scholarly journals Analysis and Synthesis of Weighted Marked Graph Petri Nets: Exact and Approximate Methods

2019 ◽  
Vol 169 (1-2) ◽  
pp. 1-30
Author(s):  
Raymond Devillers ◽  
Thomas Hujsa
Keyword(s):  
Petri Nets ◽  
Approximate Methods ◽  
Analysis And Synthesis ◽  
Marked Graph ◽  
Exact And Approximate Methods

scholarly journals The effect of the application of the exact and approximate methods on values of selected ecological indices

2014 ◽  
Vol 67 (1) ◽  
pp. 39-46
Author(s):  
Maria Ługowska ◽  
Zofia Rzymowska
Keyword(s):  
Wiener Index ◽  
Ecological Indices ◽  
Exact Methods ◽  
Approximate Methods ◽  
Winter Cereals ◽  
Spring Cereals ◽  
Phytosociological Relevés ◽  
Exact And Approximate Methods ◽  
Potato Crops ◽  
Tuber Crops

<p>The work presents the results of a study on the biodiversity of agrocenoses using ecological indices. In order to calculate the measures, phytosociological relevés were made and exact methods were applied in winter cereals, spring cereals, tuber crops and stubble fields. The objective of the work was to compare ecological indices (Simpson’s index of dominance <em>C</em>, Simpson’s index of species richness <em>D,</em> and Shannon-Wiener index of biodiversity <em>H</em>’) calculated using the number of plants and their cover determined based on the degree of presence. Moreover, correlation analysis was conducted between the indices computed using the two approaches applied.</p><p>The results of the study revealed significant differences between all the indices calculated using the exact and approximate methods. In turn, comparisons of the measures computed for individual crops showed significant differences only for potato crops and winter cereals. No significant differences were found between the indicators calculated for spring cereals and stubble fields.</p>

Comparison of exact and approximate methods for analysing vibrational relaxation regions

1961 ◽  
Vol 10 (1) ◽  
pp. 33-47 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Exact Solution ◽  
Shock Waves ◽  
Numerical Integration ◽  
Vibrational Relaxation ◽  
Relaxation Frequency ◽  
Rayleigh Line ◽  
Relaxation Equation ◽  
Approximate Methods ◽  
Exact And Approximate Methods

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.

Optimal Feedback Solutions for a Class of Distributed Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 337-342 ◽  
Author(s):  
H. C. Khatri ◽  
R. E. Goodson
Keyword(s):  
Heat Transfer ◽  
Integral Equation ◽  
Control System ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Approximate Methods ◽  
Exact And Approximate Methods ◽  
Good Agreement

In the design of controllers for heat transfer systems, one must often describe the plant dynamics by partial differential equations. The problem of optimizing a controller for a system described by partial differential equations is considered here using exact and approximate methods. Results equivalent to the Euler-Lagrange equations are derived for the minimization of an index of performance with integral equation constraints. These integral equation constraints represent the solution of the partial differential equations and the associated boundary conditions. The optimization of the control system using a product expansion as an approximation to the transcendental transfer function of the system is also considered. The results using the two methods are in good agreement. Two examples are given illustrating the application of both the exact and approximate methods. The approximate method requires less computation.

scholarly journals Exact Optimum Design of Segmented Thermoelectric Generators

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
M. Zare ◽  
H. Ramin ◽  
S. Naemi ◽  
R. Hosseini
Keyword(s):  
Maximum Efficiency ◽  
Thermoelectric Generators ◽  
Approximate Methods ◽  
Design And Optimization ◽  
Compatibility Factor ◽  
Maximum Conversion Efficiency ◽  
Design Characteristics ◽  
Exact And Approximate Methods ◽  
And Performance ◽  
Theoretical Results

A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs). Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency).

scholarly journals CONTINUOUS PETRI NETS: EXPRESSIVE POWER AND DECIDABILITY ISSUES

2010 ◽  
Vol 21 (02) ◽  
pp. 235-256 ◽  
Author(s):  
LAURA RECALDE ◽  
SERGE HADDAD ◽  
MANUEL SILVA
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Expressive Power ◽  
Timed Petri Nets ◽  
Analysis And Synthesis ◽  
Continuous Petri Nets ◽  
Linear Differential ◽  
The One

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of the corresponding discrete model. The expected gains are twofold: improvements in complexity and in decidability. In the case of autonomous nets we prove that liveness or deadlock-freeness remain decidable and can be checked more efficiently than in Petri nets. Then we introduce time in the model which now behaves as a dynamical system driven by differential equations and we study it w.r.t. expressiveness and decidability issues. On the one hand, we prove that this model is equivalent to timed differential Petri nets which are a slight extension of systems driven by linear differential equations (LDE). On the other hand, (contrary to the systems driven by LDEs) we show that continuous timed Petri nets are able to simulate Turing machines and thus that basic properties become undecidable.

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