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The time-fractional Emden-Fowler model is an interesting mathematical model because it is widely used and important in mathematics and applied sciences. The current investigation compiles the Elzaki transform homotopy perturbation method (ET-HPM) and the Laplace transform homotopy perturbation method (LT-HPM) for the analytical solution of the considered model. In their developments, we show that fractional orders are simple to compute, and the resulting series lead to accurate results after a few iterations. We consider the fractional orders in the context of the Caputo form. The primary aim of these approaches is to compare the analytical results of the models under consideration. These schemes do not impose any constraints on the parameters or make any assumptions that could complicate the process of obtaining the analytical results. We show that the derived outcomes are in convergent sequence with a rapid iterative formula. The iterative series and the graphical illustrations in various fractional orders confirm the efficiency of the proposed approaches. The derived results are also compared to the precise solutions, which show that our suggested approaches are simple, effective, and accurate. [ABSTRACT FROM AUTHOR]

The time-fractional Emden-Fowler model is an interesting mathematical model because it is widely used and important in mathematics and applied sciences. The current investigation compiles the Elzaki transform homotopy perturbation method (ET-HPM) and the Laplace transform homotopy perturbation method (LT-HPM) for the analytical solution of the considered model. In their developments, we show that fractional orders are simple to compute, and the resulting series lead to accurate results after a few iterations. We consider the fractional orders in the context of the Caputo form. The primary aim of these approaches is to compare the analytical results of the models under consideration. These schemes do not impose any constraints on the parameters or make any assumptions that could complicate the process of obtaining the analytical results. We show that the derived outcomes are in convergent sequence with a rapid iterative formula. The iterative series and the graphical illustrations in various fractional orders confirm the efficiency of the proposed approaches. The derived results are also compared to the precise solutions, which show that our suggested approaches are simple, effective, and accurate. [ABSTRACT FROM AUTHOR]

With the emergence of the Internet of Things (IoT) and many smart gadgets that support artificial intelligence, it is easier than ever to acquire, reproduce, and disseminate a large number of digital data. However, these great technologies have made it possible for intruders to easily violate issues related to copyright protection, identity theft, and privacy leakage. To address such issues, several approaches have been developed, among which image watermarking has been proven to be an ideal solution. In this paper, a blind watermarking approach for RGB color images based on joint Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) is proposed. First, a self-adaptive color selecting strategy is used to select either the blue or green channel of the host image for embedding purpose. Subsequently, the selected color is subdivided into non-overlapping square blocks of size 4 × 4, and then DCT is applied to each block. Afterward, the DC values obtained from each block are decomposed into four sub-bands using DWT, and then the LH middle frequency sub-band is further decomposed into four sub-bands using DWT. Lastly, the LH1 obtained from LH is utilized for watermark embedding. To provide security to the proposed approach, the watermark image is encrypted before embedding using a chaotic sequence originated from a logistic map method. Experimental results reveal that the proposed approach not only enhances watermark invisibility but also provide excellent watermark robustness, meeting the main requirements of image watermarking. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation's natural protraction, the (2+1) Fokas system, illustrates how a pulse moves across monomode optical fibers. Three efficient methods the Sardar sub-equation approach, the Bernoulli sub-ODE method, and the generic Kudryashov's method are used in this study to offer various families of solutions. Several sorts of function solutions, including those for hyperbolic, trigonometric, power, exponential, and rational functions, are provided by our suggested approaches. In order to highlight the many solutions found, numerous graphs are given toward the conclusion of the text. [ABSTRACT FROM AUTHOR]

Cadmium (Cd) has been recognized as one of the most toxic heavy metals, which is continuously discharged into environments through anthropogenic (industrial activities, fertilizer production, and waste disposal) and natural sources with anthropogenic sources contributing greater than the natural sources. Therefore, Cd concentration sometimes increases in feeds, fodders, water bodies, and tissues of livestock including poultry in the vicinity of the industrial areas, which causes metabolic, structural, and functional changes of different organs of all animals. In poultry, bioaccumulation of Cd occurs in several organs mainly in the liver, kidney, lung, and reproductive organs due to its continuous exposure. Intake of Cd reduces growth and egg laying performance and feed conversion efficiency in poultry. Chronic exposure of Cd at low doses can also alter the microscopic structures of tissues, particularly in the liver, kidney, brain, pancreas, intestine, and reproductive organs due to increased content of Cd in these tissues. Continuous Cd exposure causes increased oxidative stress at cellular levels due to over-production of reactive oxygen species, exhausting antioxidant defense mechanisms. This leads to disruption of biologically relevant molecules, particularly nucleic acid, protein and lipid, and subsequently apoptosis, cell damage, and necrotic cell death. The histopatholocal changes in the liver, kidneys, and other organs are adversely reflected in hemogram and serum biochemical and enzyme activities. The present review discusses about Cd bioaccumulation and histopathological alterations in different tissues, pathogenesis of Cd toxicity, blood-biochemical changes, and its different ameliorative measures in poultry. [ABSTRACT FROM AUTHOR]

In present digital era, multimedia like images, text, documents and videos plays a vital role, therefore due to increase in usage of digital data; there comes high demand of security. Encryption is a technique used to secure and protect the images from unfair means. In cryptography, chaotic maps play an important role in forming strong and effective encryption algorithm. In this paper 3D chaotic logistic map with DNA encoding is used for confusion and diffusion of image pixels. Additionally, three symmetric keys are used to initialize 3D chaos logistic map, which makes the encryption algorithm strong. The symmetric keys used are 32 bit ASCII key, Chebyshev chaotic key and prime key. The algorithm first applies 3D non-linear logistic chaotic map with three symmetric keys in order to generate initial conditions. These conditions are then used in image row and column permutation to create randomness in pixels. The third chaotic sequence generated by 3D map is used to generate key image. Diffusion of these random pixels are done using DNA encoding; further XOR logical operation is applied between DNA encoded input image and key image. Analysis parameters like NPCR, UACI, entropy, histogram, chi-square test and correlation are calculated for proposed algorithm and also compared with different existing encryption methods. [ABSTRACT FROM AUTHOR]

In this paper, we use the Hirota bilinear method. With the help of symbolic calculation and applying this method, we solve the (2+1)-dimensional bidirectional Sawada-Kotera (bSK) equation to obtain some new lump-kink, lump-solitons, periodic kink-wave, periodic soliton and periodic wave solutions. [ABSTRACT FROM AUTHOR]