Γ─纯整半群

印度数学家Ｍ．Ｋ．Ｓｅｎ和Ｎ．Ｋ．Ｓａｈａ在１９８６年给出了Γ－半群的概念和讨论了Γ－半群的若干性质。本文引入了Γ－正则半群和Γ－纯整半群的概念。并讨论了这两种重要的Γ－半群类的若干特性。最后通过三个有趣的实例说明了纯整Γ－半群类和Γ－纯整半群类是互不包含但交非空的两个Γ－半群类。     

对"计量学指南联合委员会"工作方针的评论(续)

由于GUM95对B类评定的基本特点缺乏认识，因此它的B类评定方法仅仅是A类评定方法的翻版．实际上是无法执行的。     

不确定度的B类评定方法

在不确定度评定中，Ｂ类评定十分重要．本文讨论不确定度Ｂ类评定方法．给出应用实例，以便有关人员在无法用Ａ类评定不确定度时，按被测量可能变化的信息，作出Ｂ类评定．     

致密磷酸钙陶瓷在动态SBF中类骨磷灰石层形成研究

磷酸钙陶瓷植入体内后其表面类骨磷灰石层的形成是诱导成骨的先决条件．本实验在模拟体液(ｓｉｍｕｌａｔｅｄ ｂｏｄｙ ｆｌｕｉｄ,ＳＢＦ)以人体骨骼肌组织内体液的正常生理流率(２ｍＬ/１００ｍＬ·ｍｉｎ)和偏离正常生理流率流动的动态条件下,研究在动态ＳＢＦ中影响致密磷酸钙陶瓷表面类骨磷灰石层形成的因素．结果表明:在生理流率条件下,材料的粗糙表面有利于类骨磷灰石的形成,加大ＳＢＦ中Ｃａ^２＋、ＨＰＯ_４^２－离子浓度,类骨磷灰石层的形成速度加快．比起通常使用的静态浸泡试验,ＳＢＦ以生理流率流动的动态试验能够更好地模拟类骨磷灰石生长的体内环境．动态ＳＢＦ对了解类骨磷灰石形成,进而了解磷酸钙陶瓷在体内诱导成骨机理是十分有用的．     

抗干涉齿轮集机构的循环着色优化编码方法

抗干涉齿轮集（counter-meshing gears,CMG）机构是一种可用于微型或微小型机械组合锁的密码鉴别机构,其复舍齿轮的齿牙编码是CMG机构设计的核心问题．文中结合两个典型算例,介绍了CMG机构循环着色优化编码方法的原理与应用步骤．该方法采用三色循环交替模式,对二维迷宫映射图中全部或主体部分的关键陷阱格点依序着色,实现关键陷阱格点的最小色数着色．这种编码方法适用于第1类和第2类CMG机构,优点是无需计算、简单易用,可获得最优编码,即密码齿轮的层数最少．虽然该方法不适用于第3类CMG机构,但第3类CMG机构并不常用,因此该方法具有重要的实用价值．     

一种新的模拟电路故障模糊集确定算法

提出了一种在模拟电路故障诊断中故障类模糊集的确定算法．该算法基于测前仿真法,不但同时适用于线性电路和非线性电路,而且可以确定元件模糊组以外的故障类模糊集．算法利用电路仿真故障特征数据计算故障的类间差异矩阵,从而完成故障类模糊集的确定．计算示例验证了该算法的有效性．     

可装卸式加油设备的管路系统装配设计研究

由于在不同装配空间的管路系统装配结构存在相似性和差异性,可装卸式加油设备的管路系统装配设计十分复杂．针对该问题,提出了基于谱系聚类法的管路系统装配空间聚类方法,使聚类后的每类装配空间能够通用多套已装配好的管路系统．通过定义类的典型装配空间及装配半径,使新设计的加油设备按其管路系统装配空间尺寸,迅速地找到符合要求的已装配好的管路系统．最后,以对一些典型的装配空间进行聚类及如何应用聚类结果为例,验证了该方法的有效性和合理性．     

