THE CAUCHY INTEGRAL OF MANY COMPLEX VARIABLES PASSIVE OPERATORS AND MULTIDIMENSIONAL DISPERSION RELATIONS

This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance

Effect of Correlation Level on the Use of Auxiliary Variable in Double Sampling for Regression Estimation

While an auxiliary information in double sampling increases the precision of an estimate and solves the problem of bias caused by non-response in sample survey, the question is that, does the level of correlation between the auxiliary information x and the study variable y ease in the accomplishment of the objectives of using double sampling? In this research, investigation was conducted through empirical study to ascertain the importance of correlation level between the auxiliary variable and the study variable to maximally accomplish the importance of auxiliary variable(s) in double sampling. Based on the Statistics criteria employed, which are minimum variance, coefficient of variation and relative efficiency, it was established that the higher the correlation level between the study and auxiliary variable(s) is, the better the estimator is.

On the Relationship between Climatic Variables and Pressure Systems over Saudi Arabia in the Winter Season

The synoptic circulation over Saudi Arabia is complicated and frequently governed by the effect of large-scale pressure systems. In this work, we used NCEP–NCAR global data to illustrate the relationship between climatic variables and the main pressure systems that affect the weather and climate of Saudi Arabia, and also to investigate the influence of these pressure systems on surface air temperature（SAT） and rainfall over the region in the winter season. It was found that there are two primary patterns of pressure that influence the weather and climate of Saudi Arabia. The first occurs in cases of a strengthening Subtropical High（Sub H）, a weakening Siberian High（Sib H）, a deepening of the Icelandic Low（Ice L）, or a weakening of the Sudanese Low（Sud L）. During this pattern, the Sub H combines with the Sib H and an obvious increase of sea level pressure（SLP） occurs over southern European, the Mediterranean, North Africa, and the Middle East. This belt of high pressure prevents interaction between midlatitude and extratropical systems, which leads to a decrease in the SAT,relative humidity（RH） and rainfall over Saudi Arabia. The second pattern occurs in association with a weakening of the Sub H, a strengthening of the Sib H, a weakening of the Ice L, or a deepening of the Sud L. The pattern arising in this case leads to an interaction between two different air masses： the first（cold moist） air mass is associated with the Mediterranean depression travelling from west to east, while the second（warm moist） air mass is associated with the northward oscillation of the Sud L and its inverted V-shape trough. The interaction between these two air masses increases the SAT, RH and the probability of rainfall over Saudi Arabia, especially over the northwest and northeast regions.

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.

Batch process monitoring based on WGNPE–GSVDD related and independent variables

In many batch processes, there are related or independence relationships among process variables. The traditional monitoring method usually carries out a single statistical model according to the related or independent method, and in the feature extraction there is not fully taken into account the characterization of fault information, it will make the process monitoring ineffective, so a fault monitoring method based on WGNPE(weighted global neighborhood preserving embedding)–GSVDD(greedy support vector data description) related and independent variables is proposed. First, mutual information method is used to separate the related variables and independent variables. Secondly, WGNPE method is used to extract the local and global structures of the related variables in batch process and highlight the fault information, GSVDD method is used to extract the process information of the independent variables quickly and effectively. Finally, the statistical monitoring model is established to achieve process monitoring based on WGNPE and GSVDD. The effectiveness of the proposed method was verified by the penicillin fermentation process.

Presence of circulating tumor cells is associated with metabolic-related variables in postoperative patients with early-stage breast cancer

Objective：Although circulating tumor cells（CTCs）have been well-established as promising prognostic biomarkers in both early breast cancer and metastatic settings,little is known regarding the prognostic relevance of CTCs in the long-term postoperative monitoring of patients with non-metastatic breast cancer（non-MBC）.In this study,we investigated the associations of CTCs with clinicopathological features and metabolic-related variables,such as obesity and hyperglycemia.Methods：In this retrospective study,we recruited 264 patients with postoperative stage Ⅰ–Ⅲ breast cancer at Guangdong General Hospital from January 2009 to December 2015.The prevalence and number of CTCs were assessed using the Cell Search System at a median time of 19.0 months[interquartile range（IQR）,7.8–33.0]after surgery.The CTC assay results were correlated with the clinicopathological features and metabolic-related variables.A multivariate logistic regression analysis was performed to further determine the independent predictors of CTCs.Results：CTCs were detected in 10.6%of all patients.The positive rate of CTCs in patients with infiltrating ductal carcinoma was lower than that in patients with other pathological types（9.0%vs.28.6%,P=0.020）.More importantly,the presence of CTCs was correlated with blood glucose level（P=0.015）and high-density lipoprotein level（P=0.030）.The multivariate logistic regression analysis showed that the pathological type[odds ratio（OR）：1.757,95%CI：1.021–3.023;P=0.042]and blood glucose level（OR：1.218,95%CI：1.014–1.465;P=0.035）were independent predictors of the presence of CTCs.Conclusions：This study revealed potential associations between CTCs and metabolic-related factors in Chinese patients with non-MBC and supports the hypothesis that metabolic dysfunction in breast cancer patients might influence the biological activity of metastatic breast cancer,leading to a higher prevalence of CTCs.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

New Refinement Relations of Z Specifications for Multiple Viewpoints Oriented Requirements Method

In this paper we develop several new refinement relations of Z for multiple viewpoints oriented requirements method (MVORM). The original motivation is that we found the standard Z refinement relation is not adequate or correct when considering specifications that have temporal relationships of operations. The concept of temporal state variables is introduced into Z. Then new implementation relations are defined and new refinement relations are deduced, mainly for temporal state variables to process temporal relationships of operations. We use state transition systems to abstract the temporal state transitions. A simple example is used to show the procedures of MVORM. Finally some directions of further work are forwarded.

