In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

  The study (Quality in the Industrial Products Designs and its Reflection on Achieving Competitive Advantage) focused on developing the products in a way that satisfies human desires through the impact of technology on products design systems and performance enhancement. The study question is: how to effectively achieve quality in industrial products designs that influences competitiveness? The aim of the research is to show the design contexts for the product and its reflection on competitiveness. The study is limited to (LG) products in 2017-2018. The results and conclusions reached at by the researcher are included in the study.
The sample models adopted contexts, forms and relational relations transcending traditional contex

In this paper, the theoretical cross section in pre-equilibrium nuclear reaction has been studied for the reaction  at energy 22.4 MeV. Ericson’s formula of partial level density PLD and their corrections (William’s correction and spin correction) have been substituted  in the theoretical cross section and compared with the experimental data for  nucleus. It has been found that the theoretical cross section with one-component PLD from Ericson’s formula when  doesn’t agree with the experimental value and when . There is little agreement only at the high value of energy range with  the experimental cross section. The theoretical cross section that depends on the one-component William's formula and on-component corrected to spi

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

The microbend sensor is designed to experience a light loss when force is applied to the sensor. The periodic microbends cause propagating light to couple into higher order modes, the existing higher order modes become unguided modes. Three models of deform cells are fabricated at (3, 5, 8) mm pitchand tested by using MMF and laser source at 850 nm. The maximum output power of (8, 5, 3)mm model is (3, 2.7, 2.55)nW respectively at applied force 5N and the minimum value is (1.9, 1.65, 1.5)nW respectively at 60N.The strain is calculated at different microbend cells ,and the best sensitivity of this sensor for cell 8mm is equal to 0.6nW/N.

The origin of this technique lies in the analysis of François Kenai (1694-1774), the leader of the School of Naturalists, presented in Tableau Economique. This method was developed by Karl Marx in his analysis of the Departmental Relationships and the nature of these relations in the models of " "He said. The current picture of this type of economic analysis is credited to the Russian economist Vasily Leontif. This analytical model is commonly used in developing economic plans in developing countries (p. 1, p. 86). There are several types of input and output models, such as static model, mobile model, regional models, and so on. However, this research will be confined to the open-ended model, which found areas in practical application.

This study discussed a biased estimator of the Negative Binomial Regression model known as (Liu Estimator), This estimate was used to reduce variance and overcome the problem Multicollinearity between explanatory variables, Some estimates were used such as Ridge Regression and Maximum Likelihood Estimators, This research aims at the theoretical comparisons between the new estimator (Liu Estimator) and the estimators

The current research dealt with the rapid development of industrial product design in recent times, and this development in the field of design led to the emergence of modern trends in many terms and theories to direct greater interest in the cognitive foundations of design and its relationship with the components of other natural sciences, and despite the impressive technological development, nature remains With its content of formative values and structural dimensions, it is the first source of inspiration and the source of all modern mathematical sciences and theories, as God made them tend towards organization to continue to provide us with endless inspiration. Hence, the fractional one, which is an important part of dedicating the d

The current research dealt with the development of sciences and arts over the course of human history, and the development of sciences with their natural and human trends are important areas in developing the knowledge and application base for industrial product design and design in its various fields. Bionic science is one of the sciences that works on applying biological methods and systems found in nature to study and design engineering systems and modern technology, and for industrial products to be highly efficient, durable and resistant to natural variables in daily life for use. The transfer of technology between life forms and industrial products is desirable because the processes of development at the level of science in general