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Ni₄₂Cu₅Ti₂₀Zr_21.5Al₈Si_3.5 bulk metallic glasses rods with diameters of 1 mm and 3 mm, were prepared by arc melting of composing elements in a Ti-gettered argon atmosphere. The compressive deformation and fracture behavior of the amorphous alloy samples with different size were investigated by testing machine and scanning electron microscope. The compressive stress-strain curves of 1 mm and 3 mm samples exhibited 4.5% and 0% plastic strain, while the compressive fracture strength for 1 mm and 3 mm rod is 4691 MPa and 2631 MPa, respectively. The compressive fracture surface of different size sample consisted of shear zone and non-shear one. Typical vein patterns with some melting drops can be seen on the shear region of 1 mm rod, while fish-bone shape patterns can be observed on 3 mm specimen surface. Some interesting different spacing periodic ripples existed on the non-shear zone of 1 and 3 mm rods. On the side surface of 1 mm sample, high density of shear bands was observed. The skip of shear bands can be seen on 1 mm sample surface. The mechanisms of the effect of sample size on fracture strength and plasticity of the Ni-based amorphous alloy are discussed.

The sample size based on the Linex loss function and Blinex loss function is studied in this paper, and the analytical solution of the optimal sample size is deduced on the assumption that the Linex loss function and the normal distribution exist. For the Blinex loss function, an accurate algorithm was presented to obtain the optimal sample size. Furthermore, the optimal sample size is obtained, respectively, by taking Poisson distribution and normal distribution as examples. Due to the wide application of Blinex function in reality, the algorithm presented in this paper has immediate applications.

In industry, bogey testing, also known as the zero-failure testing, is often used to demonstrate that a product achieves the required reliability at a high confidence level. This test method is simple to apply; however, it requires excessive test time and/or a large sample size, and thus is usually unaffordable. For some products whose failure is defined as a performance characteristic exceeding a threshold, it is possible to measure the performance characteristic during testing. The measurement data can be employed to predict whether or not a test unit will fail by the end of test. When there are sufficient data to make such a prediction with a high degree of confidence, the test of the unit can be terminated. As a result, the test time is reduced. Yang studies the test time reduction for Weibull and binomial distributions.¹ This paper describes the test method for lognormal distribution. In particular, this paper describes the sample size, degradation models, and cost function for the lognormal distribution. Then the paper describes the optimum test plans, which choose the optimal sample size and the expected test time, by minimizing the total test cost and simultaneously satisfying the constraints on the type II error and the available sample size. An example is given to illustrate the test method.

Survey analysis method is widely used in many areas such as social study, marketing research, economics, public health, clinical trials and transportation data analysis. Minimum sample size determination is always needed before a survey is conducted to avoid huge cost. Some statistical methods can be found from the literature for finding the minimum required sample size. This paper proposes a method for finding the minimum total sample size needed for the survey when the population is divided into cells. The proposed method can be used for both the infinite population case and the finite population case. A computer program is needed to realize the sample size calculation. The computer program the authors used is SAS/IML, which is a special integrated matrix language (IML) procedure of the Statistical Analysis System (SAS) software.

Post hoc assignment of patterns determined by all pairwise comparisons in microarray experiments with multiple treatments has been proven to be useful in assessing treatment effects. We propose the usage of transitive directed acyclic graphs (tDAG) as the representation of these patterns and show that such representation can be useful in clustering treatment effects, annotating existing clustering methods, and analyzing sample sizes. Advantages of this approach include: (1) unique and descriptive meaning of each cluster in terms of how genes respond to all pairs of treatments; (2) insensitivity of the observed patterns to the number of genes analyzed; and (3) a combinatorial perspective to address the sample size problem by observing the rate of contractible tDAG as the number of replicates increases. The advantages and overall utility of the method in elaborating drug structure activity relationships are exemplified in a controlled study with real and simulated data.

In our previous study, the empirical relationship between Sharpe measure and its risk proxy was shown to be dependent on the sample size, the investment horizon and the market conditions. This important result is generalized in the present study to include Treynor and Jensen performance measures. Moreover, it is shown that the conventional sample estimate of ex ante Treynor measure is biased. As a result, the ranking of mutual fund performance based on the biased estimate is not an unbiased ranking as implied by the ex ante Treynor measure. In addition, a significant relationship between the estimated Jensen measure and its risk proxy may produce a potential bias associated with the cumulative average residual technique which is frequently used for testing the market efficiency hypothesis. Finally, the impact of the dependence between risk and average return in Friend and Blume’s findings is also investigated.

No abstract received.

Many methods for inferring species trees from gene trees have been developed when incongruence among gene trees is due to incomplete lineage sorting. A method called STAR (Liu et al, 2009), assigns values to nodes in gene trees based only on topological information and uses the average value of the most recent common ancestor node for each pair of taxa to construct a distance matrix which is then used for clustering taxa into a tree. This method is very efficient computationally, scaling linearly in the number of loci and quadratically in the number of taxa, and in simulations has shown to be highly accurate for moderate to large numbers of loci as well as robust to molecular clock violations and misestimation of gene trees from sequence data. The method is based on a particular choice of numbering nodes in the gene trees; however, other choices for numbering nodes in gene trees can also lead to consistent inference of the species tree. Here, expected values and variances for average pairwise distances and differences between average pairwise distances in the distance matrix constructed by the STAR algorithm are used to analytically evaluate efficiency of different numbering schemes that are variations on the original STAR numbering for small trees.