Adaptive Space Expansion for Fast Motion Planning

The sampling process is very inefficient for sam-pling-based motion planning algorithms that excess random sam-ples are generated in the planning space.In this paper,we pro-pose an adaptive space expansion(ASE)approach which belongs to the informed sampling category to improve the sampling effi-ciency for quickly finding a feasible path.The ASE method enlarges the search space gradually and restrains the sampling process in a sequence of small hyper-ellipsoid ring subsets to avoid exploring the unnecessary space.Specifically,for a con-structed small hyper-ellipsoid ring subset,if the algorithm cannot find a feasible path in it,then the subset is expanded.Thus,the ASE method successively does space exploring and space expan-sion until the final path has been found.Besides,we present a particular construction method of the hyper-ellipsoid ring that uniform random samples can be directly generated in it.At last,we present a feasible motion planner BiASE and an asymptoti-cally optimal motion planner BiASE*using the bidirectional exploring method and the ASE strategy.Simulations demon-strate that the computation speed is much faster than that of the state-of-the-art algorithms.The source codes are available at https://github.com/shshlei/ompl.

Driving Mechanism of Urban Space Expansion in Luoyang, China

Urban space expansion is the result of the interaction between internal and external forces of the urban. Based on the remote sensing image data of 1990, 2000, 2010, and 2020, and the social and economic development data, this paper analyzes the driving mechanism of the Luoyang space expansion characteristics and its correlation characteristics. By using urban land use efficiency index, urban expansion elastic index;urban allometric growth index, and grey correlation analysis in 4 times sections and 3 periods. The research results show that the urban space expansion of Luoyang mainly comes from the needs and support of economic development, the coordination between urban space expansion and population development is poor, and urban space expansion effectively attracts the inflow of external funds, and the settlement of migrants, drives the development of the tertiary industry, and increases the local revenue.

Characteristics Analysis of Urban Space Expansion in Luoyang, China

The characteristics of urban space expansion reflect the changes of urban space layout and space structure, as well as the urban developing direction and urban orientation in the future. Based on the remote sensing image data of 1990, 2000, 2010 and 2020, this paper analyzes the urban space expansion characteristics of Luoyang, by using the urban land compaction index, expansion intensity index and centroid distribution in 4 time sections and 3 periods. The results show that: 1) the urban land area of Luoyang has expanded rapidly, the urban planning policy has successfully guided the urban expansion. 2) In the first period, the urban expansion belongs to the rapid expansion type, mainly filling the built-up area and natural expansion to outward;the second period is of high-speed expansion type, the urban expansion mainly enlarges the urban framework, then fills the expanded district, and the influence of urban natural growth factor is very small;the third period belongs to the high-speed expansion type, and the expansion rate is significantly lower than that in the second period, the urban expansion is mainly to fill in the urban framework enlarged in the previous period and continue to enlarge the urban framework, and the influence of urban natural growth factor is very little. 3) The urban land centroid gradually migrates to the southeast with the azimuth of 151.47°, the annual migration distance is of 138.29 m. The migration rate in the second period is the fastest, which is about 7.43 times that of the first period, and 2.70 times that of the third period. In the first period, the urban land is mainly expanded to southward, with the main azimuth of 201.13°. Compared with the urban land centroid in 2000, the urban land in the second period mainly expands to east-southeast and southward along the azimuths of 141.92° and 154.17° respectively. Compared with the urban centroid in 2010, the urban land in the third period mainly expands in the orientations of southeast and eastward along the azimuth of 96.24° and 133.45°.

Singularity analysis for single gimbal control moment gyroscope system using space expansion method

Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.

