We present a geometric proof of the addition formulas for the hyperbolic sine and cosine functions, using elementary properties of linear transformations.

Through the modification of the kernel on a Ubuntu system, we managed to solve the n-Queens problem after changing the default time-slice, swappiness, latency and wakeup-granularity to different values and testing the problem.

The Linux kernel controls the way tasks (or processes) are managed in the running system. The task scheduler, sometimes called process scheduler, is the part of the kernel that decides which task to run next. In this project its analyzed the behavior of scheduler by changing a default value from the runtime scheduling. The default value is 950000µs, or 0.95 seconds for the sched\_rt\_runtime\_us or scheduler realtime running variable. Meaning that 5% of the CPU time is reserved for processes that don't run under a real-time or deadline scheduling policy. This value in this file specifies how much of the "period" time can be used by all real-time and deadline scheduled processes on the system. The AIO-Stress which shows the obtained results in the different tests is an a-synchronous I/O benchmark created by SuSE which is is a German Linux distribution provider and business unit of Novell, Inc.

Here we discuss the path integral formalism for quantization of fields. The basic idea is reviewed and explained. This is completely based on the book ``Quantum Field Theory A Modern Introduction" by Michio Kaku. For calculation natural system of units is taken.

On the basis of the conclusions selectively gleaned from the history of ontological thought, it was assumed that the real geometry of the space of the Universe is the geometry of topologically fixed 3-dimensional hyper sphere. It claims that the understanding of metaphysical principles of space formation is important, resulting in the simplest mathematical approach to the calculation of actual astronomical distances. The comparisons of calculated lengths of trajectories of photons with the actual intergalactic distances reported by observers for different \(z\)-values are carried out using the selected assumptions. Photon mileage \(L_f = f (L_z, R_D)\) don't equal to the astronomical distance \(L_z\) detected by \(z\) value if \(R_D\) is the discrete quantum length of one of 4 space dimensions, associated with the curvature of space as a whole. The research concludes there is a good agreement between data obtained this way for star brightness with experimental data, when we speak about the hypothesis presupposing an accelerating growth of the Universe and abnormal brightness of supernovae; besides conclusions imply that adjustments to this hypothesis forward in the search of the values of brightness attenuation undetectable by today's tools are needed, otherwise, it could be talk about a possible expansion of our Universe in our era without accelerating.