The Hawking Hubble Temperature as the Minimum Temperature, the Planck Temperature as the Maximum Temperature, and the CMB Temperature as Their Geometric Mean Temperature

Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble temperature and the maximum Planck temperature of the expanding universe over the course of cosmic time. This mathematical discovery suggests a re-consideration of Rh=ctcosmological models, including black hole cosmological models, even if it possibly could also be consistent with the Λ-CDM model. Most importantly, this paper contributes to the growing literature in the past year asserting a tightly constrained mathematical relationship between the CMB temperature, the Hubble constant, and other global parameters of the Hubble sphere. Our approach suggests a solid theoretical framework for predicting and understanding the CMB temperature rather than solely observing it.1.

Geometric Mean Decomposition Based Hybrid Precoding for Millimeter-Wave Massive MIMO

Hybrid precoding can reduce the number of required radio frequency(RF)chains in millimeter-Wave(mmWave) massive MIMO systems. However, existing hybrid precoding based on singular value decomposition(SVD) requires the complicated bit allocation to match the different signal-to-noise-ratios(SNRs) of different sub-channels. In this paper,we propose a geometric mean decomposition(GMD)-based hybrid precoding to avoid the complicated bit allocation. Specifically,we seek a pair of analog and digital precoders sufficiently close to the unconstrained fully digital GMD precoder. To achieve this, we fix the analog precoder to design the digital precoder, and vice versa. The analog precoder is designed based on the orthogonal matching pursuit(OMP) algorithm, while GMD is used to obtain the digital precoder. Simulations show that the proposed GMD-based hybrid precoding achieves better performance than the conventional SVD-based hybrid precoding with only a slight increase in complexity.

基于混沌理论与蜉蝣优化K-means算法的变压器绕组松动故障特征分析方法

为了更加准确有效地对变压器绕组状态进行分析,提出了一种基于混沌理论与蜉蝣优化K-means算法的变压器绕组松动故障特征分析方法。首先,运用C-C法重构变压器振动信号的相空间,分析变压器振动信号的混沌特性,得到关联维数、Kolmogorov熵作为混沌特征。然后,将蜉蝣优化算法引入K-means聚类分析中,对高维相空间轨迹的簇中心选取进行优化,得到相轨迹的簇中心矩之和、矢径偏移,并作为几何特征。实验结果表明:变压器振动信号的最大Lyapunov指数均大于0,适用于混沌特性分析;由变压器振动信号计算出的混沌特征能够表征变压器绕组的松紧程度;同时,经蜉蝣优化的K-means算法得到的簇中心能够作为特征点提取整个相空间轨迹的几何特征,也能够区分绕组的松动故障;将两种特征结合能够实现变压器绕组状态的准确监测,从而为变压器绕组在线检修提供了一种理论依据。

Sample geometric mean versus sample median in closed form framework of seismic reliability evaluation: a case study comparison

Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results.

An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not equal to?b ?

Assessment and Potential Survey of Lands in Khuzestan Province Using the Buckley Geometric Mean Model and Geographic Information System (GIS)

Today environmental assessment is considered and used as the basis and foundation of any kind of human activity. This is the science which gives human the consciousness about abilities and disabilities of his surroundings. This study tried to assess and provide the potential survey of lands in Khuzestan province for agricultural activities by taking into account the climatic elements and displaying different elements in different seasons. To achieve this goal, first produced data were analyzed in GIS software and then the data was tested by professors and experts of department of soil science and was weighted using the Buckley geometric mean model. Finally, the obtained weights were applied in the software and the obtained results are as follow: except some east parts of Khuzestan province which have proper climate for agricultural activities, other regions are not in good conditions and it is necessary to use cultivation with low water requirements and high resistance to heat and sunlight in these areas.

On Maps Preserving Unitarily Invariant Norms of the Spectral Geometric Mean

We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between C*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.

On Some Properties of the Norm of the Spectral Geometric Mean

In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A-1#B|| ≤ ||A-1σsB||. Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. Let A ∈ B(H). If ||A#X|| = ||AσsX||, ?X ∈ B(H)++, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσsB||, then is commutative.

Combinatoral Inequality of the Arithmetic and Geometric Means

We get Combinatoral

GEOMETRIC RIGIDITY THEOREM FOR SUBMANIFOLDS WITH POSITIVE CURVATURE

A geometric rigidity theorem for submanifolds with parallel mean curvature and positive curvature in a space form is proved. It is a generalization of the famous rigidity theorems due to S. T. Yau and others.

Means of Choice for Interactive Management of Dynamic Geometry Problems Based on Instrumented Behaviour

Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What information about learning do related problems returned by the system provide us? We answer the first question according to the didactic engineering, whose mode of validation is internal and based on the confrontation between an a priori analysis and an a posteriori analysis that relies on data from experiments in schools. We consider the student as a subject whose adaptation processes are conditioned by the problem and the possible interactions with the computer environment, and also by his knowledge, usually implicit, of the institutional norms that condition his relationship with geometry. Choosing a set of good problems within the system is therefore an essential element of the learning model. Since the source of a problem depends on the student’s actions with the computer tool, it is necessary to wait and see what are the related to problems that are returned to him before being able to identify patterns and assess the learning. With the simultaneity of collecting and analysing interactions in each class, we answer the second question according to a grounded theory analysis. By approaching the problems posed by the system and the designs in play at learning blockages, our analysis links the characteristics of problems to the design components in order to theorize on the decisional, epistemological, representational, didactic and instrumental aspects of the subject-milieu system in interaction.