Towards an Algebraic Theory of Orthogonal Polynomials in Several Variables

In this paper, we review on a general theory of orthogonal polynomials in several variables (O.P.S.V) in which we present two different approaches for the three-term recurrence relation. We draw attention to the fact that it is possible to take advantage of the orthogonal projection approach of the three-term recurrence relation towards the development of the algebraic theory of O.P.S.V.

On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments

In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.

The Equation of the Universe (According to the Theory of Relation)

A new equation is found in which the concept of matter-space-time is mathematically connected;gravitation and electromagnetism are also bound by space-time. A mechanism is described showing how velocity, time, distance, matter, and energy are correlated. We are led to ascertain that gravity and electricity are two distinct manifestations of a single underlying process: electro-gravitation. The force of gravitation arises of electromagnetism—inherently much stronger—divided by the cosmological space-time. The radius of space-time belongs to the family of electromagnetic waves: the wavelength is the radius (1026 m) of the universe and the period (1017 s) is its cosmological age. For the first time, the cosmological time, considered as a real physical object, is integrated into a “cosmological equation” which makes coherent what we know regarding the time (its origin, its flow …), the matter, and space. It sets up a mathematical model allowing us to interpret dark energy (or cosmological constant) as being both “negative” and “tired” energy. After an introduction with a brief history of unifications and the presentation of two roughly equal ratios arising out from Dirac’s large-number hypotheses which relate to the ratio of electric force to gravitational force and the ratio of the age of the universe to the atomic time unit associated with atomic processes, we present in §2 this new equation of quantum cosmology which operates the reconciliation between the macrocosm and the microcosm. In §3 and §4, we discuss the irreversible cosmological time resulting from the equation, as well as the role of the mass (heavy) relative to the gravitational constant G. In §5 we discuss the links that the equation establishes between gravitation (structure of condensation) and electromagnetism (structure of expansion), between relativity and quantum theory. We apply the formula to Planck’s time. We speak of the new essential variable? ?, and briefly of a new principle, the principle of compensation. In §6 we discuss the negative energy solutions banned by physics, and we deplore that half of the universe escapes us. We present the electro-gravitation in §7, from the equation which represents a super hydrogen atom. In § 8 we show that the global mass (gravitational) is variable: it increases during the expansion while the mass of the elementary particles decreases. In §9 we approach the spontaneous symmetry breaking;when it occurs, the arrows of the equation are momentarily reversed: such a mechanism would apply to the Allais effect, also mentioned in §6.4. §10 and §11 deal with the energy linked by the equation to matter through expansive space-time. The equation transforms electromagnetic kinetic energy into a gravitational mass, considered as a potential energy. Entropy increases according to the arrow of time towards the future. In §12 we discuss of the prevailing theory of inflation. We note the similarity between the proclaimed acceleration of current expansion and inflation. Physicists have interpreted the positive cosmological constant in terms of vacuum energy which would be 10120 times higher than the dark energy density deduced from the astronomical measurements. However, the high theoretical value of the vacuum energy (and the cosmological constant) has no observable pending in the cosmos. In §13 we suggest that these several orders of magnitude difference problem are solved by the theory of relation, which indicates a deceleration of the expansion. Finally, in § 14, we close by speaking of a model of cyclic universe and about the object of this paper, a dynamic equation that allows to build a quantum cosmology.

Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling

In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.

Cultural Variables and International Business

By analyzing a set of dynamic variables of culture, this paper reaches the conclusion that there is a link between successful global business and cultural awareness and sensitivity.

具有系数相关性的可变分数时延滤波器设计方法

针对可变分数时延滤波器设计中的复杂度问题提出一种设计方法,将时域插值与泰勒级数展开相结合对Farrow结构进行系数配置,推导出相应的滤波器系数相关公式。该方法设计出的滤波器具有系数相关性,可使近一半滤波器系数独立,并得到低复杂度的滤波器实现结构。从复杂度、幅频响应及群时延、误差方面进行理论推导和仿真验证,分析结果表明,所提方法能有效降低可变分数时延滤波器的复杂度和计算成本。

