Another Look at Nonholonomic Systems

1973 ◽  
Vol 40 (1) ◽  
pp. 101-104 ◽  
Author(s):  
C. E. Passerello ◽  
R. L. Huston
Keyword(s):  
Analytical Methods ◽  
Classical Problem ◽  
Nonholonomic Systems ◽  
Constraint Forces ◽  
Advantages And Disadvantages ◽  
Arbitrary Choice ◽  
Special Cases ◽  
Dependent Variables ◽  
Automatic Elimination ◽  
General Method

The relative advantages and disadvantages of various analytical methods for nonholonomic systems are briefly presented and discussed. The techniques of Kane’s method are then used to develop a derivation of a general method which consolidates and employs the advantages of the various classical methods. These advantages include the automatic elimination of nonworking constraint forces while avoiding the computation of vector components of acceleration. The method also provides for the arbitrary choice of dependent variables so that it may be adapted to a variety of nonholonomic systems. Two special cases are considered and the method is then illustrated in the classical problem of the rolling coin.

scholarly journals Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1003-1010
Author(s):  
Asıf Yokuş ◽  
Hülya Durur ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah ◽  
Münevver Tuz ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Analytical Methods ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Mathematical Tool ◽  
Symbolic Calculation ◽  
Advantages And Disadvantages ◽  
Wave Solutions

Abstract In this article, the Sinh–Gordon function method and sub-equation method are used to construct traveling wave solutions of modified equal width equation. Thanks to the proposed methods, trigonometric soliton, dark soliton, and complex hyperbolic solutions of the considered equation are obtained. Common aspects, differences, advantages, and disadvantages of both analytical methods are discussed. It has been shown that the traveling wave solutions produced by both analytical methods with different base equations have different properties. 2D, 3D, and contour graphics are offered for solutions obtained by choosing appropriate values of the parameters. To evaluate the feasibility and efficacy of these techniques, a nonlinear evolution equation was investigated, and with the help of symbolic calculation, these methods have been shown to be a powerful, reliable, and effective mathematical tool for the solution of nonlinear partial differential equations.

Dynamics of Nonholonomic Systems

1961 ◽  
Vol 28 (4) ◽  
pp. 574-578 ◽  
Author(s):  
T. R. Kane
Keyword(s):  
Differential Equations ◽  
Nonholonomic Systems ◽  
General Method

A general method for obtaining the differential equations governing motions of a class of nonholonomic systems is presented. Several supplementary theorems are stated, and the use of the method is illustrated by means of two examples.

scholarly journals Quantum key distribution with correlated sources

2020 ◽  
Vol 6 (37) ◽  
pp. eaaz4487 ◽  
Author(s):  
Margarida Pereira ◽  
Go Kato ◽  
Akihiro Mizutani ◽  
Marcos Curty ◽  
Kiyoshi Tamaki
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
The Other ◽  
Correlated Sources ◽  
Information Theoretic ◽  
Security Proofs ◽  
Information Theoretic Security ◽  
Special Cases ◽  
New Framework ◽  
General Method

In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.

scholarly journals On the Use of Structural Equation Models in Experimental Designs

1989 ◽  
Vol 26 (3) ◽  
pp. 271-284 ◽  
Author(s):  
Richard P. Bagozzi ◽  
Youjae Yi
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Advantages And Disadvantages ◽  
New Methods ◽  
Special Cases ◽  
Test Of Homogeneity ◽  
General Test ◽  
Step Down ◽  
New Procedures

New procedures are developed and illustrated for the analysis of experimental data with particular emphasis on MANOVA and MANCOVA designs. The authors begin with one-way designs, including overall tests of significance, step-down analyses, and the use of latent variables. Next they describe a general test of homogeneity and consider a procedure that is applicable even under conditions of heterogeneity. Two-way designs then are derived as special cases of the more general n-way case. Finally, advantages and disadvantages of the new methods are considered.

Structuralism? Functionalism? Behaviorism? Or mechanism? Looking for a better approach to AI

2008 ◽  
Vol 1 (3) ◽  
pp. 325-336 ◽  
Author(s):  
Yixin Zhong
Keyword(s):  
Intelligent System ◽  
New Approach ◽  
Content Type ◽  
Advantages And Disadvantages ◽  
Special Cases ◽  
Powerful Approach ◽  
Reasonable Approach ◽  
The Common ◽  
To Come ◽  
The One

