The Hausdorff Dimension and Hausdorff Measure of Full Parry Measure Subset of Finite Type

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.

Estimate on the Dimension of Global Attractor for Nonlinear Higher-Order Coupled Kirchhoff Type Equations

In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate assumptions, we acquire a precise estimate of the upper bound for its Hausdorff and Fractal dimensions.

Higher dimensional bianchi type-V universe in creation-field cosmology

We have studied the Hoyle-Narlikar C-field cosmology with Bianchi type-V non static space- time in higher dimensions. Using methods of Narlikar and Padmanabham [1], the solutions have been studied when the creation field C is a function of time t only as space time is non static. The geometrical and physical aspects for model are also studied.

The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping

In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.

DIMENSION RESULTS FORORNSTEIN-UHLENBECK TYPE MARKOVPROCESS

Let {X-t, t greater than or equal to 0} be an Ornstein-Uhlenbeck type Markov process with Levy process A(t), the authors consider the fractal properties of its ranges, give the upper and lower bounds of the Hausdorff dimensions of the ranges and the estimate of the dimensions of the level sets for the process. The existence of local times and occupation times of X-t are considered in some special situations.

Three-dimensional Extension of the Unit-Feature Spatial Classification Method for Cloud Type

We describe how the Unit-Feature Spatial Classification Method(UFSCM) can be used operationally to classify cloud types in satellite imagery efficiently and conveniently.By using a combination of Interactive Data Language(IDL) and Visual C++(VC) code in combination to extend the technique in three dimensions(3-D),this paper provides an efficient method to implement interactive computer visualization of the 3-D discrimination matrix modification,so as to deal with the bi-spectral limitations of traditional two dimensional(2-D) UFSCM.The case study of cloud-type classification based on FY-2C satellite data (0600 UTC 18 and 0000 UTC 10 September 2007) is conducted by comparison with ground station data, and indicates that 3-D UFSCM makes more use of the pattern recognition information in multi-spectral imagery,resulting in more reasonable results and an improvement over the 2-D method.

The Global Attractors and Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Damping

The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.

K-Dimension and Hlder Exponent for Bush Type Fractal Functions

Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.

Hausdorff Dimension and Fractal Dimension of the Global Attractor for the Higher-Order Coupled Kirchhoff-Type Equations

This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.

The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Nonlinear Coupled Kirchhoff-Type Equations

This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.

SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes, we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with alpha-stable processes could collide with probability one.

Solution and Type Curve Analysis of Fluid Flow Model for Fractal Reservoir

Conventional pressure-transient models have been developed under the assumption of homogeneous reservoir. However, core, log and outcrop data indicate this assumption is not realistic in most cases. But in many cases, the homogeneous models are still applied to obtain an effective permeability corresponding to fictitious homogeneous reservoirs. This approach seems reasonable if the permeability variation is sufficiently small. In this paper, fractal dimension and fractal index are introduced into the seepage flow mechanism to establish the fluid flow models in fractal reservoir under three outer-boundary conditions. Exact dimensionless solutions are obtained by using the Laplace transformation assuming the well is producing at a constant rate. Combining the Stehfest’s inversion with the Vongvuthipornchai’s method, the new type curves are obtained. The sensitivities of the curve shape to fractal dimension (θ) and fractal index (d) are analyzed;the curves don’t change too much when θ is a constant and d change. For a closed reservoir, the up-curving has little to do with θ when d is a constant;but when θ is a constant, the slope of the up-curving section almost remains the same, only the pressure at the starting point decreases with the increase of d;and when d = 2 and θ = 0, the solutions and curves become those of the conventional reservoirs, the application of this solution has also been introduced at the end of this paper.

Fractal Determination of Coastal Types Based on GIS——A Case Study of China

The probability of fractal determination of coastal types based on GIS is preliminarily discussed with China as an example. Finally, some significant conclusions are drawn: (1) The fractal dimension of coastline of the bedrock coast is larger than that of the plain coast on the same scale map; (2) As far as the bedrock coast is concerned, the larger fractal dimension of coastline of the bedrock coast on the same scale map indicates that the bedrock coast is probably not typical; (3) As far as the plain coast is concerned, the smaller fractal dimension of coastline of the plain coast on the same scale map indicates that it is probably the silt plain coast; (4) The different substantial compositions affect the fractal ,dimensions of coastlines of different coastal types. In generalthe coast which lies in the north of the Hangzhou Bay consists of sand mainly, its surface is flat, and it is connected with the coastal plain, its landform is broad shoal, its total change is comparatively homogenous in the tidal dynamic process, and thus, the relatively smaller fractal dimension of coastline results from this. For the bedrock coast, there is more bedrock, the coastline is comparatively smooth and straight, being affected by the faults and ocean dynamic process, which result in the larger fractal dimension.

