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Pure mathematics should be used very carefully when applying it to many fields that have special considerations and special axioms.I used a simple example of runners waiting for the start of a race. I concluded thanks to Riemann’s definition of integrals that a runner can cheat if he has time in order to win.The demonstration in this paper is very simple but the analogy of the proposed example with many fields can make the researcher be careful when using the definition of Riemann for the integrals., Maghrebian Journal of Pure and Applied Science, Vol. 9, No 1 (2023)

Most physics lovers asked themselves several times: Why should we limit the velocities in our nature to the velocity of light C ? And why a particle of light shouldn't have an ordinary mass even if the redshift or blueshift of light have been discovered. In my previous work about the michelson morley experiment, I concluded that the light can be studied easily like all the other waves. Actually, many scientists venerated the light by some theories that gave a limit to the velocities of photons and abolished their mass. This work makes a conclusion about Einstein’s relativity after an easy study about the Pound-Rebka experiment which deals with the Gravitational effect of light, and you will find also some logical remarks about the Doppler effect., Maghrebian Journal of Pure and Applied Science, Vol. 9, No 1 (2023)

This is a mathematical article that deals with the domain of complex numbers in order to contribute in the worldwide collaboration of mathematicians who want to study and explain the Riemann's Zeta Function. The aim of this work is to propose new mathematical statements of complex numbers and to give a new easy criterion that may help to identify or deny the possible Landau-Siegel Zeros. Furthermore, this work invites the mathematicians to study a new possible useful homomorphism. Hence, this is a good article to be read by specialists of Analysis or Algebra and even by the beginners of mathematics who want to improve their skills., Maghrebian Journal of Pure and Applied Science, Vol. 9, No 1 (2023)

Thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in order to prove new formulas about the cardinality of each group of problems and about the intersection of each one of these sets. This work uses logical considerations about the complexity of NP-Hard problems in order to provea theoremabout the complexity ofproblems that allows us to identify NP problems even if their algorithms have infinite time of execution. This work ends by proving that the set of NP-Problems is definitely bigger than the set of P-Problems. Hence, I invite all the readers to develop the results of this article and to present their opinions about the used considerations in this work.

Thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in order to prove new formulas about the cardinality of each group of problems and about the intersection of each one of these sets. This work ends with a theoremabout the complexity ofproblems that allows us to identify NP problems even if their algorithms have infinite time of execution. Hence, I invite all the readers to use and develop the formulas of this article and to present their opinions about them.

In many industrial fields, there is an ever growing market demand for highly profitable engines. This fact encouraged to produce very developed engine parts, namely sophisticated injection systems. Consequently, the electronically enhanced injection systems are becoming very widespread for their high efficiency and cause the mechanical automatic systems to be neglected without enough studies. However, the electronically commanded injection is difficult to maintain because of the risks of short-circuits, and it is also difficult and expensive to repair since its captors are in high pressure and temperature areas. This paper aims to introduce a mathematical study of the basic direct injection operation by proving formulas representing forces, velocities and the energy involved in the injection mechanical mechanism without any electronic or computational complications. This theoretical mathematical modeling is useful for the efficiency experimental studies in order to improve the manufacturing and maintenance of all direct injection systems.

When the light photons bounce off a moving mirror, they react with its atoms to be reflected, consequently, the photons change their velocity vector after each impact depending on the velocity vector of the mirror and thus of the atom. The Michelson-Morley experiment was the event that changed the modern science about "the light" by leading to Lorentz and Einstein's theories about time.I made the formulas of the Michelson-Morley experiment by considering the effects of the reflection on the light and The rate (percentage) of fringe shift calculated by the formulas which I demonstrated is perfectly null. As a result not all physics must be wrong ,but only a principle that Einstein and Lorentz stated by fixing the light speed for all observers, which makes us study light in a very difficult way. The formulas demonstrated in this work allow us to study the light as a normal wave and to understand easily all the other light effects without being obliged to use any relativity of the time., Maghrebian Journal of Pure and Applied Science, Vol 6, No 2 (2020)

This work dates from January 2016 as a result of my remarks related to physics made during my high studies. I try in this work to explain the cause behind the inability of Newtonian mechanics to describe correctly many phenomena where the studied object rotates at a very high linear speed. I proved that, in this case, the velocity field is not equiprojective and that the famous formula for changing the reference frame is not correct. I made an application to the case of the GPS system satellites, then I presented a new method for studying a rotating system velocity without needing the conventional steps of changing reference frames. I finished my work by demonstrating the formulas of the main differential operators and I presented them with all the related steps and calculations by using the elementary surfaces. I am eager to discuss the results of this work further with physics and mathematics specialists, and I hope that my formulas will help to simplify the study of many difficult physics phenomena., Maghrebian Journal of Pure and Applied Science, Vol 6, No 1 (2020)