In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel

The aim of the study was to evaluate the efficacy of diode laser (λ=940 nm) in the management of gingival hyperpigmentation compared to the conventional bur method. Materials and methods: Eighteen patients with gingival hyperpigmentation were selected for the study with an age between 12-37 years old. The site of treatment was the upper gingiva using diode laser for the right half and the conventional method for the left half. All patients were re-evaluated after the following intervals: 3 days, 7 days, 1 month and 6 months post-operation. Pain and functions were re-evaluated in each visit for a period of 1 day, 3 days and 1 week post-operation. Laser parameters included 1.5 W in continuous mode with an initiated tip (400 μm) placed in

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

The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

This study aims to examine the technologies of education and their importance, shedding light on their reality and  status in Sudan especially in the secondary stage. It has become necessary to invest these technologies and include them in different aspects of the technical education curricula. Such a step helps cope with the innovative scientific development in the advanced countries, qualify professors and technicians, develop the factories and workshops, and create an attractive technical educational environment to the pupils. Thus, the researcher has adopted a descriptive analytical approach that is based on conducting pilot visits to certain technical schools in Al-Khartoum state. Different aspects of such schools were examined

The importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It pro

Class consciousness represents its highest stage in the contemporary Marxist thought of Rosa Luxemburg and Antonio Gramsci, not just a reflection of reality, but rather a dialectical form through the reflection of consciousness on reality and its reproduction. The superiority over the infrastructure (historical materialism) promised the revolutionary class consciousness to be achieved spontaneously, and the seeds of a breakthrough are mass strikes, denying the role of the party to organize this awareness, limiting its role to the interconnection between classes, emphasizing the role of socialist democracy as a conscious vanguard for organizing spontaneity, struggle, and developing awareness during the revolutionary process and the leader

beef and chicken meat were used to get Sarcoplasim, the chicken Sarcoplasim were used to prepare antibody for it after injected in rabbit, the antiserums activity were 1/32 by determined with Immune double diffusion test, the self test refer to abele for some antiserums to detected with beef sarcoplasim, which it mean found same proteins be between beef and chicken meat, which it refer to difficult depended on this immune method to detect for cheat of chicken meat with beef, so the antibody for beef sarcoplasim were removed from serum by immune absorption step to produce specific serum against chicken sarcoplasim that it used in Immune double diffusion test to qualitative detect for cheat beef with 5% chicken meat or more at least, and the

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc