A Technique for Estimation of Box Dimension about Fractional Integral

This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals.

On the Connection between the Order of Riemann-Liouvile Fractional Calculus and Hausdorff Dimension of a Fractal Function

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouvile fractional integrals and the Hausdorff dimension of a fractal function.

Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions

A completely integrable Toda-like lattice equation in 2+1 dimensions is studied.Four kinds of exact solutions to this equation are derived by virtue of variable separation and the Hirota bilinear approach.The relations between each two solutions are also presented.

Energy Planning Considering the Policy Dimension Seeking for Sustainable Development

The objective of this work is to analyze the intrinsic aspects for policy dimension inside the energy planning and energy long term sustainability. In that sense, the methodology intends to take the Brazilian example as a case study and offer a somewhat unorthodox perspective on the subject of State energy planning. This matter is, beyond a purely technical question or a problem for the field of exact sciences, a point of primary interest to the field of social and human sciences. More the backbone methodology in this research is the Integrated Energy-Resources Planning (IRP), chosen for its ability to integrate both the supply and demand perspectives in the discussions about energy planning [1] [2]. A historical perspective is a guideline to approach issue: starting at the early Twentieth century, this study covers the major landmarks of the country energy concern to the present day;particularly noteworthy are the implications of the realpolitik—that is, the elements in politics that are developed within the institutional frameworks, such as governmental plans and decisions. As a result, it presents a complex picture, which we try to understand from the perspective of supply and demand integration. The originality of the study lies in the refusal to accept fallacious technical statements, as we consider the issue primarily a human and social problem, but considering the validity of technical statements that are correct.

Gorenstein dimensions for weak Hopf-Galois extensions

The representation of weak Hopf algebras is studied by investigating the Gorenstein dimensions of weak Hopf algebras and weak Hopf-Galois extensions.Let H be a weak Hopf algebra with a bijective antipode,A a weak right H-comodule algebra and B the H-coinvariant subalgebra of A.First,some properties of Gorenstein projective H-modules in the representation category are studied,and the fact that Gorenstein global dimension of H is the same as the Gorenstein projective dimension of its left unital subalgebra is demonstrated.Secondly,by applying the integral theory of weak Hopf algebras,on the one hand,a sufficient and necessary condition that a projective A-module is a projective B-module is given;on the other hand,the separability of the functor AB-and that of the restriction of scalar function B(-)are described,respectively.Finally,as a mean result,the Gorenstein global dimension of a weak Hopf-Galois extension is investigated under the condition that H is both semisimple and cosemisimple.

Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series

Analysis of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using embedded solid concentration time series collected from a 76 mm internal diameter and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s air velocity and 50 to 550 kg/m2s solids flux of spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3. Data were analyzed using prepared FORTRAN 2008 code to get correlation integral followed by determination of correlation dimensions with respect to the hyperspherical radius and their profiles, plots of which were studied. It was found that correlation dimension profiles at the centre have single peak with higher values than the wall region profiles. Towards the wall, these profiles have double or multiple peaks showing bifractal or multifractal flow behaviors. As the velocity increases the wall region profiles become random and irregular. Further it was found that, as the height increases the correlation dimension profiles shift towards higher hyperspherical radius at the centre and towards lower hyperspherical radius in the wall region at r/R = 0.81. The established method of mapping correlation dimension profiles in this study forms a suitable tool for analysis of high-flux riser dynamics compared to other analyses approaches. However, further analysis is recommended to other gas-solid CFB riser of different dimensions operated at high-flux conditions using the established method.

On a Hypothetical Vector Field Associated with the Classic Electromagnetic Wave in a Space of Four Dimensions

In two previous papers [1] and [2], a structure for vector products in n dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.

