等因数个数的数所成集合的最小元问题研究

给出了因数个数相同的数所构成的集合最小元的必要条件,以及特殊情形下的充分必要条件,得 到了某些情形下的最小元。

最大公因数矩阵的行列式

设Ｓ＝｛ｘ１，ｘ２，…，ｘｎ）是含ｎ个不同正整数的集合，（Ｓ）表示定义在Ｓ上的最大公因数矩阵，本文证明了且等号成立当且仅当Ｓ是最大公因数封闭集．

商品住宅经济性能的模糊综合评价

在分析探讨住宅经济性能指标体系的前提下 ,建立了基于模糊数学的经济性能综合评价方法 ,利用此方法对住宅经济性能可作出客观评价 。

minH(n)在n=∏ from i=1 to m q_i(m≤π(8×10^(15)))下的结果

证明了当n=∏ from i=1 to m q_i(qi是素数,qi>qi+1,i=1,2,…,m-1,m≤π(8×1015))时minH(n)=∏ from i=1 to m piqi-1。

Carmichael猜想的一个标注

Carmichael猜想是数论的一个经典猜想,很多数学家都对该猜想做过各种研究。Carl Pomerance是第1个对该猜想进行理论研究的,并提出了该猜想的一个充分条件。通过引进φ-子集概念,文章研究了关于未知数n的方程φ(n)=x的解的个数,证明该猜想的一个充要条件为:Carmichael猜想成立当且仅当猜想在集{2^43^37^243k,k为任意正整数}上成立。

LCM矩阵的可逆性与不定方程ayz+bzx+cxy=xyz+1的解(英文)

设Ｓ＝｛ｘ１，ｘ２，…ｘｎ｝是不同正整数的集合. 已经知道当ｎ≤７时在最大公因数封闭集Ｓ上的．ＬＣＭ矩阵是可逆的；也知道当ｎ≥９时有无限多个包含整数１的最大公因数封闭集它们的ＬＣＭ矩阵是奇异的；这篇文章的主要结果是证明当ｎ＝８且包含整数１时，除了２０个最大公因数封闭集外，其余所有最大公因数封闭集上的ＬＣＭ矩阵都是可逆的，而这归结为解一个不定方程．

GCD矩阵和LCM矩阵的性质

设S＝｛x1，x2，…，xn｝是含n个不同正整数的集合，（S）、［S］分别是定义在S上的GCD矩阵和LCM矩阵．给出了对偶因数封闭集的定义，讨论了对偶因数封闭集和最小公倍数封闭集上的矩阵（S）和［S］的性质．

Heavy metal distribution patterns and environmental quality assessment of the mariculture areas in Nanao,Shantou

The Fe, Zn, Mn and Pb concentrations in the seawater dissolved phase were investigated in the sea-surface microlayer （SML）, subsurface water （SSW） and bottom water （BW） samples collected at of three mariculture areas of the Nanao Island ocean zone. The results showed that the SML and the BW were important compartments for these heavy metals in the mariculture areas and the concentrations varied from 23.0 μg/L to 268.0 μg/L（Fe）, 11.0 μg/L to 82.2 μg/L（Zn）, 1.5 μg/L to 11.0 μg/L（Mn） and 6.0 μg/L to 40.5 μg/L（Pb） in SSW, while a clear enrichment is observed in the SML, where these ranged from 27.5 μg/L to 286.5 μg/L（Fe）, 13.5/lg/L to 89.0μg/L（Zn）, 3.0μg/L to 12.0 μg/L（Mn） and 7.0 μg/L to 46.0μg/L（Pb）. The enrichment factors were in the range of 1.07 - 1.39 which showed a slight enrichment. The average enrichment factors of Fe, Zn, Pb and Mn were 1.18, 1.13, 1.12 and 1.30, respectively. The average enrichment factors in shellfish, fish and gracilaria lemaneaformis farming areas were 1.26, 1.19 and 1.11, respectively, which showed that the surface activity was highest in the shellfish farming area. Furthermore, the heavy metals concentrations were lowest in the gracUaria lemaneaformis farming area. The results of single factor contamination index showed that the investigated areas were slightly contaminated with Zn, while the partial farming areas were seriously contaminated with Pd during a certain period of time.

Mining Weights of Land Evaluation Factors Based on Cloud Model and Correlation Analysis

The veracity of land evaluation is tightly related to the reasonable weights of land evaluation fac- tors. By mapping qualitative linguistic words into a fine-changeable cloud drops and translating the uncertain factor conditions into quantitative values with the uncertain illation based on cloud model, and then, inte- grating correlation analysis, a new way of figuring out the weight of land evaluation factors is proposed. It may solve the limitations of the conventional ways.

