scholarly journals Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 289 ◽  
Author(s):  
Jie Shen ◽  
Jian Zhou
Keyword(s):  
Numerical Integration ◽  
Linear Function ◽  
Nonlinear Function ◽  
Risk Measurement ◽  
Integration Process ◽  
Entropy Optimization ◽  
Simulation Algorithms ◽  
Simplified Calculation ◽  
Discretization Process ◽  
Fuzzy Interval

Entropy has continuously arisen as one of the pivotal issues in optimization, mainly in portfolios, as an indicator of risk measurement. Aiming to simplify operations and extending applications of entropy in the field of LR fuzzy interval theory, this paper first proposes calculation formulas for the entropy of function via the inverse credibility distribution to directly calculate the entropy of linear function or simple nonlinear function of LR fuzzy intervals. Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. Compared to the existing simulation algorithms, the numerical results show that the advantage of the algorithms is well displayed in terms of stability, accuracy, and speed. On the whole, the simplified calculation formulas and the effective simulation algorithms proposed in this paper provide a powerful tool for the LR fuzzy interval theory, especially in entropy optimization.

scholarly journals NON LINEAR FEEDBACK STREAM CIPHER

2012 ◽  
pp. 132-138
Author(s):  
Dr .R. Siva Ram Prasad ◽  
G. Murali ◽  
S. Gopi Krishna
Keyword(s):  
Linear Function ◽  
Stream Cipher ◽  
Nonlinear Function ◽  
Linear Feedback ◽  
Synchronous Mode ◽  
Plain Text ◽  
Cipher Text ◽  
Security Software ◽  
Non Linear ◽  
New Generation

The main aim of this paper is to develop a new generation and innovative security software for applications. We proposed new stream cipher called NLFS. NLFS means Non-linear feedback stream cipher, which is a fast and secure stream cipher for egovernance applications. This stream cipher uses AES secure non-linear function and AES key generation. NLFS uses primitive polynomial generated S-boxes in byte substitution step. NLFS uses two similar AES round functions and these two proceed parallelly to produce key-stream. Non-linear *function of NLFS has AES nonlinear function steps (add-round key, byte substitution, mix column, shift rows) and it extra includes value-based rotation step. In value based rotation step it rotates each 8-bit word by its first 3-bit (decimal) value.NLFS have two modes basic mode that is synchronous mode and self synchronous mode. In synchronous mode key stream is independent of plain text and cipher text. In selfsynchronous mode key stream generation depending on cipher text. In self synchronous mode generated keystream update first 512-bit buffer and cipher text update the second buffer.

scholarly journals Dynamic Prey Predator Model and multiple forms of Harvest of Infected Prey

2019 ◽  
Vol 24 (4) ◽  
pp. 87
Author(s):  
S. A. Wuhaib ◽  
M. H. Mansour
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Response Type ◽  
Multiple Forms ◽  
Predator Model ◽  
The Stability ◽  
The Relationship ◽  
Infected Prey

In this paper, the dynamic of prey predator model was discussed when the relationship between them is functional response type III. In addition, when prey exposure to the disease as nonlinear function. Also the infected prey exposed to harvest as a nonlinear and as linear function. The bounded and positive solutions, periodic, conditions of equilibrium points and the stability were we discussed Some results were illustrated in numerical simulations, and show we can use the linear function of harvesting to control on the dices   http://dx.doi.org/10.25130/tjps.24.2019.079

scholarly journals How to make a kin selection model when marginal fitness is non-linear?

2014 ◽  
Author(s):  
Roberto H. Schonmann ◽  
Robert Boyd ◽  
Renato Vicente
Keyword(s):  
Linear Function ◽  
Social Environment ◽  
Kin Selection ◽  
Mutant Allele ◽  
Nonlinear Function ◽  
Selection Model ◽  
Fitness Functions ◽  
Non Linear ◽  
Monomorphic Population ◽  
Function Of Two Variables

We observe that the Taylor-Frank method for making kin selection models when fitness $w$ is a nonlinear function of a continuous actor's phenotype $y$ and the average phenotype $z$ in its social environment requires $w(y,z)$ to be differentiable (as a function of two variables, i.e., jointly in $y$ and $z$). This means that even if $w(y,z)$ is non-linear globally, locally it must be close to linear, meaning that its graph must be well approximated by a plane. When more than two individuals interact, this assumption is only satisfied when the marginal fitness of the actor is a linear function of the fraction of individuals in its social environment that share its phenotype. This assumption sometimes fails for biologically important fitness functions, for instance in microbial data and the theory of repeated n-person games. In these cases, the Taylor-Frank methodology cannot be used, and a more general form of direct fitness must replace it, to decide when a social mutant allele can invade a monomorphic population.

scholarly journals Light-induced changes of sensitivity in Limulus ventral photoreceptors.

