Singular Points Near an X_0-breaking Double Singular Fold Point in Z_2-symmetric Nonlinear Equations

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On stable least squares solution to the system of linear inequalities

The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable and degenerate problems primarily.      

多重经济增长路径,多重稳态解和分歧

该文给出一个具有可解内生生育率的Cass-Koopmans（C-K）经济增长模型．证明参数满足时，模型存在多重经济增长路径和多重稳态解；当时，经济增长路径和稳态解唯一，即描述模型的微分动力系统出现分歧．文中讨论了多重经济增长路径的几何形态、位置关系和主要结果的经济意义．     

Neue quaternäre Chalkogenohalogenide

The quaternary chalcogeno halides AgHgSI, AgHgSBr and CuHgSI have been synthesized by annealing mixtures of silver (copper) halides and mercury sulphide. AgHgSI decomposes peritectoidally at 593±3 K and crystallizes in the orthohombic system with lattice constants ofa=772.3 (3),b=847.7 (3) andc=707.3 (3) pm. The phase diagram AgI-HgS resembles the AgI-Ag₂S system closely. Contrary to the literature the only stable compound in this system is AgHgSI. The previously mentioned Ag₂HgSI₂ is metastable. The reported compound Ag₂HgSBr₂ could not be synthesized. The substitution of Hg²⁺ by Cd²⁺ in CuHgSI leads to a red phase Cu₂Cd₃S₂I₄ which crystallizes in the wurtzite type structure with lattice parameters ofa=424.7 (1) andc=695.2 (1) pm.

     

矿山岩体工程的系统工程

用系统工程学的观点, 重新认识矿山岩体工程的特点。建立矿山岩体工程稳定性的系统的概念。提出地质模型、设计模型、施工模型的构思, 使工程地质、设计、施工三者密切结合, 共同解决矿山岩体工程稳定问题。通过动态监测和信息反馈, 在工程施工的动态过程中不断地获得新的认识, 以便对工程实施做出新的决策。     

Inverse colloidal crystal membranes for hydrophobic interaction membrane chromatography

A collaborative study on the robustness and portability of a capillary electrophoresis‐mass spectrometry method for peptide mapping was performed by an international team, consisting of 13 independent laboratories from academia and industry. All participants used the same batch of samples, reagents and coated capillaries to run their assays, whereas they utilized the capillary electrophoresis‐mass spectrometry equipment available in their laboratories. The equipment used varied in model, type and instrument manufacturer. Furthermore, different types of sheath‐flow capillary electrophoresis–mass spectrometry interfaces were used. Migration time, peak height and peak area of ten representative target peptides of trypsin‐digested bovine serum albumin were determined by every laboratory on two consecutive days. The data were critically evaluated to identify outliers and final values for means, repeatability (precision within a laboratory) and reproducibility (precision between laboratories) were established. For relative migration time the repeatability was between 0.05 and 0.18% RSD and the reproducibility between 0.14 and 1.3% RSD. For relative peak area repeatability and reproducibility values obtained were 3–12 and 9–29% RSD, respectively. These results demonstrate that capillary electrophoresis‐mass spectrometry is robust enough to allow a method transfer across multiple laboratories and should promote a more widespread use of peptide mapping and other capillary electrophoresis‐mass spectrometry applications in biopharmaceutical analysis and related fields.     

Analysis of peptides and protein digests by reversed phase high performance liquid chromatography–electrospray ionisation mass spectrometry using neutral pH elution conditions

In this study, the advantages of carrying out the analysis of peptides and tryptic digests of proteins under gradient elution conditions at pH 6.5 by reversed-phase liquid chromatography (RP-HPLC) and in-line electrospray ionisation mass spectrometry (ESI-MS) are documented. For these RP separations, a double endcapped, bidentate anchored n-octadecyl wide pore silica adsorbent was employed in a capillary column format. Compared to the corresponding analysis of the same peptides and protein tryptic digests using low pH elution conditions for their RP-HPLC separation, this alternative approach provides improved selectivity and more efficient separation of these analytes, thus allowing a more sensitive identification of proteins at different abundance levels, i.e. more tryptic peptides from the same protein could be confidently identified, enabling higher sequence coverage of the protein to be obtained. This approach was further evaluated with very complex tryptic digests derived from a human plasma protein sample using an online two-dimensional (2D) strong cation-exchange (SCX)-RP-HPLC-ESI-MS/MS system. Again, at pH 6.5, with mobile phases of different compositions, improved chromatographic selectivities were obtained, concomitant with more sensitive on-line electrospray ionisation tandem mass spectrometric (ESI-MS/MS) analysis. As a consequence, more plasma proteins could be confidently identified, highlighting the potential of these RP-HPLC methods with elution at pH 6.5 to extend further the scope of proteomic investigations.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

挠性多体系统动力学

本文以递推形式给出了挠性多体系统的动力学方程。此方程具有如下特点:(1)对整个系统而言,方程数目多,但递推的每一步只需要解低维的方程组,从而避免了高维矩阵的求逆,减少了计算量。(2)对不同类型的问题,方程形式具有很高的相似性,便于程序编制,各个需要求逆的矩阵都是对称正定的,这样减少了计算量和计算机内存单元。(3)这种方程形式处理非树形和带有约束条件的系统很方便。     

Representation of discrete sequences with high-dimensional iterated function systems

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piece-wise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the high-dimensional piece-wise hidden-variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore, the result is very general.