Mario Gonzalez-Lee

Universal character of the fractional space-time electromagnetic waves in dielectric media

This work presents an alternative solution for the mathematical analysis of the fractional waves in dielectric media. For the fractional wave equation, the Caputo fractional derivative was considered, the order of the spatial and temporal fractional derivatives are , respectively. In this analysis, we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space and time derivatives into the fractional wave equation. We will consider source free Maxwell equations in isotropic and homogeneous dielectric medium. The general solutions obtained in our research have been expressed in terms of the multivariate Mittag–Leffler functions, these functions depend only on the parameters and preserving the appropriated physical units according to the system studied.

Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Pade posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

Direct application of Padé approximant for solving nonlinear differential equations

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant.AMS Subject Classification34L30

Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel

We present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes distributed elements of the Cole model type. In addition to maintaining consistency in adjusted electrical parameters, a detailed methodology is proposed to build the equivalent circuits. Illustrative examples are given and the Nyquist and Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. The advantage of our representation appears according to the comparison between our model and models presented in the paper, which are not physically acceptable due to the dimensional incompatibility. The Markovian nature of the models is recovered when the order of the fractional derivatives is equal to 1.

Enhancing Biomedical Images Using the UFIR Filters with Recursive Responses

In this paper we present a novel computational scheme to determine the impulse response of the UFIR filters. A recursive form of impulse response is developed using the theory of the discrete orthogonal polynomials. An example of an enhanced of medical image is considered to compare its performance versus the matrix formulation of the impulse response UFIR filters. Finally, some quantitative and qualitative evaluations are carried out to verify its efficiency based on RMSE analysis.

Optimal detection of multiplicative watermarks in Laplacian channels

In this work, we propose a model for an optimal detector of digital watermarks for Laplacian channels, the watermark embedding algorithm is the multiplicative embedding rule in time domain, the optimal detection equation and the threshold equation are derived using maximum likelihood (ML) and Neyman-Pearson criterion. The resulting system is blind and has very low complexity. Computer simulations are carried out applying the proposed model to audio signals and results prove that the proposed system is able to detect watermarks even if the watermarked object was severely attacked by noise, low pass filtering among other attacks.

UHF RFID antennas integrated on flexible substrate for health care environments

Most of RFID tags for radiofrequency identification applications are different among them since its design and fabrication process rely on intended application environment. Thus, RFID tag antennas should be made of materials suitable for its target application scenario allowing in the end, an efficient means for identification. In this paper, design and fabrication details of flexible RFID tags antennas is discussed, those tags were attached to a chip in order to measure the working area of the tags. Three prototypes of RFID antennas working in the UHF band of the spectrum were built by integrating it in Rogers RT/Duroid 5880 substrate which is flexible, can be easily finished and resist most chemicals used for printed circuit board fabrication, that is why is widely used for making antennas.

Deduction of the impulse response of the p-step UFIR filter using kth moments

This paper we present a new computational scheme to derive the impulse response of p-step UFIR filter. We use a set of polynomials that can be expressed in terms of their kth moment to derive the same impulse response obtained by other methods. Furthermore, we apply the p-step UFIR filter in two cases: enhanced of a square signal and the denoisy image processing. Finally, some quantitative and qualitative evaluations are carried out to verify filters efficiency based on RMSE analysis.

Integer Wavelet Transform Based Watermarking System for PCM Signals

In this paper, a watermarking system based on the integer wavelet transform is proposed. A set of different wavelets was chosen for this propose so their performance as watermark transmission channel can be analyzed. The watermark is embedded in the second decomposition level of the wavelet transform of a PCM signal in a block wise approach, the coefficients of the wavelet transform are assumed to be accurately modeled as a Laplacian channel. A set of attacks were performed in order to test system’s robustness, we found that this approach is robust against several attacks such as additive white noise, low pass filtering, cropping, among other attacks; the best suited wavelet class for developing watermarking systems was identified too.