Integration/Inclusion in and with Sport for All---Families, Politics, Management and Citizens in Responsibility

The slogan ＂Sport for All＂ as a program of TAFISA （The Association For International Sport for All） is an invitation for all target groups and target persons in all societies worldwide to be active in sports, to organize and to create sport activities with a variety of aims. Integration and inclusion are strategies to open the world of sports for people with disabilities or a migrant background as well. Families, politics, the management within companies and all citizens are in responsibility. The development of Sport for All depends on various dimensions, e.g. the different kinds of sport, target groups and aims/motives.

“五育并举”视域下推进高校体育工作高质量发展的现实逻辑与路径探索——以北京联合大学为例

体育是“五育并举”育人体系的重要组成部分,对培养德智体美劳全面发展的高素质人才具有重要意义。北京联合大学立足“五育并举”的时代背景,围绕立德树人根本任务,秉持健康第一的教育理念,发挥“以体育人”功能,通过明确目标导向、深化理念融合、健全体制机制等举措,强化体育工作的顶层设计,在体育课程建设、群众体育发展、体育竞赛参与、体育文化培育等方面不断改革创新,探索形成了推进高校体育工作高质量发展的实践路径,以适应新一轮本科教育教学审核评估的要求。

Paradigm shift in psychiatric neuroscience:Multidimensional integrative theory

Abnormal structure and function of the human brain cause various mental and neurological disorders.The search for neurobiological mechanisms and biomarkers associated with psychiatric disorders has always been a focal point and a challenging issue in neuroscience.Functional magnetic resonance imaging(fMRI)allows the noninvasive re-cording of high spatial-temporal resolution brain activity in patients,making it one of the primary research methods in integrative neuroscience.

FRACTIONAL INTEGRAL AND FRACTAL FUNCTION

In this paper, the relationship between Riemann-Liouville fractional integral and the box-counting dimension of graphs of fractal functions is discussed.

Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

Research on a Diagnosis Method Based on a Correlation Integral

For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the correlation integral to scale, so extracting featuresdirectly from the correlation integral can avoid the bottleneck problem of determining the range ofnon-scale length. Several features extracted from the correlation integral are better than thesingle feature of the correlation dimension when describing the signal. It is obvious that thismethod utilizes more information of the signal than does the correlation dimension. The diagnosisexamples verify that this method is more accurate and more effective.

Hamiltonian, Path Integral and BRST Formulations of the Restricted Gauge Theory of <i>QCD₂</i>

We study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin (BRST) formulations of the restricted gauge theory of QCD2 à la Cho et al. under appropriate gauge-fixing conditions.

Dimension Accuracy and Surface Integrity of Creep Feed Ground Titanium Alloy with Monolayer Brazed CBN Shaped Wheels

Titanium alloy tenon is creep feed ground with monolayer brazed cubic boron nitride （CBN） shaped wheels. The dimension accuracy of the tenon is assessed and the results indicate that it completely meets the requirement of blade tenon of aero-engine. Residual stresses, surface roughness, microstructure and microhardness are measured on ground surfaces of the specimen, which are all compared with that ground with vitrified CBN wheels. Under all the circumstances, compressive residual stress is obtained and the depth of the machining affected zone is found to be less than 40 μm. No phase transformation is observed at depths of up to 100 lain below the surface, though plastic deformation is visible in the process of grain refinement. The residual stress and microhardness of specimens ground with brazed CBN wheels are observed to be lower than those ground with vitrified ones. The arithmetic mean roughness （Ra） values obtained are all below 0.8μm.

