METHOD OF THEORY OF DIMENSIONS IN EXPERIMENTAL RESEARCH OF SYSTEMS AND PROCESSES

The method and parameters of experimental modelling of systems and processes in mechanical engineering are substantiated. The theory of similarity and dimensionality is used as an intermediate link between theory and experiment. The dimension of the factor space depends on the number of factors. The set of factors is grouped into dimensionless similarity criteria. The selected criteria are in certain dependence, such as the Galileo test, Euler and Reynolds numbers. Examples of application in experimental studies are given. The use of dimension theory in a factor-planned experiment allows reducing the number of factors, simplifies the mathematical interpretation of the response criterion and provides a graphical representation in the form of 3-D model.

Unstable entropies and dimension theory of partially hyperbolic systems

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We then establish some basic results in dimension theory for Bowen unstable topological entropy, including an entropy distribution principle and a variational principle in general setting. As applications of this new concept, we study unstable topological entropy of saturated sets and extend some results in Bowen (1973 Trans. Am. Math. Soc. 184 125–36); Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56). Our results give new insights to the multifractal analysis for partially hyperbolic systems.

A PERCEPÇÃO DOS BOLSISTAS DO PROJETO DE EXTENSÃO “A INSERÇÃO DA UNIVERSIDADE NO FUTEBOL” A RESPEITO DA RELAÇÃO TEORIA E PRÁTICA

In Physical Education, there is a discussion about the theory and practice dichotomy, and how much one provides support to the other to obtain legitimacy. This leads to thinking about the training of the new professionals in the area. In the training environment, there are theoretical subjects, which seem to be far from a reality outside of the university. This causes a misinterpretation of the real situation of education. The aim of this study was to verify the perception of the scholarship students about the extension Project “The insertion of the university in soccer” regarding the dimension theory and practice in the Physical Education training. It was conducted qualitative research, with a qualitative approach, and composed of five scholarship students from the extension project. The data were collected through an open questionnaire, applied to the students, and analyzed with the theoretical framework searching for the results. The data analysis indicates the tension maintenance between theory and practice, which the first one concentrates on the setting of a conceptual framework far from the practice conceived as a limited “experience of yourself” during an educational activity. However, the extensionists practices allowed to widen the knowledge of the professional expertise and, paradoxically, the application of the theories learned in the academic environment.

-modules on rigid analytic spaces III: weak holonomicity and operations

We develop a dimension theory for coadmissible $\widehat {\mathcal {D}}$ -modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic $\mathcal {D}$ -modules in the algebraic setting. We discuss a number of pathologies contained in this subcategory (modules of infinite length, infinite-dimensional fibres). We prove stability results for closed immersions and the duality functor, and show that all higher direct images of integrable connections restricted to a Zariski open subspace are coadmissible of minimal dimension. It follows that the local cohomology sheaves $\underline {H}^{i}_Z(\mathcal {M})$ with support in a closed analytic subset $Z$ of $X$ are also coadmissible of minimal dimension for any integrable connection $\mathcal {M}$ on $X$ .

Determining the types of internet plus government platform usage behaviour in selected cities of China

Purpose Although internet plus government platforms (IPGPs) are being increasingly used by citizens around the world, questions emerge regarding the public adoption, utilization and use of IPGPs. This study aims to explore the determinants of citizens’ differentiated IPGPs usage behaviors. Design/methodology/approach An analytical framework has been built upon the rational choice theory and the cultural dimension theory. The present study draws on a survey of 866 citizens from Guangzhou, Wuhan and Chengdu. Findings The empirical findings suggest that the perceived functional benefits and personalization features both significantly affect citizens’ informational, service and participatory uses of IPGPs, to varying degrees. Furthermore, long-term orientation plays a moderating role in the relationship between perceived functional benefits and the service use of IPGPs. Originality/value The findings demonstrate that the public’s rational choice of a new digitalized service channel depends on to what extent and to what degree the absolute and relative benefits they consider important compare to other possible channels. Users also consider how the new service channel satisfies their personalized demands of digitalized services. Also, users’ long-term orientation can affect their rational choices by adjusting the perceived functional benefits of the channel when that channel is used for service transactions.

Study on Mesoscopic Damage Evolution Characteristics of Single Joint Sandstone Based on Micro-CT Image and Fractal Theory

The different directions of joints in rock will lead to great differences in damage evolution characteristics. This study utilizes DIP (digital image processing) technology for characterizing the mesostructure of sandstone and combines DIP technology with RFPA2D. The mesoscale fracture mechanics behavior of 7 groups of jointed sandstones with various dip angles was numerically studied, and its reliability was verified through theoretical analysis. According to digital image storage principle and box dimension theory, the box dimension algorithm of rock mesoscale fracture is written in MATLAB, the calculation method of fractal dimension of mesoscale fracture was proposed, and the corresponding relationship between mesoscale fractal dimension and fracture damage degree was established. Studies have shown that compressive strength as well as elastic modulus of sandstone leads to a U-shaped change when joint dip increases. There are a total of six final failure modes of joint samples with different inclination angles. Failure mode and damage degree can be quantified by D (fractal dimension) and ω (mesoscale fracture damage degree), respectively. The larger the ω, the more serious the damage, and the greater the D, the more complex the failure mode. Accumulative AE energy increases exponentially with the increase of loading step, and the growth process can be divided into gentle period, acceleration period, and surge period. The mesoscale fracture damage calculation based on the fractal dimension can be utilized for quantitatively evaluating the spatial distribution characteristics of mesoscale fracture, which provides a new way to study the law of rock damage evolution.

Dimension estimates for iterated function systems and repellers. Part II

This is the second part of our study on the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on $\mathbb {R}^d$ . In the first part [D.-J. Feng and K. Simon. Dimension estimates for $C^1$ iterated function systems and repellers. Part I. Preprint, 2020, arXiv:2007.15320], we proved that the upper box-counting dimension of the attractor of every $C^1$ IFS on ${\Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of every ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Here we introduce a generalized transversality condition (GTC) for parameterized families of $C^1$ IFSs, and show that if the GTC is satisfied, then the dimensions of the IFS attractor and of the ergodic invariant measures are given by these upper bounds for almost every (in an appropriate sense) parameter. Moreover, we verify the GTC for some parameterized families of $C^1$ IFSs on ${\Bbb R}^d$ .

On Carr’s Eleven-Dimensional Dramaturgy

Contemporary Irish playwright Marina Carr integrates eleven-dimension theory into her post dramatic art creation, forming a unique eleven-dimensional dramaturgy. This unique eleven-dimensional dramaturgy runs through Carr's whole drama creation career, and has different focuses in different periods: in her early drama, Carr concentrated on the expression of the concept of “non-linear time”. In the mid-land drama, she focuses on the creation of “high dimensional space”, while in the later drama of death and fantasy, she focuses on the presentation of “multidimensional worlds”. Finally, with the connection of the eleven-dimensional dramaturgy, Carr created a “non-linear”, “high dimensional” and “multi-dimensional” dynamic post-dramatic theater, and conveyed the eleven-dimensional philosophy of life beyond time and space.