Inverse Estimation on Trigger Factors of Simultaneous Slope Failures with Purification of Training Data Sets

This paper presents an procedure for purifying training data sets （i.e., past occurrences of slope failures） for inverse estimation on unobserved trigger factors of ＂different types of simultaneous slope failures＂. Due to difficulties in pixel-by-pixel observations of trigger factors, as one of the measures, the authors had proposed an inverse analysis algorithm on trigger factors based on SEM （structural equation modeling）. Through a measurement equation, the trigger factor is inversely estimated, and a TFI （trigger factor influence） map can be also produced. As a subsequence subject, a purification procedure of training data set should be constructed to improve the accuracy of TFI map which depends on the representativeness of given training data sets of different types of slope failures. The proposed procedure resamples the matched pixels between original groups of past slope failures （i.e., surface slope failures, deep-seated slope failures, landslides） and classified three groups by K-means clustering for all pixels corresponding to those slope failures. For all cases of three types of slope failures, the improvement of success rates with respect to resampled training data sets was confirmed. As a final outcome, the differences between TFI maps produced by using original and resampled training data sets, respectively, are delineated on a DIF map （difference map） which is useful for analyzing trigger factor influence in terms of ＂risky- and safe-side assessment＂ sub-areas with respect to ＂different types of simultaneous slope failures＂.

Weekend and nighttime effect on the prognosis of peptic ulcer bleeding

AIM:To evaluate whether weekend or nighttime admission affects prognosis of peptic ulcer bleeding despite early endoscopy.METHODS:Retrospective data collection from four referral centers,all of which had a formal out-of-hours emergency endoscopy service,even at weekends.A total of 388 patients with bleeding peptic ulcers who were admitted via the emergency room between January 2007 and December 2009 were enrolled.Analyzed parameters included time from patients' arrival until endoscopy,mortality,rebleeding,need for surgery and length of hospital stay.RESULTS:The weekday and weekend admission groups comprised 326 and 62 patients,respectively.There were no significant differences in baseline characteristics between the two groups,except for younger age in the weekend group.Most patients (97%) had undergone early endoscopy,which resulted in a low mortality rate regardless of point of presentation (1.8% overall vs 1.6% on the weekend).The only outcome that was worse in the weekend group was a higher rate of rebleeding (12% vs 21%,P = 0.030).However,multivariate analysis revealed nighttime admission and a high Rockall score (≥ 6) as significant independent risk factors for rebleeding,rather than weekend admission.CONCLUSION:Early endoscopy for peptic ulcer bleeding can prevent the weekend effect,and nighttime admission was identified as a novel risk factor for rebleeding,namely the nighttime effect.

Analyses of local ingredients and dishes on menus of the Budapest-Middle-Danube touristic region

The background of the study is based on previous studies dealing with the areas of Transdanubia of Hungary. Those works have proved the hypothesis of author that local ingredients and dishes represent minimum role on menus. The question is how similar or different the choice of menus of Budapest-Middle-Danube compared with the previously examined areas of Hungary. There can be another question about the usage of local ingredients available near to the catering units. This piece of work has studied 79 menus of Budapest-Middle-Danube, Hungary. The material was collected from different types of restaurants, small restaurants （vendeglo in Hungarian） and roadside restaurants （csarda in Hungarian）. The method of the work was on the one hand, data collecting, and on the other hand, examination of the differences between the catering units in details： the number of dishes, the right order of dishes, the appearance of local ingredients and dishes, the consideration of seasonality, the usage of different cooking methods and group of dishes. The study reflects the main problems of countryside restaurants in Hungary. Only minimum number of dishes could be connected to local dishes out of more than thousands. All in all, dishes are not as precise and perfect as the ＂old ones＂, so that is why it is important for every expert keep the traditions alive in daily routines and strategic mean too.

Interaction of a circular cavity and a beeline crack in right-angle plane impacted by SH-wave

The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Firstly,we constructed a suitable Green's function,which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity while bearing out-of-plane harmonic line source load at arbitrary point.Secondly,based on the method of crack-division,integration for solution was established,then expressions of displacement and stress were obtained while crack and circular cavities were both in existence.Finally,the dynamic stress concentration factor around the circular cavity and the dynamic stress intensity factor at crack tip were discussed to the cases of different parameters in numerical examples.Calculation results show that the crack produces adverse engineering influence on both of the dynamic stress concentration factor and the dynamic stress intensity factor.

