解奇异非光滑方程组的牛顿法和不精确牛顿法

本文主要解决奇异非光滑方程组的解法。应用一种新的次微分的外逆，我们提出了牛顿法和不精确牛顿法，它们的收敛性同时也得到了证明。这种方法能更容易在一引起实际应用中实现。这种方法可以看作是已存在的解非光滑方程组的方法的延伸。     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

On outer automorphism groups of coxeter groups

Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ ₁ andΠ ₂ any two bases of the root system ofW, thenΠ ₂ = ±ωΠ ₁ for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett. This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards

We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.      

Outer product analysis of electronic nose and visible spectra: application to the measurement of peach fruit characteristics

Visual aspect and aroma are among the most important features of fruit that determine consumer preferences. Electronic nose and spectroscopic techniques have shown positive results in evaluating some basic analytical parameters of fruit and global features such as the cultivar.In this paper, we illustrate and discuss a study aimed at evaluating the improvement derived by the fusion of visible spectra and electronic nose data. These experiments were performed on a population of yellow peaches belonging to two cultivars. Each sample was measured by visible optical spectroscopy and by electronic nose. In addition, a number of reference parameters were also measured by conventional destructive methodologies.Collected data were analysed individually and then fused together in order to classify the two cultivars and to estimate the reference parameters. Data fusion was performed building the outer product matrix for each measurement. The set of matrices was then successively unfolded and analysed by conventional chemometrics tools.Results were improved using outer products, for instance in classification average percentage errors of 25, 10, and 7 for electronic nose, spectra, and outer product, respectively was achieved. Regression analysis provides the evidence of a substantial orthogonal appearance of the datasets, which offer former hidden information on fruit classification.     

Study of Sorption of 2,4‐D on Outer Peristaltic Part of Waste Tire Rubber Granules

From this study it was evident that outer peristaltic parts of waste tire granules gave the highest removal. Film and pore diffusions are the major factors controlling rates of sorption from solution by porous adsorbents. For sorption of 2,4‐D on waste tire rubber granules, the sorption rate coefficient of second‐order kinetic equation was utilized indirectly to determine the rate‐limiting step. The diffusion coefficient lies in the scale of 10^?8 cm²/s, and the pore diffusion coefficient is in the range of 10^?9–10^?10 cm²/s. So both film and pore diffusion are rate limiting. Considering external mass transfer from fluid to particle, using the effect of initial concentration, and using the effect of adsorbent size, no conclusion was reached regarding rate‐controlling steps. It is apparent from the study that external mass transfer (film diffusion) as well as intra‐particle diffusion (pore diffusion) play significant roles in the sorption process for 2,4‐D removal from water onto rubber granules.     

A comparison of the surface nanostructure from two different types of gram-negative cells: Escherichia coli and Rhodobacter sphaeroides

Bacteria have been studied using different microscopy methods for many years. Recently, the developments of high-speed atomic force microscopy have opened the doors to study bacteria in new ways due to the fact that it uses much less force on the sample while imaging. This makes the high-speed atomic force microscope an indispensable technique for imaging the surface of living bacterial cells because it allows for the high-resolution visualization of surface proteins in their natural condition without disrupting the cell or the activity of the proteins. Previous work examining living cells of Magnetospirillum magneticum AMB-1 demonstrated that the surface of these bacteria was covered with a net-like structure that is mainly composed of porin molecules. However, it was unclear whether or not this feature was unique to other living bacteria. In this study we used the high-speed atomic force microscope to examine the surface of living cells of Escherichia coli and Rhodobacter sphaeroides to compare their structure with that of M. magneticum. Our research clearly demonstrated that both of these types of cells have an outer surface that is covered in a network of nanometer-sized holes similar to M. magneticum. The diameter of the holes was 8.0 ± 1.5 nm for E. coli and 6.6 ± 1.1 nm for R. sphaeroides. The results in this paper confirm that this type of outer surface structure exists in other types of bacteria and it is not unique to Magnetospirillum.     

不同地区大气光学湍流内外尺度测量

 用光学湍流参数自动测量系统对内陆地区和沿海地区光学湍流内外尺度进行了大量的实验观测。分析了湍流尺度的日变化规律，给出了其频数分布。结果表明：两地内尺度的均值为十几mm，外尺度的均值约为2 m；内陆地区内尺度日变化趋势较为复杂，而外尺度的日变化趋势与湍流强度十分相似；沿海地区内外尺度与湍流强度均无明显关系。大气湍流尺度的大小和分布状态是随时间和空间变化的，因此，在估算实际大气湍流对光学系统的影响时，需要实测湍流尺度以便得到准确的结果。     

Multicategory ψ-Learning and Support Vector Machine: Computational Tools

Many margin-based binary classification techniques such as support vector machine (SVM) and ψ-learning deliver high performance. An earlier article proposed a new multicategory ψ-learning methodology that shows great promise in generalization ability. However,ψ-learning is computationally difficult because it requires handling a nonconvex minimization problem. In this article, we propose two computational tools for multicategory ψ-learning. The first one is based on d.c. algorithms and solved by sequential quadratic programming, while the second one uses the outer approximation method, which yields the global minimizer via sequential concave minimization. Numerical examples show the proposed algorithms perform well.     

Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze how the computational efficiency of a d.c.optimization algorithm depends on the representation we choose for the objective function, and we address the problem of characterizing and obtaining a computationally optimal representation. We introduce some theoretical concepts which are necessary for this analysis and report some numerical experiments.