مجله پژوهش های نوین در ریاضی
پیاپی 41 (فروردین و اردیبهشت 1402)

The speed of calculation and the level of ability to perform calculations for a computing system are two fundamental questions in computer science. Also, the concept of complexity of performing calculations in machine language and the measure provided for complexity are important quantities. In this article, we calculate the growth rate of the complexity of performing calculations for an asynchronous oscillator by using mathematical methods and specifically using the disturbance theory. The reason for choosing an oscillator is that most physical systems can be simulated with an oscillator. Also, we calculate the maximum dynamic evolution of the quantum states that changes the computation rate, and as an important achievement of this work, we show that for even-order perturbation, the rate of complexity increases, while for odd-order perturbation, the rate We will have a decreasing behavior. This method can be considered as a theoretical model for the upper limit of calculations.

In this paper, the effect of magneto-hydrodynamic flow on two aerodynamic geometries (2D & 3D) is investigated. The results (Lift and drag coefficients) for two and three-dimensional geometries, which have been tried to be similar to rocket wings, at high altitudes where the pressure is high and the temperature low, as well as Machs at 6 and 8 and at 9 different angles of attacks, are obtained in two modes with and without magnets. At the end, it was observed that adding a magnet to the problem increases the lift coefficient which maximum increment (77.5%) occurred for 3D geometry at Mach 8 and 50000 m height. Also, comparing the two-dimensional and three-dimensional geometries, it was observed that the stall angle did not occur in the two-dimensional geometry at 9000 altitude and Mach 6, but in the three-dimensional geometry and the same conditions, the stall angle was observed for the non-MHD mode, which is due to flow line of two-dimensional geometry. However, it was further observed that this angle was delayed by adding a magnet to the 3D geometry with the mentioned solution conditions.

One of the most important methods for solving linear and nonlinear problems is the homotopic analysis method, which was proposed by Liao in 1992. The main purpose of this paper is to present a modification of homotopy analysis method (HAM), which is called successive homotopy analysis method (SHAM). Several numerical examples are presented to present a comparison between the results obtained by homotopy analysis method and its successive type. The results show that the calculation volume in the successive homotopy analysis method is less that the homotopy analysis method. Also, unlike the homotopy analysis method, the numerical solutions obtained by the successive homotopy analysis method are satisfactory over a relatively wide range. So, by using the successive homotopy analysis method, various types of linear and nonlinear mathematical equations and also some nonlinear equations which are obtained in other scientific branches, for instance physics, mechanics and etc, can be solved numerically.

Let G be a discrete group that acts on C^*-algebra A. We prove that in the category of G-AF-algebras and completely positive linear G-equivariant the finite-dimensional G-AF-algebra must be injective. One consequence of this is that no infinite-dimensional G-AF-algebra could be injective in the category of G-C^∗-algebras.Also, we show that the following statements are equivalent for a separable essentially simple G-C^*-algebra A: (i) A̅_G, regular completion of A, is a G-W^*-algebra (von-Neumann algebra).(ii) I_G(A), injective envelope of A, is a G-W*-algebra (von-Neumann algebra).(iii) A is G-isomorphic to a direct sum of elementary G-C^*-algebras K(H_n), which H_n is a Hilbert space. Since the K(H_n) is G-AF-algebra, and we know that the category of G-AF-algebras is closed under taking the countable direct sum. Therefore, we prove this G-C^*-algebra is a G-AF-algebra.Further, we show that if separable essentially simple G-C^∗-algebra A is post liminal, then A is liminal G-C^∗-algebra.