Variation in the timing of river entry of Atlantic salmon (Salmo salar L.) in the Baltic

The timing of river entry in the Atlantic salmon is known to depend on genetic, demographic and environmental factors, but little is known about the relative magnitude of among population and among year variation and covariation in this respect in natural state Atlantic salmon rives. To investigate this, variability in the timing of river entry in three historical Finnish Atlantic salmon populations were analyzed using salmon trap data collected during 1870- 1902. The analyses reveled that 1 ） the timing of river entry differed substantially and consistently among the rivers, and that 2） variation among the rivers was much larger than variation among years. Annual variations were not explained by regional environmental conditions, whereas in one river the timing of the local flood peak was a significant predictor of the timing of river entry. Differences in the timing of salmon entry to geographically closely situated rivers suggests that a regionally fixed opening date for coastal fisheries might not be the best management strategy as it may lead to uneven exploitation of salmon populations from different rivers [ Current Zoology 55 （5） ： 342 - 349, 2009] .

Teat Length and Lactation Period as A Predisposition Factor of Subclinical Mastitis in Dairy Cattle in Bandung, Indonesia

In order to improve the practical approach to clinical diagnosis of subclinical mastitis, 72 dairy cattle from KPSBU Lembang Bandung Regency was used in this research. The purpose of this research was to study the correlation between udder length and lactation period with the profile of subclinical mastitis. Lactation period data was collected from interviews with farmers. Subclinical mastitis testing by IPB-1 Mastitis Test reagent and udder length measured using measuring tape （cm）. Data was analyzed using Duncan test and logistic regression. The highest correlation of subclinical mastitis occurred to dairy cattle with average udder length of 7.5 cm and was in the third and forth lactation period. This result shows that udder length and lactation period of dairy cattle is a predisposing factor for subclinical mastitis. This finding is important to improve the milking management as well as a way to diagnose subclinical mastitis.

Factors Influencing the Success of Agricultural Information System （AIS）： A Factor Analysis

This study aims at investigating the AIS （Agricultural Information System） in Hamedan province, Iran, benefiting from the list of criteria for well functioning AISs that were identified in earlier researches. For this purpose, a survey method with multi-stage stratified random sampling technique was used to select 31 agricultural researchers, and 62 extension workers in the province. The data were acquired by questionnaire and structured interviews. The instrument for data collection was subjected to pre-testing, validation and reliability tests. The results of the factor analysis revealed that the criteria could be categorized into four overarching groups based on their inter-correlation. The analysis of mentioned criteria in Hamedan province AIS showed less efficiency and effectiveness than studies conducted in other areas. But among these, two desirable criteria existed. It is recommended that the ecological knowledge system （EKS） should be integrated with AIS, and some ecological and sustainable development criteria should be added to the existing ones.

Understanding human diseases with high-throughput quantitative measurement and analysis of molecular signatures

Microarray and deep sequencing technologies have provided unprecedented opportunities for mapping genome mutations,RNA transcripts,transcription factor binding,and histone modifications at high resolution at the genome-wide level.This has revolutionized the way in which transcriptomes,regulatory networks and epigenetic regulations have been studied and large amounts of heterogeneous data have been generated.Although efforts are being made to integrate these datasets unbiasedly and efficiently,how best to do this still remains a challenge.Here we review major impacts of high-throughput genome-wide data generation,their relevance to human diseases,and various bioinformatics approaches for data integration.Finally,we provide a case study on inflammatory diseases.

Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrdinger equations

A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.

mRNA enrichment protocols determine the quantification characteristics of external RNA spike-in controls in RNA-Seq studies

RNA-Seq promises to be used in clinical settings as a gene-expression profiling tool;however,questions about its variability and biases remain and need to be addressed.Thus,RNA controls with known concentrations and sequence identities originally developed by the External RNA Control Consortium(ERCC) for microarray and qPCR platforms have recently been proposed for RNA-Seq platforms,but only with a limited number of samples.In this study,we report our analysis of RNA-Seq data from 92 ERCC controls spiked in a diverse collection of 447 RNA samples from eight ongoing studies involving five species(human,rat,mouse,chicken,and Schistosoma japonicum) and two mRNA enrichment protocols,i.e.,poly(A) and RiboZero.The entire collection of datasets consisted of 15650143175 short sequence reads,131603796(i.e.,0.84%) of which were mapped to the 92 ERCC references.The overall ERCC mapping ratio of 0.84% is close to the expected value of 1.0% when assuming a 2.0% mRNA fraction in total RNA,but showed a difference of 2.8-fold across studies and 4.3-fold among samples from the same study with one tissue type.This level of fluctuation may prevent the ERCC controls from being used for cross-sample normalization in RNA-Seq.Furthermore,we observed striking biases of quantification between poly(A) and RiboZero which are transcript-specific.For example,ERCC-00116 showed a 7.3-fold under-enrichment in poly(A) compared to RiboZero.Extra care is needed in integrative analysis of multiple datasets and technical artifacts of protocol differences should not be taken as true biological findings.