On the Minimum Spanning Tree Determined by n Points in the Unit Square

Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.

The Translation of a Few Words With Old-Fashioned Meanings in Pride and Prejudice

Word meanings change with time. This paper analyzes the meanings of three language units from Jane Austen＇s Pride and Prejudice and their Chinese renderings by seven translators. These three units are recollect, handsome, and come upon the town. By studying the linguistic, situational, or cultural contexts of each language unit, the analysis shows that of the renderings of these three language units, the accuracy rate is three out of seven, one out of seven, and two out of seven respectively. The paper points out that one of the most important causes of the low accuracy rates is that these language units denote old-fashioned meanings. Another cause of the low accuracy rates is that some of the translators are not careful enough in their identification of the meanings of these language units. The paper suggests that in the translation of a classic novel like Pride and Prejudice, translators need to analyze carefully the linguistic, situational, or cultural contexts of a tricky language unit in the novel for very likely it denotes an old-fashioned meaning. Translators could also consult and compare what a tricky language unit means in other places of the novel, use an encyclopedic dictionary instead of a dictionary of contemporary English, and study the notes on tricky words in the novel made by established scholars.

The Calendar Anomalies of Stock Return in Thailand

This paper aims to examine the existence of calendar anomalies including month-of-year effect, turn-of-month effect, and weekend effect in Thai stock market. The stock return is computed from SET index during 1988 to 2009 and the SET50 index gathered since it was created in 1995. The unit root test is performed to ensure that the stock return series have no unit root. The multiple regression techniques using dummy variables are employed to test the difference of the return during each calendar anomalies period. If the regression model suffers from conditional heteroskedasticity, the GARCH （1, 1） model will be used instead of normal ordinary least square regression. It was found that the calendar anomalies exist in Thai stock market. The return is abnormally high during December and January, which can be addressed to be the turn-of-year effect. The return during the turn-of-month period, which can be defined as the last trading day and the first four trading days of the following months, is also abnormally high. Finally, the return is also abnormally high on Fridays but abnormally low on Mondays, which is addressed as weekend effect. This may create the opportunity to make above-average profit to investors exploiting these calendar anomalies. Although these calendar anomalies may be difficult to be exploited in practice because of transaction costs and ability to replicate the stock index, the existing evidence of calendar anomalies can help investors as the clue for the timing of investment.

Recognition of Production and Morphological Traits in Macoei Sheep Breed

In this study, the data of Macoei sheep from 1994 to 2008 were collected in Affair Animal Breeding Unit, Agriculture Organization of West Azerbijan province of Iran for recognition of reproductive and morphological characteristics. The trait in this research include birth weight （BW）, 3 （W3）, 6 （W6）, 9 （W9）, 12 （W12） months weight, fleece weight （WF） （as production traits）, body length（BL）, size of femur（F）, thorax（TX）, testis（TS）, height of lumber（L） and shoulder（SH） （as morphological traits）. Variance components, least square means and standard error of production and morphological traits were estimated and environmental factors （including effects of year of birth, season, sex, type of birth and age of dam） were studied with GLM procedure of SAS 9.1 software. The results showed that the all environmental factors have significant effect, male lambs weight more than females, and twins were more performance than single. Production and apparent performance characteristics of phenotypic traits was different in year of birth, maternal age, season. This study shows that Macoie sheep breed at the various management environment have suitable performance and genetic potential.

C_∞ Compactness for Minimal Submanifolds in the Unit Sphere

In this paper we study the C3 compactness for minimal submanifolds in the unit sphere. We obtain two compactness theorems. As an application, we prove that there is a positive number δ(n), such that if the square of the length of the second fundamental form of a minimal subrnanifold in the unit sphere is less than 2n/3+δ(n), it must be totally geodesic or diffeomorphic to a Veronese surface.

Effects of microcracks on the poroelastic behaviors of a single osteon

It has been suggested that microcracks do play a key role in the triggering of the bone remodeling process.In order to evaluate the influence of microcracks on the poroelastic behaviors of an osteon,a finite element model is established and investigated by using the Comsol Multiphysics software.The findings show that the presence of a microcrack in the osteon wall strongly modifies(enlarges)its local fluid pressure and velocity.Especially,the pressure and velocity amplitudes produced in the microcracked region are larger than those of the non-cracked region.Thus,this study can also be used for proposing a likely mechanism that bone can sense the changes of surrounding mechanical environments.

ADRC BASED INPUT DISTURBANCE REJECTION FOR MINIMUM-PHASE PLANTS WITH UNKNOWN ORDERS AND/OR UNCERTAIN RELATIVE DEGREES

The capability of ADRC is studied for linear time-invariant SISO minimum-phase systems with unknown orders, uncertain relative degrees, and unknown input disturbances. It is proved that ADRC can reject the unknown input disturbance and guarantee the close-loop stability for the plants with unknown but bounded relative degrees. Meanwhile, some close-loop performances can be achieved. The influence of the sensor noise is also discussed. And it is demonstrated by numerical examples that one ADRC with fixed parameters can be applied to a group of plants of different orders, relative degrees, and parameters.

Robust structured total least squares algorithm for passive location

A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted structured total least squares(WSTLS)framework and improved based on the robust estimation theory.Moreover, the improved Danish weight function is proposed according to the robust extremal function of the WSTLS, so that the new algorithm can detect outliers based on residuals and reduce the weights of outliers automatically. Finally, the inverse iteration method is discussed to deal with the RSTLS problem. Simulations show that when outliers appear, the result of the proposed algorithm is still accurate and robust, whereas that of the conventional algorithms is distorted seriously.