Search results

The purpose of this paper is simplification of some mathematical theories for the needs of school education.

This work is a result of long‐lasting regular observations of extra‐curriculum classes with primary school pupils. This research is based on some maxima given in a paper written by Zvonkin.

This work gives examples of simplified math models that satisfy the claimed concept, accompanied with the set of problems attainable for primary school pupils.

This work represents a set of criteria, with the guidance of which, any mathematician would be capable of creating a set of problems that would lead the pupils into the area of his research not as observers, but as participants.

Two important methodologies having some common grounds, but based on differing contexts and paradigms are Physical System Theory (PST) and System Dynamics (SD). The developments in both the fields have taken place almost independently, and attempts have been made to integrate the two to complement their strengths and limitations. This paper provides an overview of PST in terms of its foundations, philosophy, fundamental postulates, recent developments on its simplification and enlargement, and applications to socio‐economic and managerial systems. A comparison of PST is made with SD on different fronts so as to understand their similarities and differences for carving out their place in modelling of managerial and socio‐economic systems and integrating the two more meaningfully and flexibly. The paper is concluded emphasizing the need for a ‘Flexible System Theory’ which can relate many such systems based approaches and techniques on the whole continuum from hard to soft systems thinking to cater the whole spectrum of problem situations effectively.

This paper aims to present a mathematical model of the dynamics of the unmanned aerial vehicle (UAV) vertical take-off and landing (VTOL). It will be used to develop control laws to a multirotor that is inherently unstable. Also, the model will be used to design algorithms to estimate the attitude of an object.

The physical model of UAV assumes that it is a rigid body with six degrees of freedom acted by forces generated by the propellers, motors, aerodynamic forces, gravity and disturbance forces. The mathematical model was described by differential equations. However, drive system (propeller, BLDC motor and BLDC motor controller) was described by six transfer functions. These transfer functions were demarcated with Matlab/Simulink identification toolbox from data received from a specially designed laboratory stand. Moments of inertia of the platform have been analytically determined and compared with empirical results from the pendulum. The mathematical model was implemented in Matlab/Simulink.

The paper confirms the need of designing mathematical models. Moreover, mathematical models show that some parts of the object are better to be replaced by experimental results than by equations, which is proved by the data. The paper also shows advantages of using Matlab/Simulink. What is more the simulation of the model proves that multirotor is an unstable object.

The test results show that drive units are strongly dependent on ambient conditions. An additional problem is the different response of the drive set to increasing and decreasing the control signal amplitude. Next tests will be done at different temperatures and air densities of the environment, also it is need to explore drag forces.

The mathematical model is a simplification of the physical model expressed by means of equations. The results of simulation like accelerations and angular rate are noise-free. However, available sensors always have their errors and noise. To design control loops and attitude estimation algorithms, there is a need for identification of sensors’ errors and noise. These parameters have to be measured.

The paper describes a solution of correct identification of drive unit, which is a main component of the UAV.

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

We present a detailed explanation of a mathematical method and numerical technique applied to solve an irregular non‐linear fitting problem that results from attempts to model the calorimetric profiles generated by the binding of phenolic ligands to the insulin hexamer. The method employed uses a non‐traditional approach to modeling data. Rather than start with a simplified model, we use a hierarchical tree of physical models with different degrees of sophistication. Starting with the model of highest dimension, we work our way to an optimum model which is of a lower dimension and is less complex. The algorithm uses two complementary techniques. First, a sensitivity analysis in the vicinity of the optimal point for each model is used to estimate errors in the parameters; that, in turn, provides the user with insight for model simplification. Second, we utilize the optimized model in the prediction of new experimental curves. The core of the method combines a strategy based on the proper split of the initial global numerical task into three locally independent subtasks, and induces a specific split in the search space. The application of three different optimization techniques (two parametric and one variational) with an alternating objective function defined in corresponding subspaces, in combination with the search along the hierarchical tree of mathematical models, enables us to overcome difficult computational problems, including over‐parametrization. We have obtained very accurate fits to a number of calorimetric curves, resulting in a quantitative description of intrinsic functional (free ligand concentration) and vector (equilibrium coefficients and enthalpies of binding) parameters. These quantitative results can now be used to improve the stability of insulin formulations. We believe that, with small modifications to the model, the method and algorithms presented in this article can be applied to other protein‐ligand systems.

Virtual assembly process plays an important role in assembly design of complex product and is typically time- and resource-intensive. This paper aims to investigate a dynamic assembly simplification approach in order to demonstrate and interact with virtual assembly process of complex product in real time.

The proposed approach regards the virtual assembly process of complex product as an incremental growth process of dynamic assembly. During the growth process, the current-assembled-state assembly model is simplified with appearance preserved by detecting and removing its invisible features, and the to-be-assembled components are simplified with assembly features preserved using conjugated subgraphs matching method based on an improved subgraph isomorphism algorithm.