两指标鞅的停止

首次用可选增道路来停止两指标随机过程．得出了类RR鞅的停止仍然是鞅．     

聚砜/聚醚类高聚物共混相容性及超滤膜的研究

研究了由聚砜(PSf)和自制的聚醚类高聚物制备的共混超滤膜的组分相容性、性能及膜结构．利用差示扫描量热仪(DSC)测定了纯PSf、纯聚醚类高聚物以及不同PSf／聚醚类高聚物共混配比制得的超滤膜的玻璃化转变温度(Tg)．实验结果表明，PSf与聚醚类高聚物组分在整个配比范围内完全相容．所测定的共混膜的Tg与利用Fox方程得出的理论计算值相一致．PSf／聚醚类高聚物共混膜的水通量要高于纯PSf和纯聚醚类高聚物且截留率几乎没有变化．通过扫描电子显微镜(SEM)观察了膜的形态并对膜的超滤性能进行了解释．     

不同规模数据集下的人脸识别方法

系统研究了类内变化和类数目增加所引起的人脸识别中的非线性识别问题，并比较了线性识别方法和非线性识别方法在不同用户集规模下的适用性．采用CAS-PEAL大型人脸数据库中的表情集（330人）和姿势集（1000人）进行了3组实验．实验结果表明：当训练集的人数在300人（表情集）以内时，增加类内的变化不会对线性识别方法造成影响，并可以提高识别的准确率；但是，当保持类内图片数不变而增加类的数目时，类数（人数）增加对线性方法和非线性方法产生了不同的影响．随着人数增加，线性识别方法的识别准确率逐渐降低，而基于核方法的非线性方法却能够一直保持识别准确率的稳定．因此，应该根据类的总数合理地选择识别方法，并合理地设计类内的图片数，这样有助于提高人脸识别系统的识别率．同时，实验也验证了基于核方法（kernel）的非线性人脸识别方法更适宜于人数规模较大的情况．     

Parametrization of Cosserat equations

The solution space of many systems of ordinary differential (OD) or partial differential (PD) equations in engineering or mathematical physics “can/cannot” be parameterized by a certain number of arbitrary functions behaving like potentials. Among the well-known OD examples, we recall that a classical control system is parametrizable if and only if it is controllable. One interesting PD case is concerned with continuum mechanics where the first-order stress equations admit a rather simple second-order parametrization by means of the single Airy function in dimension 2. The purpose of this paper is to apply the new techniques of “Algebraic Analysis”, a mixture of differential geometry and homological algebra, in order to give a positive and explicit answer concerning the possibility to obtain a first-order parametrization of the stress/couple-stress equations met in the study of Cosserat media. At the same time, as a corollary of the homological test involved, we shall give for the first time the reason for which the compatibility conditions (CC) for the deformation tensor in classical elasticity theory are “second order” while the corresponding CC for the Cosserat fields are only “first order” and explain why this order is equal to the order of the corresponding parametrization. Finally, a close link existing between Cosserat elasticity and Weyl electromagnetism is also provided within a conformal framework.     

A combinatorial approach to involution and δ-regularity II: structure analysis of polynomial modules with pommaret bases

Much of the existing literature on involutive bases concentrates on their efficient algorithmic construction. By contrast, we are here more concerned with their structural properties. Pommaret bases are particularly useful in this respect. We show how they may be applied for determining the Krull and the projective dimension, respectively, and the depth of a polynomial module. We use these results for simple proofs of Hironaka’s criterion for Cohen–Macaulay modules and of the graded form of the Auslander–Buchsbaum formula, respectively. Special emphasis is put on the syzygy theory of Pommaret bases and its use for the construction of a free resolution which is generically minimal for componentwise linear modules. In the monomial case, the arising complex always possesses the structure of a differential algebra and it is possible to derive an explicit formula for the differential. Here a minimal resolution is obtained, if and only if a stable module is treated. These observations generalise results by Eliahou and Kervaire. Using our resolution, we show that the degree of the Pommaret basis with respect to the degree reverse lexicographic term order is always the Castelnuovo–Mumford regularity. This approach leads to new proofs for a number of characterisations of this invariant proposed in the literature. This includes in particular the criteria of Bayer/Stillman and Eisenbud/Goto, respectively. We also relate Pommaret bases to the recent work of Bermejo/Gimenez and Trung on computing the Castelnuovo–Mumford regularity via saturations. It is well-known that Pommaret bases do not always exist but only in so-called δ-regular coordinates. We show that several classical results in commutative algebra, holding only generically, are true for these special coordinates. In particular, they are related to regular sequences, independent sets of variables, saturations and Noether normalisations. Many properties of the generic initial ideal hold also for the leading ideal of the Pommaret basis with respect to the degree reverse lexicographic term order, although the latter one is in general not Borel-fixed. We present a deterministic approach for the effective construction of δ-regular coordinates that is more efficient than all methods proposed in the literature so far.     

