We introduce the seemingly new concept of a rigid matrix based on the comparison of its sparsity to the sparsity of the natural powers of the matrix. Our results could be useful as a usage guide in the scheduling of various iterative algorithms that appear in numerical linear algebra. Especially in Sparse matrix-vector multiplication and they could also be used in matrix norm error analysis.
Francisco A. Betancourt, Dalia M. Muñoz Pizza, Anibal Muñoz Loaiza, John F. Arredondo Montoya, Carlos A. Abello Muñoz, Oscar A. Manrique Arias, Julian A. Olarte, Steven Raigosa Osorio, Hans Meyer Contreras, Valentina Zuluaga Zuluaga
It is formulated and analyzed an optimal control problem for the transmission dynamics of the SEIS-like pulmonary tuberculosis (TB) including prevention by means of non-linear differential equations, which are linked to a functional cost. Also, it is established and analyzed the use of optimal control to reduce the latent and infectious populations by using the Pontryaguin's maximum principle (a Hamiltonian function which establishes a problem with numerical limits). After that, simulations of the problem are done. Finally, with an analysis of the viability of strategies to control the disease, we have concluded that the application of effective control measures in the prevention generates a significant decrease in the infected population as well as affects directly the propagation of the infection.
This paper handles a prominent problem of project management, namely that of project scheduling under uncertainty. The paper models this problem as a vector-weighted voting system and expresses the indicator variable for the successful (on-time) completion of project activities as a vector-threshold Boolean function. The paper presents a solution of the problem in the Boolean domain using solely Boolean tools. The paper also presents another solution of the problem via recursive relations and boundary conditions. This solution is given as an insightful visual representation in terms of a signal-flow graph that resembles the Reduced-Ordered Binary Decision Diagram (ROBDD). The effect of the order of variables used in the recursive method is also explored.
The wind speed equation of circular cyclone is a set of non-linear partial differential equations (PDE) with 4 unknown functions u (wind speed), ρ (density), p (pressure) and T (temperature) and is separated to 14 unknown functions, 4 unknown constants related by 15 equations. The solution is found analytically by method of separating variables, dimension analysis, and iteration method guided by periodic g-contractive mapping theorem. Isolated system is defined and the uniform circular motion (UCM) of steady flow in a horizontal plane is studied. Application to calculation of wind speed, temperature, mass density and mechanical energy are given. Comparing with results based on statistics, probability, or involving random factor, the result of this paper has 3 features: (1) it belongs to certainty-type; (2) four factors uθ, ρ, p and T linked; (3) these four factors are expressed by functions of r and z ; while in others, they belong to uncertain-type; three factors ρ, p are T are linked and are expressed by function of z only. Finally, conclusion is made.
Wearable electronics are electronic products which are implemented by using both electronics technologies and computing devices that a person can wear usually on a daily basis and integrated into clothing. Wearable devices come in many forms with various levels of complexity. Currently, the market for these products is quickly growing, especially within the devices targeted at the common consumer. This is due to the rapid improvements in electronic and computing technology during the last decade. However, despite these advances there still remain unanswered questions on the future success of these products. As a result both this technology and the potential benefits and drawbacks for everyday wearable electronics, a lot of research is on. The main aim of this study is to provide a literature focus to the researchers working on wearable electronics.