmax＝550nm；于NaOH介质中吸光度下降，波长略为红移．在固定介质，或中，EDAC性质一年同内未发现变化，能与还原精作用生成Cu2O沉淀，而本身的量减少，其吸光度与还原糖在0．063～1．64mg（六碳糖）内线性相关，相关系数绝对值｜ρ｜＞0．998．实测样品回收率在98％～103％之间．本法试剂易得、性稳定，操作简便，取样量少．灵敏度较高．en是一种常用试剂，有关用EDAC络合物测定还原糖的方法尚未见报导．     

Block Krylov Subspace Methods for Solving Large Sylvester Equations

In the present paper, we propose block Krylov subspace methods for solving the Sylvester matrix equation AX–XB=C. We first consider the case when A is large and B is of small size. We use block Krylov subspace methods such as the block Arnoldi and the block Lanczos algorithms to compute approximations to the solution of the Sylvester matrix equation. When both matrices are large and the right-hand side matrix is of small rank, we will show how to extract low-rank approximations. We give some theoretical results such as perturbation results and bounds of the norm of the error. Numerical experiments will also be given to show the effectiveness of these block methods.     

Computing eigenspaces with specified eigenvalues of a regular matrix pair (A,B) and condition estimation: theory,algorithms and software

Theory, algorithms and LAPACK-style software for computing a pair of deflating subspaces with specified eigenvalues of a regular matrix pair (A, B) and error bounds for computed quantities (eigenvalues and eigenspaces) are presented. Thereordering of specified eigenvalues is performed with a direct orthogonal transformation method with guaranteed numerical stability. Each swap of two adjacent diagonal blocks in the real generalized Schur form, where at least one of them corresponds to a complex conjugate pair of eigenvalues, involves solving a generalized Sylvester equation and the construction of two orthogonal transformation matrices from certain eigenspaces associated with the diagonal blocks. The swapping of two 1×1 blocks is performed using orthogonal (unitary) Givens rotations. Theerror bounds are based on estimates of condition numbers for eigenvalues and eigenspaces. The software computes reciprocal values of a condition number for an individual eigenvalue (or a cluster of eigenvalues), a condition number for an eigenvector (or eigenspace), and spectral projectors onto a selected cluster. By computing reciprocal values we avoid overflow. Changes in eigenvectors and eigenspaces are measured by their change in angle. The condition numbers yield bothasymptotic andglobal error bounds. The asymptotic bounds are only accurate for small perturbations (E, F) of (A, B), while the global bounds work for all (E, F.) up to a certain bound, whose size is determined by the conditioning of the problem. It is also shown how these upper bounds can be estimated. Fortran 77software that implements our algorithms for reordering eigenvalues, computing (left and right) deflating subspaces with specified eigenvalues and condition number estimation are presented. Computational experiments that illustrate the accuracy, efficiency and reliability of our software are also described.     

稀土和磷改性对裂化催化剂反应性能的影响

我们采用稀土以及稀土和磷两种方式对Y型沸石表面进行修饰，NH3-TPD测试表明稀土和磷复合改性Y沸石(P—RE—USY)的酸性分布更集中在中强酸范围．在固定床和提升管装置上评价了含有P—RE-USY沸石催化剂的反应性能．经过稀土和磷复合改性，增强了沸石孔道的酸性中心，而表面活性中心在磷和稀土相互作用的改性中得以减少和弱化．这种修饰作用引导更多的烃分子进入沸石孔道中进行反应，减少了烃分子通过表面反应形成大量烯烃分子的几率．同时，由于烯烃的降低不完全来自二次氢转移反应的饱和过程，所以，适度降低二次反应有效地减少了中间馏分油的裂解，提高了柴油收率．     

在照相明胶层中金催化的铜无电沉积

利用X射线光电子能谱的原位氩离子束溅射和ESCA技术，研究了无电沉积前后照相明胶中硫元素化学形态的变化，对无电沉积所形成的导电膜进行了深度剖析，探讨了照相明胶层中金催化的铜无电沉积机理．结果表明：在酸性条件下（pH＝3．20），明胶大分子的蛋氨酸亚砜对AU3 仍具有较大的还原能力，明胶大分子的蛋氨酸、蛋氨酸亚砜将Au3 最终还原为胶态金，而蛋氨酸和蛋氨酸亚砜均被氧化为蛋氨酸砜．在无电沉积初期，胶态金作为催化中心引发铜的无电沉积，之后的反应为Cu2 在新生态铜的自催化下的还原沉积．在无电沉积过程的碱性条件下（pH＝12．50），明胶中的部分蛋氨酸砜又被甲醛还原为蛋氨酸．     

New mechanistic insights on Justicia vahlii Roth: UPLC-Q-TOF-MS and GC–MS based metabolomics,in-vivo,in-silico toxicological,antioxidant based anti-inflammatory and enzyme inhibition evaluation

Justicia vahlii Roth. (acanthaceae) is an important medicinal food plant used in pain relief and topical inflammation. The present study aimed to evaluate phytochemical composition, toxicity, anti-inflammatory, antioxidant and enzyme inhibition potential of n-butanol extract of J. vahlii (BEJv). The extract prepared through maceration was found rich in total phenolic contents (TPC) 196.08 ± 6.01 mg of Gallic acid equivalent (mg GAE/g DE) and total flavonoid contents (TFC) 59.08 ± 1.32 mg of Rutin equivalent (mg RE/g DE). The UPLC-Q-TOF-MS analysis of BEJv showed tentative identification of 87 compounds and 19 compounds were detected in GC–MS analysis. The HPLC-PDA quantification showed the presence of 14 polyphenols amongst which kaempferol (3.45 ± 0.21 µg/ mL DE) and ferulic acid (2.31 ± 1.30 µg/ mL DE) were found in highest quantity. The acute oral toxicity study revealed the safety and biocompatibility of the extract up to 3000 mg/kg in mice. There was no effect of BEJv on human normal liver cells (HL 7702) and very low cytotoxic effect on liver cancer cells (HepG2) and breast cancer cells (MCF-7). In anti-inflammatory evaluation, the BEJv treated groups showed significant inhibition (p < 0.001) of late phase carrageenan induced paw edema at 400 mg/kg and increased the levels of oxidative stress markers; catalase, superoxide dismutase (SOD) and glutathione (GSH) while decreased the inflammatory markers; interleukin-1beta (IL-β) and tumor necrosis factor alpha (TNF-α) in paw tissue of mice. BEJv displayed highest results in Ferric reducing antioxidant power (FRAP) assay 97. 21 ± 2.34 mg TE (trolox equivalent)/g DE, and highest activity 3.32 ± 0.31 mmol ACAE (acarbose equivalent)/g D.E against α-glucosidase. Docking study showed good docking score by the tested compounds against the various clinically significant enzymes. Conclusively the current study unveiled J. vahlii as novel non-toxic source with good antioxidant-mediated anti-inflammatory potential which strongly back the traditional use of the species in pain and inflammation.     

Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations

An eigenvalue perturbation theory under rank-one perturbations is developed for classes of real matrices that are symmetric with respect to a non-degenerate bilinear form, or Hamiltonian with respect to a non-degenerate skew-symmetric form. In contrast to the case of complex matrices, the sign characteristic is a crucial feature of matrices in these classes. The behaviour of the sign characteristic under generic rank-one perturbations is analyzed in each of these two classes of matrices. Partial results are presented, but some questions remain open. Applications include boundedness and robust boundedness for solutions of structured systems of linear differential equations with respect to general perturbations as well as with respect to structured rank perturbations of the coefficients.