Spatial Characteristics Analysis of Urban Expansion in Luoyang, China

The characteristics of urban space expansion reflect the changes of urban spatial layout and structure, as well as the orientation of urban development in the future. This paper uses the regional sector division method to divide the urban land into 8 orientations, based on the urban land space compaction index, and designs a sector partition compaction index. Based on the remote sensing image data of 1990, 2000, 2010, and 2020, the spatial characteristics of urban land expansion of Luoyang are analyzed by using the partition compaction index, expansion intensity index, fractal dimension, and standard deviation ellipse. The results show that: from 1990 to 2020, the urban overall planning of Luoyang has effectively guided the urban development, the urban land expands rapidly, the urban land compaction has been maintained at a low level, and the urban form has been tending to be reasonable;the urban land centroid gradually shifts to the southwest, and the distribution axis rotates clockwise from southwest-northeast to northwest-southeast, and the directionality of distribution gradually disappears;the urban land has gone through the development process of land filling-enlarging-refilling. The urban land expansion is relatively active in the region with an azimuth of 90°- 225°, and the urban expansion in the north of Luo River is relatively stable and is always filling mode.

一种新型钻孔采样数据管理方案

论述了在进行工程勘察软件设计中实际存在的一些问题。针对这些问题在对钻孔采样数据管理时,通过进行科学的数据空间的划分和结构重组提出了一种新型的钻孔数据管理方案,并成功地利用了的维数据处理功能解决了实际存在的困难。文章就该方案实现MAPGIS2.5的数据模型以及模型中使用的关键性技术分别进行了阐述。最后讨论了该模型可能存在的问题以及相应的解决方法。

Some Properties of Solutions for a Degenerate Diffusion System

In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.

The Impact of Nature, The Teaching and Learning of Elementary Lessons in Students 9-11 Years Old (Case Study: Shiraz Elementary Schools)

In today’s world some changes have been occurred in human lifestyle,these changes,along with the advantages,have led to a series of disadvantages including their disconnection with the nature.One of the most important areas to re-establish the relationship is the school.The presence of nature at schools,and holding some classes in nature,in addition to meeting the special needs of children causes their separation from those small and boring classes as well as their interest in courses.This study aimed to investigate the role of nature in children’s learning.For this purpose,third,fourth and fifth grade classes of 3 schools were held outside the school environment and in the nature in 5 courses.The study is a combinational research and field,indirect observation and library data collection methods were applied,where in the indirect observation,two types of questionnaires were prepared related to the students and teachers and were randomly distributed among 580 students and 50 elementary school teachers.Test reliability was assessed using Cronbach’s alpha and it was obtained to be 0.890.The results of this study indicate that the physical place as one of the factors in children’s learning has the maximum impact on teaching and learning of children.At the end of the study and by investigating the existing factors in the environment we understood that the expansion of the nature and natural light of it causes the students’interest in lessons in nature.

Anisotropic Hardy-Lorentz spaces and their applications

Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.

A comprehensive understanding of grain selection in spiral grain selector during directional solidification

It is of great importance to further investigate grain selection mechanism for the production of single crystal(SX) turbine blade because a single crystal with optimized crystal orientation will enhance service performance of the blade severely.In this paper,single crystals with different deviation angles,i.e.6°,12° and 29°, were obtained using directional solidification under the same casting conditions.It has been found that the grain selection in spiral selector is a coupling process where high order dendrites branch in the front side and primary dendrites disappear in the back side based on the metallographic analysis and electron back scatter diffraction(EBSD).Considering the development of liquid/solid interface by numerical simulation,a combination effect with space expansion,geometrical restriction and grain competition was proposed for spiral grain selection.The space expansion mechanism dominates the process as it provides growth space and driving force for high order dendrites advancing.Thereby,the smaller the take-off angle(θ) is,the larger space and the stronger driving force high order dendrites will get,and the higher efficient the selector will be. The competitive growth between the secondary dendrites plays more contribution than that of primary dendrites,i.e.grain with preferred secondary dendrites instead of preferred primary dendrites could outcompete during grain selection,and this is the reason why spiral grain selector cannot optimize the orientation of the primary dendrites.These findings provide experimental evidence for spatial control of SX growth,and benefit the sophistic casting fields such as turbine blade casting for improved yield.