1975 ◽  
Vol 66 (4) ◽  
pp. 473-488 ◽  
Author(s):  
J E Lisman ◽  
J E Brown
Keyword(s):  
Linear Function ◽  
Light Adaptation ◽  
Nonlinear Function ◽  
Light Response ◽  
Total Current ◽  
Peak Current ◽  
Proportionality Constant ◽  
Induced Currents ◽  
Conductance Increase ◽  
Induced Changes

The responses of Limulus ventral photoreceptors to brief test flashes and to longer adapting lights were measured under voltage clamp conditions. When the cell was dark adapted, there was a range of energy of the test flashes over which the peak amplitude of the responses (light-induced currents) was directly proportional to the flash energy. This was also true when test flashes were superposed on adapting stimuli but the proportionality constant (termed peak currently/photon) was reduced. The peak current/photon was attenuated more by brighter adapting stimuli than by less bright adapting stimuli. The peak current/photon is a measure of the sensitivity of the conductance-increase mechanism underlying the light response of the photo-receptor. The response elicited by an adapting stimulus had a large initial transient which declined to a smaller plateau. The peak current/photon decreased sharply during the declining phase of the transient and was relatively stable during the plateau. This indicates that the onset of light adaptation is delayed with respect to the onset of the response to the adapting stimulus. If the adaptational state just before the onset of each of a series of adapting stimuli was constant, the amplitude of the transient was a nearly linear function of intensity. When the total intensity was rapidly doubled (or halved) during a plateau response, the total current approximately doubled (or halved). We argue that the transition from transient to plateau, light-elicited changes of threshold, and the nonlinear function relating the plateau response to stimulus intensity all reflect changes of the responsiveness of the conductance-increase mechanism.

scholarly journals Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yeguo Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Integration ◽  
Delay Differential Equations ◽  
Weighted Sobolev Space ◽  
Laguerre Functions ◽  
Integration Process ◽  
Spectral Accuracy ◽  
Long Time ◽  
Delay Differential

We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.

A PIECEWISE LINEAR DYNAMICAL SYSTEM WITH TWO DROPPING SECTIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 1367-1372 ◽  
Author(s):  
VALERY A. GAIKO ◽  
WIM T. VAN HORSSEN
Keyword(s):  
Dynamical System ◽  
Linear Function ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Nonlinear Function ◽  
Piecewise Linear Function ◽  
Singular Points ◽  
Linear Dynamical System ◽  
Global Bifurcations ◽  
Local And Global Bifurcations

In this paper, we consider a planar dynamical system with a piecewise linear function containing two dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system, with five singular points, can have at most four limit cycles, three of which surround the foci one by one and the fourth limit cycle surrounds all of the singular points of this system.

Research on Feed-Forward Controller for Electronic Throttle Control of GDI Engine Based on Nonlinear Model

2013 ◽  
Vol 860-863 ◽  
pp. 1720-1724
Author(s):  
De Gang Li ◽  
Chuang Li ◽  
Wen Ku Shi ◽  
Tao Jiang ◽  
Xiao Yan Wang
Keyword(s):  
Feedback Control ◽  
Linear Function ◽  
Nonlinear Function ◽  
Velocity Estimation ◽  
Operating Conditions ◽  
Hammerstein Model ◽  
Electronic Throttle ◽  
Feed Forward ◽  
Feed Forward Control ◽  
Observer Model

The nonlinear Hammerstein model was designed. The model was used to compensate the dynamic behavior of an electronic throttle body at different operating conditions. It consisted of a static nonlinear function and a dynamic linear function. The static nonlinear function was used to representing the coulomb friction and limp-home return springs and the dynamic linear function was used to representing dynamic piecewise-linear characteristic. An observer model, known as kalman was used for the on-line throttle position and angular velocity estimation. The control strategy was designed which combined the feed-forward control based on Hammerstein model and feedback control based on proportional-integral-derivative (PID) controller. The control structure has the quick response characteristic of the feed-forward control and disturb compensation characteristic of the feedback control. The experimental results revealed that the dynamic position control delay less than 100ms, the static position error less than 0.5o and the controller satisfied requirement of GDI for precise in-charge control.

Bias in Regressions With a Lagged Dependent Variable

1987 ◽  
Vol 3 (3) ◽  
pp. 371-386 ◽  
Author(s):  
David Grubb ◽  
James Symons
Keyword(s):  
Sample Size ◽  
Linear Function ◽  
General Expression ◽  
Nonlinear Function ◽  
Estimating Equation ◽  
Exogenous Variables ◽  
Lagged Dependent Variable ◽  
Maximum Bias

We give an expression to order O(T-1), where T is the sample size, for bias to the estimated coefficient on a lagged dependent variable when all other regressors are exogenous. The general expression is a nonlinear function of the coefficient on the lagged dependent variable, the autoregressive structure of the exogenous variables, and the coefficients on the exogenous variables. The maximum bias that can arise is a linear function of the number of exogenous regressors in the estimating equation.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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