Analytical Solutions for the Two-Dimensional Magnetic Fields in Disc-Type Permanent Magnet Machines

A two dimensional analytical method for predicting the magnetic field in the airgap/magnet region of a permanent magnet (PM) disc type machine is presented. The solutions of the governing field equations are given in both Cartesian and cylindrical coordinates. The expressions derived in this paper can be used conveniently for optimal design of machine. The computed results using the proposed 2D analytical method are validated by the more accurate, though a lot more complicated, 3D finite element analyses.

l^(2) Decoupling for Certain Surfaces of Finite Type in R^(3)

In this article,we establish an 2 decoupling inequality for the surface F_(4)^(2):={(ξ1,ξ2,ξ_(1)^(4)+ξ_(2)^(4)):(ξ1,ξ2)∈[0,1]^(2)}associated with the decomposition adapted to finite type geometry from our previous work[Li,Z.,Miao,C.,Zheng,J.:A restriction estimate for a certain surface of finite type in R^(3).J.Fourier Anal.Appl.,27(4),Paper No.63,24 pp.(2021)].The key ingredients of the proof include the so-called generalized rescaling technique,an l^(2) decoupling inequality for the surfaces{(ξ1,ξ2,φ1(ξ1)+ξ42):(ξ1,ξ2)∈[0,1]^(2)}with φ1 being non-degenerate,reduction of dimension arguments and induction on scales.

Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation

This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.

宽高比对煤柱型冲击地压影响规律的实验研究

我国深部煤炭开采日趋复杂,区段煤柱在采动、构造或坚硬顶底板影响下极易诱发煤柱型冲击地压,煤柱型冲击地压的防治已成为煤矿安全高效开采的难题,研究不同宽高比条件下区段煤柱的力学性能及冲击破坏特性对煤柱型冲击地压防治具有积极意义。采用不同宽高比煤样的“岩-煤-岩”组合体进行了单轴压缩实验,通过分析煤岩组合体的冲击倾向性、动态破坏特征、分形维数和声发射特征参数等,研究了宽高比对煤柱冲击破坏的影响规律。结果发现:①煤柱的宽高比对煤岩组合体的冲击倾向性具有显著影响,宽高比不小于2∶1时,其冲击能量指数K_(E)为1.82~2.65,冲击倾向性无明显变化;小于2∶1时冲击倾向性呈先升高后降低的趋势,1∶1时K_(E)最大,达到了15.43。②随宽高比减小,煤岩组合体破坏特征依次表现为:拉压破坏—压剪破坏—拉剪破坏。煤柱宽高比为5∶1~3∶1时,煤岩组合体破坏较为缓慢;宽高比为2∶1时开始出现片状煤屑弹出,冲击破坏剧烈程度较低;宽高比为1∶1和0.75∶1时,具有明显的冲击破坏特性;宽高比为0.5∶1时,煤岩组合体整体稳定性下降,相对0.75∶1煤岩组合体煤柱破坏的剧烈程度降低。③峰后声发射能量释放率与分形维数D变化规律相似,均随宽高比减小呈先升高后降低的趋势。宽高比不小于2∶1时,煤岩组合体破坏过程中能量持续释放时间较长,煤柱破坏平缓;宽高比为1∶1时,能量释放率和D值明显增大,相较宽高比不小于2∶1煤岩组合体的能量释放率增大了约4倍,D值增大了0.18~0.23,煤柱冲击破坏最为剧烈;宽高比0.75∶1煤岩组合体能量释放率与D值分别降低了约10%和0.01,破坏剧烈程度与1∶1煤岩组合体相近;宽高比减小至0.5∶1时,相关参数的降低幅度约为0.75∶1煤岩组合体的6倍,破坏剧烈程度相对较小。研究表明:宽高比对煤柱的冲击破坏具有显著影响,整体上,煤柱冲击破坏剧烈程度随宽高比减小(5∶1~0.5∶1)呈先升高后逐渐降低的趋势;煤柱宽高比大于3∶1时,煤柱冲击危险性相对较小,煤柱宽高比为1∶1和0.75∶1时冲击危险性较大,0.5∶1次之。

Distributional Dimension of Fractal Sets in Local Fields

The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension

面向船舶大型化的渤海湾适航客滚船船型尺度研究

为科学指导渤海湾客滚运输船舶合理大型化,统筹过海运输发展与安全,厘清客滚船大型化发展历程,研判市场需求、企业运营、行业管理等影响因素与供需矛盾。系统梳理客滚运输航线及港口布局特征,分析客滚运输企业及船舶运力结构分布,找准船港航一体化发展需求导向。基于海港总体设计规范中通航基础设施尺度的计算方法,采用逆向工程思维推导船型计算式,匹配调整理论结果、归并数值,提出渤海湾4种客滚船大型化标准船型,确定船舶总长、型宽、满载吃水、吨级等主要参数,研判提出渤海湾30个客滚泊位的大型化船型并开展适用性评价。对引导渤海湾新建省际客滚船标准化、序列化发展,强化船舶适港、适航安全保障性具有技术支撑作用。

人与自然和谐共生:中国式现代化的生态维度——基于主客体双向化运动的视角

中国式现代化开创了一条殊于西方的现代化路径,其中一个重要维度便是实现人与自然和谐共生的现代化的生态维度。中国式现代化的绿色发展模式是中国共产党在各个时期处理生态环境和经济发展的实践过程中逐步形成的一条人民主体与优美生态和谐共处的模式,具有清晰的历史脉络;与此同时,在经济发展和生态环境问题上,中国以一种全新的模式实现了对“资本宰制自然”式人类中心主义和生态中心主义的超越,既扬弃了“资本宰制自然”式人类中心主义下人与自然之间的双重异化问题,也克服了生态中心主义下主体缺位的环境保护模式之局限。中国式现代化走出了一条生产发展和生态永续并举的中国式现代化之路,实现了主客体之间的良性互动,这充分展现了中国式现代化的生态维度的独特优越性。