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.

Identification of Randomly interstratified illite - smectite, the most abundant of the mixed-layer clay minerals, is occasionally difficult. The so called magnesium chloride and ethylene glycol treatment does not always reveal all the peaks necessary for identification of these clay minerals. Therefore a new modality, lithium chloride treatment, is suggested. With the application of this treatment, the characteristic peaks related to the mixed layer as well as smectite will appear clearly. So, the illite proportion in the mixed-layer can be determined easily.

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.

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.

Piping is a phenomenon that commonly occurs at downstream of hydraulic structures such as earth dams, irrigation channels and drainage network under the influence of upward seepage. Piping is considered as the main mechanism of hydraulic structures failing. In this work an experimental program was set for determination the seepage velocity and piping resistance for unreinforced and reinforced sand silty samples. Two type of fibers (Polyester and Polyethylene terephthalate) with different diameter (0.2 mm and 0.3 mm) was used for preparing reinforced samples. The experimental tests was conducted on samples without and with different fiber content (0.5%, 0.75%, 1% and 1.25%) and fiber length (5, 25, 35 and 50 mm) under different hydraulic heeds in a special designed apparatus. Discharge and seepage velocity of water flow through unreinforced and reinforced samples was measured and calculated and Comparison was made. The results showed that the inclusion of fiber reduces the seepage velocity and increased the hydraulic gradient and piping resistance. Furthermore, increasing of hydraulic gradient and piping resistance is function of fiber content and fiber length.

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.

This paper establishes the first four moment expansions to the order o(a-1) of Sta/Ö ta, where S´n =åni=1 Vi i=1 Yi is a simple random walk with E(Yi) = 0, and tα is a stopping time given by ta = inf {n ³1 : n + Sn + zn > a} where Sn = ån i= Xi is another simple random walk with E(Xi) = 0, and { zn, n³1} is a sequence of random variables satisfying certain assumptions. These moment expansions complement the classical central limit theorem for a random number of i.i.d. random variables when the random number has the form ta, which arises from many sequential statistical procedures. They can be used to correct higher order bias and/or skewness in S´ta/Öta to make asymptotic approximation more accurate for small and moderate sample sizes.