基于灰色关联机理组合模型的压缩机电功率预测

为了精确获得压缩机电功率,通过变频滚动转子制冷系统实验台,根据灰色关联(GRM(1,m))预测模型样本需求量少、预测精度高与机理(Mechanism)模型能够反映系统本质特性的特点,利用Matlab语言编程建立GRM(1,m)-Mechanism组合预测模型。通过3种模型对压缩机电功率进行预测,结果表明:GRM(1,m)-Mechanism组合模型的预测精确性和适用性更好,其最大相对误差、平均相对误差分别为4.05%,1.71%;比机理模型分别降低了1.29%,1.09%;比灰色关联(GRM(1,m))预测模型降低了1.02%,2.19%。最后,通过压缩机变转速试验验证组合模型预测平均相对误差在1.9%以内,进一步证明GRM(1,m)-Mechanism组合模型的精确性和适用性。

河西走廊潜在蒸散发时空格局变化与气象因素的关系

蒸散发过程影响因素众多,潜在蒸散发(ET_0)与气象变量交互作用复杂,亟需揭示ET_0变化对气象变量的响应机理。基于河西走廊及周边21个气象站点气象资料,采用定性定量分析方法,以河西走廊整体及3分区2个空间尺度,揭示ET_0时空变化规律,明确ET_0对各气象因素变化敏感性及贡献。结果表明:(1)河西走廊及分区ET_0均呈显著波动上升趋势(Z>1.98),线性变化率2.94 mm·a~(-1),且黑河分区变化最明显。(2)ET_0由东南向西北递增变化,中东部石羊河分区(1003.78 mm)、黑河分区(1031.30 mm)较小,西部疏勒河分区(1171.89 mm)较大。(3)河西走廊ET_0对气象因素变化敏感性排序为相对湿度(RH)、日最高气温(T_(max))、日照时数(n)、平均风速(u)、日降水量(P),ET_0对RH减少最敏感,对P变化最不敏感。(4)u增大是造成河西走廊ET_0增大的主要原因,其次是RH减少、T_(max)升高、n增加。(5)疏勒河分区、黑河分区、石羊河分区ET_0呈增加变化,贡献最大因素分别为T_(max)(5.13%)、u(8.22%)、T_(max)(5.97%),贡献最小因素为n。气候因素中的风速和气温变化是河西走廊地区ET_0变化不容忽视的重要影响因素,研究成果对合理规划农田灌溉用水和提高农业水资源利用效率意义重大。

杭州市钱塘新区地下空间开发地质环境适宜性评价

地下空间地质环境适宜性评价是实现地下空间合理有序开发的重要环节,也是国土空间科学规划的必要前提。通过系统分析杭州市钱塘新区地质环境条件,从地形地貌、工程地质条件、水文地质条件、活动断裂及地震效应、环境地质问题等五个方面选取15个指标构建了地下空间开发地质环境适宜性评价指标体系。在此基础上,采用变权层次分析法和灰色关联分析模型,对浅层(0~15m)、次浅层(15~30m)、次深层(30~50m)地下空间进行了开发利用地质环境条件适宜性评价。结果表明,研究区浅层和次深层地下空间更适宜开发,而次浅层地下空间适宜性好和适宜性较好的总面积仅占全区的45.7%,地质环境条件复杂,具有一定的开发难度。该结果可为钱塘新区地下空间合理开发提供参考。

面向非平稳时间序列的因果关系发现算法

针对传统因果关系算法不能分析非平稳时间序列和可变时滞时间序列数据因果关系的问题,本文提出一种基于分段聚合近似可变时滞转移熵(PAAVL-TE)的因果关系算法。利用分段聚合近似法对时间序列进行转换,提取时间序列的特征信息,运用动态时间弯曲距离寻找相似程度最高的时间序列计算可变时滞时间序列的转移熵,实现了非平稳时间序列的因果分析。通过计算机仿真模拟实验将提出的算法与存在的算法相比较,证实算法有效性。将该算法用于北京市昌平区PM 2.5浓度和气象数据分析,表明本文算法具有广泛的应用性。

心率变异性与献血前心理评估的相关性研究

目的探讨献血者心率变异性(HRV)与献血前紧张程度之间是否存在关联。方法用心理焦虑自评量表(SAS)和紧张程度评估253名献血者献血前心理状态并分析其HRV时域和频域参数,分析SAS评分、紧张程度、HRV参数3者之间的相关性,比较不同类型献血者的差异性,并进行多元线性回归分析。结果247名献血者纳入分析,18~24岁献血者的HRV参数中有5项高于25岁以上献血者(P均<0.05),女性献血者焦虑程度(SAS评分41~46)高于男性(SAS评分35~43)(P<0.001);献血前SAS评分与紧张程度评估结果高度一致(r=0.970,P<0.001);献血前紧张程度、SAS评分均与HRV参数中的极低频(VLF)呈显著负相关(r=0.179,P=0.005),且关联独立于年龄、身体质量指数、性别等混杂因素(P<0.05)。结论HRV作为1种献血前心理评估工具,相对SAS和紧张程度评估,展现出更高的客观性,将HRV列入献血者常规筛查,可以评估献血前献血者焦虑程度,识别潜在的献血相关血管迷走神经反应(DRVR)风险人群,进而提升献血安全。