As an application of the improved Cauchy-Schwartz inequality due toWalker (2017), we obtain an improved version of the Cramer-Rao inequality for Randomly censored data derived by Abdushukurov and Kim (1987, pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on Randomly censored data.

In this research paper, we will present how to hide confidential information in a color image Randomly using a mathematical equation; by apply this equation to the number of image bytes after converting the image into a digital image, the number of Randomly selected bytes depends on the length of the secret message. After specifying the bytes, we include the secret message in those selected bytes utilizing least significant bit (LSB) of steganography, and return the new bytes in the same place in the original image by using the same mathematical equation, after the hiding process using steganography, and then we encrypt the image and send it to the recipient. Several statistical measures applied to the original image, compared with the image after embedding, and after the image encrypted. The results obtained are very good. The statistical measures were used the histogram, mean square error (MSE) and the peak signal to noise ratio (PSNR).The system is designed to perform these processes, which consists of two stages, hiding stage and extract stage. The first stage contains from four steps, the first step of this stage reading the image and converting it to a digital image and make an index on each byte of the image bytes and the application of the mathematical equation to select the bytes by Randomly, second step is the process of hiding the secret message in selected bytes and return those bytes to the original locations, third step is the calculation of the statistical measures to determine the rate of confusion after the inclusion of the confidential message, fourth step to encrypt the image of the message carrier and measure the rate of confusion after the encryption and compare with the original image. The extraction process consists of three steps, the first step is to use the private key to decrypt, and the second step is to apply the same mathematical equation to extract the embedded bytes of the confidential message, third step use the same method of hiding the information and extracting the confidential message.

In this work computational fluid dynamics is used to describe the fluid flow across a Randomly packed absorption tower. The CFD simulation method is employed on a packed tower that is packed with 1cm Raschig rings. Tower is 175cm in height. Air flow rate range was 1.5 to 5 m/s. The measured pressure drops were in 1.5 to 12 Pascal per height of tower in meter. The Klerk’s approach is examined to define the influence of confining walls on pressure drop in packed areas. It is concluded that CFD model that uses the Klerk’s definition of radial porosity distribution is a successful way for pressure drop prediction in packed beds. Model prediction of dry pressure drop is about 4% lower than the experimental measurements. Ergun’s pressure drop prediction is compared with that of Reichelt’s using averaged and distributed porosity profiles. In both methods Ergun’s approach in comparison with Reichelt’s approach has %6 lesser error in dry pressure drop prediction.

Natural fibers such as banana, sisal, snake grass, coir, hemp, jute and so on are armed with enormous advantages like less weight, reliability, recyclability and environmental friendly nature. Such fibers may enhance the system’s performance by acting as additives with the thermoplastics in different perspectives. Besides the natural composites, hybrid composites facilitate the design of material with specific property matched to an application. In the present work an attempt has been made to manufacture and test the banana and snake grass short fiber reinforced hybrid polyester composites in random orientation and random lay-up. Methyl Ethyl Ketone Peroxide was used as the coupling agent and Cobalt Naphthalene as the catalyst. Hand layup technique was used to manufacture the composites. Relative volume fraction of the fibers was varied between 2.5-12.5% in the ratio 1:1. Properties like tensile strength and modulus, flexural strength and modulus  are measured  for the composites  by conducting  the appropriate tests according to  ASTM standards.