Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.

Data steganography is a technique used to hide data, secret message, within another data, cover carrier. It is considered as a part of information security. Audio steganography is a type of data steganography, where the secret message is hidden in audio carrier. This paper proposes an efficient audio steganography method that uses LSB technique. The proposed method enhances steganography performance by exploiting all carrier samples and balancing between hiding capacity and distortion ratio. It suggests an adaptive number of hiding bits for each audio sample depending on the secret message size, the cover carrier size, and the signal to noise ratio (SNR). Comparison results show that the proposed method outperforms state of the art methods

Data steganography is a technique used to hide data, secret message, within another data, cover carrier. It is considered as a part of information security. Audio steganography is a type of data steganography, where the secret message is hidden in audio carrier. This paper proposes an efficient audio steganography method that uses LSB technique. The proposed method enhances steganography performance by exploiting all carrier samples and balancing between hiding capacity and distortion ratio. It suggests an adaptive number of hiding bits for each audio sample depending on the secret message size, the cover carrier size, and the signal to noise ratio (SNR). Comparison results show that the proposed method outperforms state of the art methods

I've made extensive studies on the distribution of the electric field stable heterogeneous within intensive that contain metal rings with slope diagonal positive to a site halfway to be in its maximum value, followed by decline negative and equally to the other end of the concentrated distributed by electric stable thanking sequentially and have focused empirical studies in the pastthe molecules that you focused Pantqaúha during passage

In many video and image processing applications, the frames are partitioned into blocks, which are extracted and processed sequentially. In this paper, we propose a fast algorithm for calculation of features of overlapping image blocks. We assume the features are projections of the block on separable 2D basis functions (usually orthogonal polynomials) where we benefit from the symmetry with respect to spatial variables. The main idea is based on a construction of auxiliary matrices that virtually extends the original image and makes it possible to avoid a time-consuming computation in loops. These matrices can be pre-calculated, stored and used repeatedly since they are independent of the image itself. We validated experimentally th

The economical design of plate loaded by pressure can be obtained by using stiffeners instead of increasing the thickness of plate. The main subject of this work is to obtain the effect of stiffener height on the maximum stress in the plate subjected to pressure load. Different plate-stiffener sets are selected to find the effects of stiffener thickness, plate dimensions and pressure, on the optimum stiffener height. The models under consideration are square plates clamped rigidly from four edges. Finite Element method is used to analyze 160 different models by using the Finite Element software package ANSYS version 11. Another analysis method based on maximum stress equation is used to analyze 30 models. The graphical comparison of results

The pillars of sustainable development are representing the interface between environmental, economic, and social sustainability. Sustainable development is a method of planning and managing construction projects to reduce the effect of the construction process on the environment so that there is a balance between environmental capabilities and the human needs of present and future generations. Usually, Environmental sustainability is most important and effective in construction projects. The environment suffers from significant negative impacts as a result of the implementation of construction projects; therefore, this study aims to identify the effecting factors on environmentally sustainable development. The methodology of this s