The dynamic assembly simplification approach is applied successfully to reduce the complexity of computer aided design models during the virtual assembly process and it is proved by several cases.

A new assembly features definition is proposed based on the notion of “conjugation” to assist the assembly features recognition, which is a main step of the dynamic assembly simplification and has been translated into conjugated subgraphs matching problem. And an improved subgraph isomorphism algorithm is presented to address this problem.

The purpose of this paper is to study the impact of restructuring in the manufacturing system at the conceptual stage using graph theoretic model.

Some restructuring decisions are conceptualized which reflect the aim of the organization to gradually evolve the manufacturing system towards a leaner structure. This is achieved by way of defining simplified procedures so that lesser hindrance in terms of cycles of interactions is encountered. The restructuring decisions are represented by five restructured configurations of the manufacturing system, through gradual removal of appropriate interaction links. The graph theoretic models are developed for original configuration and each of the new restructured configurations and the resulting structural characterization information is used to compare the structure of restructured configurations with the original configuration. The value of the coefficient of dissimilarity of each of the new configurations with respect to the original configuration is obtained to have a quantitative estimate of the simplification that may be achieved by different contemplated restructuring decisions.

The present work shows that the restructuring decisions can be represented by different configurations in the form of schematic diagrams involving minor changes in the interaction structure among subsystems of the manufacturing system. The quantitative analysis using coefficient of dissimilarity for restructuring decisions indicated that there are varying levels of impact created by five comparable restructuring decisions considered in the study. The findings have a potential to guide the restructuring efforts by identifying a focus area that can produce greater impact of restructuring.

The findings are valid for a particular case manufacturing organization which does not involve itself in extensive design activity. The study is based on the assumption that the schematic diagram and graph theoretic model captured all the relevant influencing factors of the manufacturing system.

The study provides an easy to use methodology for the practical decision makers in manufacturing industry striving to improve the performance of their organization. It can provide the analysis of restructuring decisions at the conceptual stage itself without the necessity of disturbing the normal functioning of the organization. There is a scope for identifying focus areas where the restructuring may yield comparatively greater dividends.

The study of restructuring by representing it in the form of changes in interactions among subsystems of a manufacturing system and investigation of the impact of such restructuring efforts at the conceptual stage using graph theoretic model has been carried out for the first time.

In this paper, some issues about model formulation and solving methods for the Lorenz’s model are discussed, which also deals with fundamental characteristics of non‐linear models. Mainly, there existed problems that Lorenz’s model was formulated based on the weak nonlinear, and spectral expansion which changed the fundamental properties of prototype of the N‐S equations. Furthermore, its solving methods, which are based on continuously smoothing schemes, not only distorted the fundamental characteristics of non‐linear models, but also led to misunderstanding of the concept of “schaos”, which has already caused confusion to people’s way of thinking. In essence, Lorenz’s chaos is an “error volute” which is trapped into “calculation of error values”. Whether it can be named “chaos” may need to be discussed with questions.

The framework, methodology and development of pansystems cybernetics are introduced. Related contents include: the postmodernizational systems thought, the epitome of pansystems methods, hi‐tech mechanism, social cybernetics, pansystems views of value, labor, management and economics, pedagogy, history and futurology, systems mathematics, general clustering analysis, observocontrollability, generalized living systems, information metascience, regret information, general fuzzy control, generalized gray systems, entropy, large scale dynamical supercomplicated Shengke systems, function simulations, transformation theory, simplification, strengthening, forming substance of subsystems of living systems of Miller’s theory, etc.

The purpose of this paper is to present an academic programme of pansystems research with a lot of new concepts, principles, methods. Universal consideration of philosophy‐mathematics‐technology is set forth with mega‐combination. The emphasis on the transfield internet‐like investigations is developed. Many theory‐methods of pansystems get further concise optimization.

The concrete contents of the paper include: historical megawave, philosophical stratagems, meta‐mathematics, meta‐methodology, technological realistic principles, unification and differentiation of encyclopedic branches, systems science, information theory, cybernetics, biosystems, generalized vitality, computer and IT, thinking science, logic, OR, AI, PR, DM, modernization of yinyang analysis combining dialectics, sociology, economics, meta‐relativity, generalized quantification and scale theory, general process of birth‐growth‐ageing‐disease‐death, the inheritance and development of 300 scholars' researches, etc.

All of the topics concerned with are reduced to the actualizations of PVOR – pansystems variational OR: V−d(xy)=^*0^*/PRR′P′/0^**, which is an integrated synthesis of 20‐PanStemCells of PanConcepts and PanMethod, and embodies a specific pansystems summarization for the core of the true and the good. Furthermore, the formula “Pansystems Researches=^*(PVOR/0^**/Pan54787721/Everything)+^*0^*=^*Pan–netlike connections of thoughts and methods” is expanded with concrete applications.

Provides information on pansystems research.