In the analysis of multiple linear regression, the problem of multicollinearity and auto-correlation drew the attention of many researchers, and given the appearance of these two problems together and their bad effect on the estimation, some of the researchers found new methods to address these two problems together at the same time. In this research a comparison for the performance of the Principal Components Two Parameter estimator (PCTP) and The (r-k) class estimator and the r-(k,d) class estimator by conducting a simulation study and through the results and under the mean square error (MSE) criterion to find the best way to address the two problems together. The results showed that the r-(k,d) class estimator is the best esti

White and black chia seeds were used in some food products, such us gluten –free biscuits processing by using rice flour and chia seeds (white and black) with these amonths 112.5, 74.25, 56.25, 27.5 g with 27.5g of quinoa seeds for treatments 1, 2, 3 and 4 respectively, and comparison sensitively with the control treatment which has no additions including the appearance and homogenization of the product, surface cracks, softness, taste and flavor, core color and the specific volume, some microbiological tests were performed for biscuit product after storage for 4 months at 30 and 50°C including bacterial total count and fungal and yeast count, results showed that there weren’t any observation of bacteria or yeast or fungal growth at

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

Vitamins k is an important fat-soluble vitamin that can be obtained from plants, bacteria and animals and is necessary for the blood clotting. It plays a key function as a cofactor in the synthesizing of blood clotting proteins in the liver; recently, the interest for its functions in extra-hepatic tissue has increased. Vitamin k deficiency is usually caused by abnormal absorption rather than in the lack of vitamin in food. Apart from its impact on clotting, chronic subclinical deficiency of vitamin K maybe a risk factor for many diseases such as osteoporosis, atherosclerosis, cancer, insulin resistance, neurodegenerative diseases and others, while current food intake guidelines be focused on the daily dose necessary to avoid blood loss.

In this research, the methods of Kernel estimator (nonparametric density estimator) were relied upon in estimating the two-response logistic regression, where the comparison was used between the method of Nadaraya-Watson and the method of Local Scoring algorithm, and optimal Smoothing parameter λ was estimated by the methods of Cross-validation and generalized Cross-validation, bandwidth optimal λ has a clear effect in the estimation process. It also has a key role in smoothing the curve as it approaches the real curve, and the goal of using the Kernel estimator is to modify the observations so that we can obtain estimators with characteristics close to the properties of real parameters, and based on medical data for patients with chro

The present research focuses on the study of the effect of mass transfer resistance on the rate of heat transfer in pool boiling. The nucleate pool boiling heat transfer coefficients for binary mixtures (ethanol-n-butanol, acetone-n-butanol, acetone-ethanol, hexane-benzene, hexane-heptane, and methanol-water) were measured at different concentrations of the more volatile components. The systems chosen covered a wide range of mixture behaviors.

The experimental set up for the present investigation includes electric heating element submerged in the test liquid mounted vertically. Thermocouple and a digital indictor measured the temperature of the heater surface. The actual heat transfer rate being obtained by multiplying the voltme

single and binary competitive sorption of phenol and p-nitrophenol onto clay modified with
quaternary ammonium (Hexadecyltrimethyl ammonium ) was investigated to obtain the
adsorption isotherms constants for each solutes. The modified clay was prepared from
blending of local bentonite with quaternary ammonium . The organoclay was characterized
by cation exchange capacity. and surface area. The results show that paranitrophenol is
being adsorbed faster than phenol . The experimental data for each solute was fitted well with
the Freundlich isotherm model for single solute and with the combination of Freundlich-
Langmuier model for binary system .