Method for the temperature-force prediction of the long-term strength of metals

A method describing the long-term strength of metals using two parameters, whose values depend on the stress, time to failure, and homological temperature, is described. A table for determination of the homological temperature of the most important classes of structural alloys is presented. Correspondence between the proposed relationship and experimental data is demonstrated.All-Union Scientific-Research Institute of Petroleum Machine Building, Moscow. Translated from Problemy Prochnosti, No. 9, pp. 6–9, September, 1989.     

Non-autonomous normal forms for Hamiltonian systems

A method for calculating normal forms for non-autonomous periodically perturbed Hamiltonian systems is developed. The solution for an autonomous Hamiltonian normal form is well known, and involves the solution of a homological equation on the vector space of homogeneous scalar polynomials. An algorithm is presented for generating an analogous non-autonomous homological equation using Lie transforms. Solution of this equation will generate a normal form for the non-autonomous Hamiltonian. Although this equation is defined on an infinite-dimensional space, it is shown that the problem can be reduced to an equivalent one on a finite-dimensional space. A solution can then be found in an analogous way to the solution for the autonomous problem. It is also shown that the normal form satisfies invariance properties. Finally, an example problem is presented to illustrate the solution technique.     

Homological scaffolds of brain functional networks

Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10, 186–198. (doi:10.1038/nrn2618)). Traditionally, the structure of complex networks has been studied through their statistical properties and metrics concerned with node and link properties, e.g. degree-distribution, node centrality and modularity. Here, we study the characteristics of functional brain networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects—homological cycles—associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds, a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. As a proof of principle, we apply these tools to compare resting-state functional brain activity in 15 healthy volunteers after intravenous infusion of placebo and psilocybin—the main psychoactive component of magic mushrooms. The results show that the homological structure of the brain''s functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.     

Boundary element color interpolation for instrumentation,imaging and internet graphics industries

Web enabled color smoothing schemes, employed in applications such as VRML, cooperative design tools and online three-dimensional game rendering engines, rely on constant color triangulation. This artifact is unsuitable for high quality medical and microelectronic images. For convex polygonal image-subsets, Wachspress' rational polynomial shape functions provide the best continuous coloring. It is available only via symbolic computer algebra. A numerical finite difference or boundary element code, which can stimulate potentials in anisotropic media, furnishes an efficient alternative. This chromatic anisotropy emerges from projective geometry and perspective transformations between changing images for which the analogous kinematics can best be modeled by boundary elements. Color mixing depends on the RGB, HSB and CMYK representations, moreover there is no unique notion of a ‘linear color distribution’ along the boundary. In monitoring medical images or controlling remote experiments, the algorithm to determine the dynamic anisotropic factor can be codified and then compiled for any web browser, which can launch a boundary element code (e.g. BEASY), to display time series data in color.     

投影变换矩阵式及变换矩阵

根据几何原理构造了投影体系矩阵(PSM),利用向量几何的形式,建立投影(包括平行投影和中心投影)变换矩阵式。得出投影体系矩阵的逆阵就是投影变换矩阵(PTM)的结论。这种构造变换矩阵的方法与实际投影(观察)过程相同。通过应用程序设计说明它简明、直观且几何意义明确,并且在中心投影(透视投影)中不会产生变形。文中还讨论了投影坐标变换和投影深度坐标等问题。     

四面投影的四维画法几何的影

本文提出了四维空间习用光线的确立,在四面投影的四维画法几何中,求基本几何元素点、线、面在投影空间的空影和在投影面上的落影的方法,并在研究基本元素的空影和落影的基础上,归纳了不从属于投影空间的一般位置几何元素与光线处于特殊位置情况下影的投影特性。从而解决了四面投影的四维画法几何中求解影的作图方法。     

Lower bounds on minimal distance of evaluation codes

In (J Pure Appl Algebra 196:91–99, 2005), the authors point out that the methods they use to find a lower bound for the minimal distance of complete intersection evaluation codes should apply to the case of (arithmetically) Gorenstein evaluation codes. In this note we show this is the case and we study other lower bounds on the minimal distance coming from the syzygies.     

四维画法几何中的曲线投射法

本文是研究以曲线作为辅助投射线,对四维空间中的点、直线、平面等几何元素进行投影变换的问题。文中采用了以平面为投射轴,以平面曲线为投射线的方法建立曲线投射的变换模型。并给出了两个实例,说明用此方法可解决些用一般四维画法几何的方法难以解决的问题。