On the determination and construction of optimal row-column designs having unequal row and column sizes

In this paper we consider experimental situations requiring usage of a row-column design where v treatments are to be applied to experimental units arranged in b ₁ rows and b ₂ columns where row i has size k _1i , i=1,..., b ₁ and column j has size k _2j , j=1,..., b ₂. Conditions analogous to those given in Kunert (1983, Ann. Statis., 11, 247–257) and Cheng (1978, Ann. Statist., 6, 1262–1272) are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.Visiting from the Indian Statistical Institute.     

Strength properties of the human aorta and their variation with age

Conclusions 1. The strength of the aorta wall in a direction transverse to the vessel axis exceeds the strength in the longitudinal direction by on average a factor of 1.9 in the thoracic and 1.8 in the abdominal sections.2. The strength of the wall of the thoracic aorta is greater than that of the abdominal aorta. The differences between the strength characteristics of the aortal wall in the transverse direction are statistically reliable (up to 8th decade of life).3. As the organism ages, the strength of the walls of the thoracic and abdominal aortas decreases in the longitudinal and transverse directions. This is indicated by the close inverse correlation between ₁, ₂ and age.4. The strength of the aorta wall changes according to the period or stage of life. In each stage it is approximated by an exponential function.5. The rate of decrease of the strength of the wall is less in the transverse than in the longitudinal direction during the initial or evolutive stage of life.6. The decrease in strength (according to the criteria , , ) indicates more rapid aging of the tissues of the abdominal (relative to the thoracic) aorta. This difference appears after the age of 40 in the transverse and 50 in the longitudinal direction of the aorta wall.Chita State Medical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 104–108, January–February, 1977.     

高强砼的轴心抗拉强度的分析计算

对国内有关轴拉试验结果进行了分析,说明高强混凝土轴心受拉强度与普通混凝土轴心受拉强度是有差异的.并给出了计算模型.     

高强混凝土立方强度尺寸效应的分析计算

对55组高强混凝土立方强度实测数据作了分析,并给出了计算公式.表明高强混凝土立方强度尺寸效应不同于普通混凝土.     

Kinetic approach to the collisional positive column

Zusammenfassung Es sollen ein Einblick in die Geschwindigkeitsverteilungsfunktion für Ionen in der Nähe der Grenze zwischen Plasma und Hülse in der positiven Stoßsäule erhalten und die Ergebnisse Friedmans mans für das gleiche Gebiet, bei denen makroskopische nicht-linearen Gleichungen angenommen waren, bestätigt werden. Eine Form der BGK-Gleichung wird annäherungsweise gelöst, wobei die unbekannte Temperatur durch die lineare Diffusiontheorie von Schottky ermittelt wurde.Die in der Verteilungsfunktion der Ionen enthaltene unbekannte Temperatur kann näherungsweise durch die Summe von Elektronen- und Ionen-Temperatur ermittelt werden. Wir erhalten die ambipolare Geschwindigkeitsverteilung an der Grenze zwischen Plasma und Hülse, die genau mit den Ergebnissen der Friedman-Analyse für die Hülsen-Stabilität übereinstimmt, bei der die Eintrittsgeschwindigkeit der ambipolaren Schallgeschwindigkeit gleichgesetzt war. Mit der Bedingung, dass alle die Wände berührenden Ionen durch die Wände absorbiert werden, erhalten wir die Beziehung zwischen der Stossfrequenz der Ionen und der Ionisations-Stossfrequenz, die das gleiche Ergebnis wie bei Friedman zeigt.     

The behavior of the QR-factorization algorithm with column pivoting

A bound on the performance of QR-factorization with column pivoting is derived and two classes of matrices are constructed for which the bound is sharp or asymptotically sharp.     

Reducing the construction cost of the component-by-component construction of good lattice rules

The construction of randomly shifted rank- lattice rules, where the number of points is a prime number, has recently been developed by Sloan, Kuo and Joe for integration of functions in weighted Sobolev spaces and was extended by Kuo and Joe and by Dick to composite numbers. To construct -dimensional rules, the shifts were generated randomly and the generating vectors were constructed component-by-component at a cost of operations. Here we consider the situation where is the product of two distinct prime numbers and . We still generate the shifts randomly but we modify the algorithm so that the cost of constructing the, now two, generating vectors component-by-component is only operations. This reduction in cost allows, in practice, construction of rules with millions of points. The rules constructed again achieve a worst-case strong tractability error bound, with a rate of convergence for 0$">.

     

Large-scale optimization with the primal-dual column generation method

The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant allows to obtain suboptimal and well-centered dual solutions which naturally stabilizes the column generation process. As recently presented in the literature, reductions in the number of calls to the oracle and in the CPU times are typically observed when compared to the standard column generation, which relies on extreme optimal dual solutions. However, these results are based on relatively small problems obtained from linear relaxations of combinatorial applications. In this paper, we investigate the behaviour of the PDCGM in a broader context, namely when solving large-scale convex optimization problems. We have selected applications that arise in important real-life contexts such as data analysis (multiple kernel learning problem), decision-making under uncertainty (two-stage stochastic programming problems) and telecommunication and transportation networks (multicommodity network flow problem). In the numerical experiments, we use publicly available benchmark instances to compare the performance of the PDCGM against recent results for different methods presented in the literature, which were the best available results to date. The analysis of these results suggests that the PDCGM offers an attractive alternative over specialized methods since it remains competitive in terms of number of iterations and CPU times even for large-scale optimization problems.     

On column generation formulations for the RWA problem

We present a review of several column generation formulations for the Routing and Wavelength Assignment (rwa) problem with the objective of minimizing the blocking rate. Several improvements are proposed, together with a comparison of the different formulations with respect to the quality of their continuous relaxation bounds and their computing solution ease. Experimental results are presented on several classical network and traffic instances.     

冲击模型中强度的预测

提出了冲击强度预测模型。结合历史数据信息,用线性最小方差方法给出了冲击强度未来n步的预测值,并在正态假设下,推导出预测值Y_t+n｜Y_t,Y_t-1,…的置信水平为1-α的置信区间。     

Nonlinear breakup of a self-gravitating column

Using the method of strained coordinates, a weakly nonlinear theory of the breakup of a gravitating column is presented. It is shown that the self-gravitating column breaks into the main celestial bodies and their satellites whose dimensions are sensitive to the wavenumbers.     

On the choice of explicit stabilizing terms in column generation

Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewise-linear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameters), and their relationships with the quality of the initial dual estimates, on the overall effectiveness of the approach are reported, providing practical guidelines for selecting the most appropriate variant in different situations.     

The shape of the strongest column with a follower load

An elastic column subjected to a follower load loses stability, as the load increases, through undamped oscillations around its equilibrium position (flutter). For a column with fixed volume and varying but similar cross section, the existence of a critical load is shown rigorously. The necessary conditions for making the critical load and the fundamental frequency of the column stationary with respect to variations in the column shape are derived. A numerical method for finding the optimal shape is given.     

On the invariance of perturbed null vectors under column scaling

Summary It is shown that the approximate null vector of a perturbed degenerate matrix behaves linearly under column scaling up to second order terms in the perturbation. This result has important consequences for an estimation technique known to numerical analysts as total least squares and to statisticians as latent root regression.Dedicated to F.L. Bauer on the occasion of his 60th birthdayDepartment of Computer Science and Institute for Physical Science and Technology, University of Maryland at College Park. This work was done while the author was at the Scientific Computing Division of the National Bureau of Standards