基于产教融合的机械专业三层次三维度实践教学体系构建与实践

产教融合将教育链、人才链与产业链、创新链有机衔接,培养面向产业的优质人才,具有深远的现实意义。但是实施过程中,教学、人才、产业以及创新等多种元素和维度发挥的体制机制问题并不十分通畅,往往没有形成长效机制。该文基于浙大宁波理工学院机电与能源工程学院的产教融合实践教学体系建设和实施实践,提出基于产教融合平台的三层次三维度有机融合的机械专业工程实践能力培养模式,将工程实践教学资源拓展为基础实践、产业实践、“双创”实践三个层次,学生、教师、雇主三个维度共同参与、共同评价实践教学效果,建立一套行之有效的运行机制,循环迭代、立体驱动学生工程实践能力的持续提升。建设成效显著,示范作用明显,吸引诸多企业踊跃参与。该文可为地方院校工科类专业开展产教融合的教学实践提供一种比较可行的实施路径。

基于会计诚信主题的“财务管理”课程思政实践探索——以江苏经贸职业技术学院为例

基于“财务管理”课程思政示范课改革试点,以“会计诚信”思政元素为主线,从课程思政的目标、教学内容、教学方式和考核评价方式等方面展开研究,以期实现诚信教育、职业道德教育与专业知识教育的有机结合。

基于分形理论的Bingham型浆液柱形扩散模型研究

为解决被注多孔介质的孔隙率和孔隙通道的多变性对现有注浆理论与试验结果误差的影响问题,引入分形理论相关知识,建立Bingham型浆液在分形多孔介质中柱形扩散的数学模型,并推导出分形渗透注浆扩散方程的解析解。通过室内注浆试验、传统注浆理论与本文理论对比验证该模型的有效性,并通过参数分析被注介质的体积分形维数和迂曲分形维数对多孔介质和浆液的影响。结果表明:1)分形渗透率常数和分形孔隙率常数与体积分形维数呈正相关、与迂曲分形维数呈负相关关系;2)随着孔隙最大直径的增加,分形渗透率常数和分形孔隙率常数也不断增加;3)随着注浆时间的增加,浆液的扩散半径、扩散速度与注浆压力和浆液的水灰质量比呈正相关、与地下水头压力和迂曲分形维数呈负相关关系;4)迂曲分形维数对浆液的扩散半径起重要作用,在直管极限条件下,浆液的扩散半径最大,随着迂曲分形维数的增加,浆液的扩散半径迅速减小。

论社会维度视角下数字经济与实体经济的深度融合

数字经济与实体经济的融合具有重要的经济价值和社会意义。目前二者在融合的过程中存在“不全”“不深”“不便”“不愿”等诸多问题。通过“社会维度”的观察视角和分析框架对社会分类、社会过程、社会结构、社会组织与社会群体进行深入考察,可以理解数字经济与实体经济融合过程的复杂性,能够为科学研究、政策制定和产业实践提供更有针对性的指导。其中,社会分类涉及“产业数字化”和“数字产业化”的不同模式、“内部孵化”与“外部对接”的不同策略。社会过程的分析有助于从时空演进和产业扩散等多个层面揭示“数实融合”的动态路径和关键节点。社会结构的支持与分化特征决定了“数实融合”的可行性与差异性。企业作为社会组织在推动“数实融合”中既要通过数字化手段实现自身的增长与再生产,又要平衡资源、整合需求、重塑架构、确保数据安全等。关注不同社会群体的参与状况和所受影响,理解他们的需求和行为,对于设计和推动数字经济与实体经济的有效融合至关重要。

论雅斯贝尔斯大学教育思想的整体性

整体性是雅斯贝尔斯大学教育思想的根本特征。雅斯贝尔斯反思了当时德国大学教育的弊病—整体性缺失:教育构成的“支离破碎”,专业教育与精神教育的分离,职业教育与精神交往的分离,职业训练、整全人的教化和科学研究三者的相互分离。基于此,他构建了大学教育思想五维度的思想体系,涉及大学理念的整体性、大学使命的整体性、大学教育目的的整体性、大学教育内容的整体性、大学育人格局的整体性。雅斯贝尔斯的大学教育思想具有整体性的特征,表现为关联性、层次性和开放性。研究雅斯贝尔斯大学教育思想的整体性,有助于我们从整体上深入地理解和把握雅斯贝尔斯大学教育思想的精神实质,形成整体性的大学教育观念。