An Alternative Approach to the Solution of Multi-Objective Geometric Programming Problems

The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.

关于大角度单摆周期近似公式的分析与探讨

对文献中的大角度单摆周期近似公式进行了全面的分析和探讨,在解析形式上,利用算术几何平均值递归法,虽然精确度最高,但考虑到计算的方便性、公式的简洁性以及实验测量精度的需求时,可选用其他简易的近似公式.

四族姊妹对称不等式的证明

推广一对姊妹对称不等式的结果,得到四族姊妹对称不等式,并加以证明.应用算术-几何平均不等式便可顺利完成对前两族对称不等式的证明.在证明后两族对称不等式时,单独使用算术-几何平均不等式已经无法完成.通过借助Popoviciu不等式和凸函数的性质,克服证明碰到的困难,使得后两族对称不等式的结论得到证明.

矩阵初等变换的几何意义

矩阵的初等变换在线性代数中应用十分广泛,以初等行变换为例,分别给出了非退化的初等变换、退化的初等变换的实例与对应的几何图形,在此基础上给出了任意角度的旋转.在教学过程中,通过挖掘初等变换的几何意义,可以使学生建立代数与几何的统一观,促进学生抽象思维与形象思维协调发展.

关于两族推广的孪生对称不等式的证明

应用Karamata不等式、Popoviciu不等式、算术-几何平均不等式和凸函数的性质,证明了两族推广的孪生对称不等式.

东北典型黑土坡耕地不同坡位土壤团聚体特征分析

“漫川漫岗”是东北黑土区典型地貌,其典型黑土土壤结构受径流、冻融等作用影响。为探明东北黑土坡耕地土壤团聚体分布特征,选取坡耕地的坡下、坡中、坡上位置采集土壤样品,测定不同坡位下水稳性团聚体粒径分布、稳定性指标及土壤性质,分析水稳性大团聚体与土壤pH、有机质、钙镁比关系及稳定性指标与团聚体粒径关系。结果表明,不同坡位下水稳性团聚体粒径分布均表现为<0.25 mm团聚体含量占比最高,>2 mm团聚体含量占比最少。<0.25 mm团聚体表现为坡下位显著高于坡中位及坡上位(P<0.05),0.25~0.5 mm、0.5~1 mm、1~2 mm、>2 mm团聚体均表现为坡上位显著高于坡下位(P<0.05)。平均重量直径和几何平均直径均表现为坡上>坡中>坡下,其中坡下位与坡上位、坡中位存在显著差异(P<0.05),团聚体水稳性表现为坡上>坡中>坡下。平均重量直径、几何平均直径均表现为与>0.25 mm团聚体呈正相关,与<0.25 mm团聚体呈负相关,其中受>2 mm团聚体影响最大(P<0.01)。有机质、pH、钙镁比均与>0.25 mm团聚体呈正相关关系(P<0.05)。因此,典型黑土坡耕地较高的有机质含量、pH、钙镁比有利于土壤团聚,促进>0.25 mm团聚体形成,提高团聚体水稳性。

基于激光扫描仪的点云配准方法

针对激光扫描仪实际扫描得到的不完整点云配准困难问题,提出了一种基于对应点对的配准方法。通过激光扫描仪进行实验,得到被测工件的实测点云数据,基于Visual Studio软件配置Point Cloud Library环境,对实测模型与理想模型的点云配准进行研究。首先对实测点云数据进行体素滤波以及均匀下采样的预处理;其次通过对应点对的方式进行对齐为后续精细配准提供较好的变换初值,后基于ICP算法实现点云配准精配准;最终以均方根误差作为点云配准精度评价指标对配准结果进行评价。借助CloudCompare软件对配准结果进行直观展示分析可知,在实测工件本身存在不绝对光滑的情况下,配准的均方根误差可控制在0.62 mm,表明该方法对于不完整点云的配准效果较好。

跟踪窗自适应的Mean Shift目标跟踪算法

针对Mean Shift算法不能很好地跟踪尺度变化目标的缺点,提出一种将Mean Shift算法和目标几何特征相结合的目标跟踪算法。该方法在Mean Shift框架下提取目标的几何特征,根据目标的面积和型心坐标对跟踪窗的位置和大小进行修正,最后更新Mean Shift的目标模板。通过大量实验仿真证明,改进的算法能很好地跟踪尺度变化的目标,对目标的仿射变化和非刚性的形态变化具有有效性和鲁棒性。

基于机器视觉的兰花几何参数测量方法

为实现兰花几何参数快速测量,以“金凤蝶”兰花为研究对象,搭建图像采集平台并设计了一套兰花花朵几何参数测量算法。采用Canny-Harris算法实现兰花角点检测,采用K-means算法、RGB阈值分割算法实现兰花分割,并采用MER算法及遍历算法实现兰花具体几何参数测量。进行兰花算法识别测量试验,结果表明:单株兰花测量仅需10 s左右,相较人工测量速率提升了近60倍,测量数据可为兰花选育种工作提供判断依据。