Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

Efficient design of FIR filter based low-pass differentiators for biomedical signal processing

This paper describes an alternative design of linear phase low-pass differentiators with a finite impulse response (type III FIR filter). To reduce the number of necessary filter coefficients, the differentiator’s transfer function is approximated by a Fourier series of a triangle function. Thereby the filter’s transition steepness towards the stopband is intentionally reduced. It can be shown that the proposed design of low-pass differentiators yields to similar results as other published design recommendations, while the filter order can be significantly reduced.

Properties of distance spaces with power triangle inequalities

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving what is called a distance space, and also what happens if the triangle inequality is replaced with a much more general two parameter relation, which is herein called the "power triangle inequality". The power triangle inequality represents an uncountably large class of inequalities, and includes the triangle inequality, relaxed triangle inequality, and inframetric inequality as special cases. The power triangle inequality is defined in terms of a function that is herein called the power triangle function. The power triangle function is itself a power mean, and as such is continuous and monotone with respect to its exponential parameter, and also includes the operations of maximum, minimum, mean square, arithmetic mean, geometric mean, and harmonic mean as special cases.

Properties of distance spaces with power triangle inequalities

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving what is called a distance space, and also what happens if the triangle inequality is replaced with a much more general two parameter relation, which is herein called the "power triangle inequality". The power triangle inequality represents an uncountably large class of inequalities, and includes the triangle inequality, relaxed triangle inequality, and inframetric inequality as special cases. The power triangle inequality is defined in terms of a function that is herein called the power triangle function. The power triangle function is itself a power mean, and as such is continuous and monotone with respect to its exponential parameter, and also includes the operations of maximum, minimum, mean square, arithmetic mean, geometric mean, and harmonic mean as special cases.

Properties of distance spaces with power triangle inequalities

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving what is called a distance space, and also what happens if the triangle inequality is replaced with a much more general two parameter relation, which is herein called the "power triangle inequality". The power triangle inequality represents an uncountably large class of inequalities, and includes the triangle inequality, relaxed triangle inequality, and inframetric inequality as special cases. The power triangle inequality is defined in terms of a function that is herein called the power triangle function. The power triangle function is itself a power mean, and as such is continuous and monotone with respect to its exponential parameter, and also includes the operations of maximum, minimum, mean square, arithmetic mean, geometric mean, and harmonic mean as special cases.

The Study of the Solution to a Generalized KdV-mKdV Equation

A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is employed to investigate a generalized KdV-mKdV equation which possesses high-order nonlinear terms. Some new solutions including the Jacobi elliptic function solutions, the degenerated soliton-like solutions, and the triangle function solutions to the equation are obtained.

MULTISCROLL CHAOTIC ATTRACTORS FROM A MODIFIED COLPITTS OSCILLATOR MODEL

A simple approach for generating (2N + 1)-scroll chaotic attractor from a modified Colpitts oscillator model is proposed in this paper. The key strategy is to increase the number of index-2 equilibrium points by introducing a triangle function to directly replace the nonlinearity term of Colpitts oscillator model. The dynamical characteristics of the new multiscroll chaotic system are studied comprehensively. A circuit realization structure is introduced and the experimental results demonstrate that (2N + 1)-scroll chaotic attractors can be obtained in practical circuit.

Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces

We introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces.

CONVOLUCION OPTICA UTILIZANDO FOTODETECTORES

When evaluating an intensity profile by using a photodector of finite area, the convolution between the function to be measured and the function which describes the photodetector response is obtained. To obtain the original function a deconvoluion operation must be performed. Another approach to the problem is to use a diaphragm or pupil against the sensible area on the front of the photodector. We present here an estimation of the error introduced for different sizes of the pupil by considering the measuremet of a typical gaussian intensity profile.Otherwise, it is possible to take profit on the capability of the photodetectors to easily obtain the optical convolution. As example, we show the optical convolution for a rectangle and a triangle function.