The article deals with construction of one specific scheme for approximate calculation of singular integrals and its use for numerical solutions of integral equations of some class in the sense of Cauchy principal value. Composed quadrature formulas makes it possible equal assessment for quite a wide variety of smooth closed contours.
Cancer is a major health issue, it presents a serious threat to human life. A deep understanding of tumor cell development, genetic mutations in cancerous cell and its biological behaviour remains a persistent need. Many scientific researches suggest that the changes in genes and their proteins expression inside a tumor cell play a crucial role in stimulating the cell division (metastasis) or in restraining its division and reducing its aggressiveness. Agent-based models are computer models that aim to capture the behaviour of individuals inside an environment, they provide a practical setting for studying complex systems. We develop an agent- based model to describe the interaction between 6 agents that represent 6 types of proteins inside a tumor cell and the effect of their exchange on tumor cell motility and metastasis. The simulation results shed light on the circumstance in which the cancerous cell has a great chance to divide and multiply.
This paper presents a method for determining vibration damping in a nonlinear dynamic system of one degree of freedom. It has been found that in the case of resonance, the vibrations of the dynamic system are damped not only by the force generated by the external excitation vibration velocity, but also by the forces generated by the displacements, velocities and accelerations of vibrations at other frequencies. It was found that the magnitude of the amplitude varies in the interval of one excitation cycle and the magnitude and regularity of its change depend on the ratio of resonant, parametric vibrations and external excitation force frequencies. It has been determined that the forces generated by a nonlinear dynamic system can be vibration-exciting forces at one time and vibration-damping forces at another. Studies have found that even in the case of resonances in a nonlinear dynamic system, the vibrations are damped severel hundred time more than in a linear dynamic system. Analytical methods have been developed to allow quadratic and cubic dynamic systems of nonlinearity to choose parameter values during design that would increase the damping of the system and reduce the vibration level of the developed system and ensure its safe operation. The certainty of the analytical methods presented in the article was verified by numerical calculations.
The use of artificial neural network to solve ordinary and elliptic partial differential equations has been of considerable interest lately [1,2,3,4,5]. The error loss optimization techniques [6,7] usually reach an undesirable minimum at some point. Further convergence is usually sought with other minimization [8]. schemes. The use of BFGS scheme has been presently investigated. The simple artificial neural network [4,5] has been applied to solve problems in higher 3 to 4 dimensions with relative ease. The results show a promising trend. The potential flow over an infinite 2D cylinder in polar coordinates has also been investigated. One would expect exact comparison with analytical solution for such a simple problem. However, due to poor convergence, the use of cartesian based neural network for polar coordinate correlation becomes an issue.
In this paper we propose two four-point secant-type methods for finding simple root of nonlinear equations. The new iterative methods do not require any derivatives and has a convergence order of 1.92. Also, we have proved the convergence order of the new methods which require only one function evaluations per full iteration. In addition, numerical examples demonstrate exceptional convergence speed of the proposed methods. It is observed that the new four-point secant-type iterative methods are very effective and robust.