PurposeResearch of artificial intelligence (AI), has aimed at making machines intelligent via the simulation of natural intelligence, particularly human intelligence. During the past decades, there have been three major approaches aimed at achieving this goal, namely structuralism, functionalism and behaviorism. Unfortunately, they work separately and contradictorily to a large extent. The purpose of this paper is to present a better and more unified approach.Design/methodology/approachThe paper analyses each of the three major approaches to AI, describing their advantages and disadvantages. There then follows an attempt to explore a new and more reasonable approach to AI. The new approach should be able to solve all the problems that the existing approaches can solve on one hand and can solve the problems that the existing approaches cannot solve on the other hand.FindingsIt was found that the more reasonable and more powerful approach is the one that directly touches the common and core mechanism of intelligence formation. This is due to the fact that the mechanism of intelligence formation is much more essential than other windows of an intelligent system, such as structure, function, or behavior. It was also found that the common and core mechanism of intelligence formation can be implemented through the information‐knowledge‐intelligence transformation. The third finding is that the three existing approaches are special cases of the mechanism approach under different conditions and can thus be harmoniously unified within the frame of the mechanism approach.Originality/valueThe three findings in the paper: the mechanism approach, the implementation of the mechanism approach, and the unification of the existed three major approaches, are important laws never found before in the literature. The breakthrough of the mechanism approach to AI will be of great significance to both theoretical and practical research in AI in the years to come.

scholarly journals Analytical quantification of electrochemical ferrates for drinking water treatments

2017 ◽  
Vol 95 (1) ◽  
pp. 105-112 ◽  
Author(s):  
Macarena A. Cataldo Hernández ◽  
Andrew May ◽  
Arman Bonakdapour ◽  
Madjid Mohseni ◽  
David P. Wilkinson
Keyword(s):  
Drinking Water ◽  
Water Treatment ◽  
Analytical Methods ◽  
Advantages And Disadvantages ◽  
Excellent Candidate ◽  
Colorimetric Measurements ◽  
Analytical Quantification ◽  
Time Required ◽  
The Cost ◽  
Water Treatments

Ferrate ions are a highly oxidizing and unstable species that are challenging to quantify and analyze. They are, however, becoming increasingly recognized as an excellent candidate for a number of applications such as for water treatment. A wider acceptance of ferrates requires an accurate assay of the produced ferrates. We report on four analytical methods (existing and new) for quantification of ferrates and discuss their advantages and disadvantages. These methods include titrimetric analysis and spectrometric techniques such as direct colorimetric measurements of ABTS or NaI colorimetric. In terms of accuracy, the cost, simplicity, and time required the modified indirect UV-Vis NaI method is shown to be the most effective of all of the four methods investigated.

scholarly journals Presentation of Keywords by Means of Interactive Drawings

2002 ◽  
Vol 5 (2) ◽  
pp. 102-109 ◽  
Author(s):  
Alfredo Campos ◽  
Ángeles Amor ◽  
María Ángeles González
Keyword(s):  
School Students ◽  
Delayed Recall ◽  
Advantages And Disadvantages ◽  
Immediate Recall ◽  
Dependent Variables ◽  
Mental Abilities ◽  
Group 2 ◽  
Spatial Test ◽  
Univariate Analyses ◽  
Group 1

One of the main outstanding problems in keyword mnemotechnics is whether this technique is more effective when the subjects generate their own keywords, or when the keywords are supplied by the experimenter. Both methods have advantages and disadvantages. An alternative method has recently been suggested, in which the keywords are generated by the subjects' peers. In the present study we aimed to investigate whether immediate or delayed recall are affected by keyword generation method (experimenter or peer generation). We also aimed to determine whether the method of keyword generation affects imaging capacity as evaluated by questionnaires or spatial tests. A total of 377 secondary-school students were selected and divided into four groups. All subjects were presented with 30 Latin words. Additionally, the subjects in Group 1 were presented with bizarre images, while the subjects of Group 2 were presented with normal images, in both cases representing the keywords selected by peers as interacting with the Latin words. The subjects in Groups 3 and 4 were likewise presented with normal or bizarre images, respectively, but representing the keywords selected by the experimenters. The subjects' imaging capacity was evaluated by means of the Vividness of Visual Imagery Questionnaire (VVIQ) and the Spatial Test of Primary Mental Abilities (ST-PMA). The results were analysed by multivariate analysis of variance (MANOVA) with three factors (ST-PMA imaging capacity, 2 levels; VVIQ imaging capacity, 2 levels; and mnemotechnic method, 4 levels) and dependent variables immediate recall and delayed recall. All three factors influenced recall. Subsequent univariate analyses of variance indicated that subjects with high ST-PMA score and subjects with high VVIQ score showed better immediate and delayed recall than subjects with low ST-PMA score and subjects with low VVIQ score. Mnemotechnic method (i.e. whether keywords are generated by the experimenter or by peers) significantly affected immediate recall but not delayed recall.

scholarly journals On the diagonalization of quadratic Hamiltonians

2021 ◽  
Author(s):  
Ville Härkönen ◽  
Ivan Gonoskov
Keyword(s):  
Unitary Transformation ◽  
Frame Of Reference ◽  
Quadratic Hamiltonians ◽  
Special Cases ◽  
Quadratic Hamiltonian ◽  
General Method

Abstract A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can establish the diagonalization of a quadratic Hamiltonian by changing the frame of reference by a unitary transformation. We give a general method to diagonalize an arbitrary quadratic Hamiltonian and derive a few of the simplest special cases in detail.

scholarly journals A Soft Interval Based Decision Making Method and Its Computer Application

2021 ◽  
Vol 46 (3) ◽  
pp. 273-296
Author(s):  
Gözde Yaylalı ◽  
Nazan Çakmak Polat ◽  
Bekir Tanay
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Computer Application ◽  
Complex Data ◽  
Soft Sets ◽  
Mathematical Algorithm ◽  
Huge Data ◽  
Special Cases ◽  
General Method

Abstract In today’s society, decision making is becoming more important and complicated with increasing and complex data. Decision making by using soft set theory, herein, we firstly report the comparison of soft intervals (SI) as the generalization of interval soft sets (ISS). The results showed that SIs are more effective and more general than the ISSs, for solving decision making problems due to allowing the ranking of parameters. Tabular form of SIs were used to construct a mathematical algorithm to make a decision for problems that involves uncertainties. Since these kinds of problems have huge data, constructing new and effective methods solving these problems and transforming them into the machine learning methods is very important. An important advance of our presented method is being a more general method than the Decision-Making methods based on special situations of soft set theory. The presented method in this study can be used for all of them, while the others can only work in special cases. The structures obtained from the results of soft intervals were subjected to test with examples. The designed algorithm was written in recently used functional programing language C# and applied to the problems that have been published in earlier studies. This is a pioneering study, where this type of mathematical algorithm was converted into a code and applied successfully.

scholarly journals AN EXAMPLE OF CALCULATION OF A FAULT TREE WITH LOGIC LOOPS

Dependability ◽  
2017 ◽  
Vol 17 (4) ◽  
pp. 10-15
Author(s):  
Y. P. Sorokoletov
Keyword(s):  
Fault Tolerance ◽  
Power Supply ◽  
Power Supply System ◽  
System Analysis ◽  
Fault Tree ◽  
Tolerance Analysis ◽  
Supply System ◽  
Tree Structure ◽  
Advantages And Disadvantages ◽  
Special Cases

Aim. In the course of fault tolerance analysis of complex technical systems using the method of fault tree-based methods, logic loops may occur when, from the point of view of fault tree structure, the system sustains itself. The recursion in the fault tree structure disrupts the logical equation and does not allow performing the calculation and associated analysis. A complex system is understood as one performing a multitude of functions, fault tolerant through a number of redundancy techniques, having intersystem communications and high level of integration of hardware and software components. This paper looks into a particular case of solving the problem of logical recurrence of a fault tree that occurred during an aircraft’s power supply system analysis for compliance with airworthiness requirements and aviation regulations.Method. The paper reviews known ways of solving the set task (both manual and automatic), describes the advantages and disadvantages, applicability and ultimately provides a comparative evaluation based on the results of calculation of occurrence probability of certain aircraft power supply system failures. The method of solving the problem of fault tree recurrence presented in this paper is based on identifying recursive elements in the tree’s structure with subsequent reduction of the cyclic connections to a converging spiral by modelling the initial state of the analyzed system.Results. The calculation of the fault tree under consideration is performed both by means of the method presented in this paper, and the most applicable in the particular case known methods of resolving recurrence. Additionally, comparative results of calculation of other special situations are shown. They are not considered in this paper but demonstrate the distinctive features of different methods. The calculations show that the methods yield the most diverging results in cases when the system is redundant and has feedbacks.Conclusions. The method presented in the paper has been tested as part of an aircraft’s power supply system fault tolerance analysis. The developed method in some cases enables manual resolution of the logic loop problem in the fault tree without a significant increase of computational resources while preserving the analytical solution (minimum fault tree cross sections). On the other hand, this solution may cause a fast growth of the fault tree size in cross-system analysis. In special cases, antithetical events like «operability» and «failure» may become mixed-up in the fault tree structure, which will entail the requirement to use complementary operator inversion and subsequently a manifold increase of the computation time. Another limitation of the method may stem from situations when it is impossible to identify the «initial» and «normal» states of the system under analysis. Given the above, the author classifies the presented method as an engineering method of limited applicability. 

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