We study an associative algebra A over an arbitrary field, that is a sum of two subalgebras B and C (i.e. A = B+C). We prove that if B has a nil ideal of bounded index, and that C has a commutative ideal, both of finite codimension in B and C, respectively, then for some nil PI ideal I of A the ring A/I has a commutative ideal of finite codimension.
In this work, we present a technique for the analytical solution of systems of sti ordinary dierential equations (SODEs) using the power series method (PSM). Three SODEs systems are solved to show that PSM can nd analytical solutions of SODEs systems in convergent series form. Additionally, we propose a post-treatment of the power series solutions with the Laplace-Pade (LP) resummation method as a powerful technique to nd exact solutions. The proposed method gives a simple procedure based on a few straightforward steps.
In this work we present a mathematical model for tumour growth based on the biology of the cell cycle. Our model reproduces the dynamics of three different tumour cell populations: Quiescent cells, cells during the inter phase and mitotic cells. Here, we investigate the stability analysis of the cancer-free equilibrium. We have implemented Homotopy perturbation method to give approximated analytical solutions of non-linear ordinary differential equations of system such as model for Tumoural growth. A modification of the homotopy perturbation method based on the use of Pade approximations is done. Some plots are presented to show the reliability and simplicity of the methods.
The article is dedicated to the creation of the fragment of table algebras theory constructed on the basis of classical relational Codd’s algebras. The distinctive peculiarity of the adapted technique is the use of set-theoretic properties of some constructions (full image of the set with respect to the function, function restriction with respect to the set, generalized direct (Cartesian) product, binary relation of functions compatibility) and their transference on a case of tables. The transference of these properties is possible in view of simplicity of signature operations representations in terms of indicated set-theoretic constructions.
Association rule mining is a data mining task that attempts to discover interesting knowledge from huge databases. Data mining researchers have studied subjective measures of interestingness to reduce the volume of discovered rules to ultimately improve the overall efficiency of KDD process. Genetic algorithm (GA) based on evolution principles have found its strong base in mining association rules (ARs). In this paper, confidence and novelty measures have been pushed into a genetic algorithm in order to generate association rules form huge data and discover a novel and hence interesting knowledge to support decision makers. A hybrid approach that uses objective and subjective measures has been used in this paper to quantify novelty of association rules during generation process in terms of their confidence and deviations from the known rules. The proposed approach has a flexible chromosome encoding involve Apriori algorithm where each chromosome should be compute its support and confidence values to performs prune process of week chromosomes. In addition each chromosome differs from another in terms of number of items and classes. The proposed approach has been experimented using real-life public datasets and tested using real life applications. The experimental results have been presented and quite promising.
The phenomenon of Fluid flow separation is associated with a number of Fluid Flow Problems faced in real life situation nowadays. To understand these flow problems even under the assumption of the incompressible viscous flow is quiet a difficult task. The complexity lies on the wide variety of laminar separated flows depending on the body shape, several low and high Reynolds number, surface roughness, transition, etc. Several attempts have been made to solve the complete unsteady Navier–Stokes equations for low Re-Laminar flow problems using a variety of formulations. Among them the vorticity-stream function and pressure–velocity formulations are widely used. In this work a type of steady–state incompressible laminar flow problem in a lid-driven unit square cavity has been studied which deals with different low and high Re. For solving this problem attempts have been made to predict the flow characteristics in a uniform laminar cavity of unit square area by solving the full time dependent, Two–dimensional Navier–Stokes equations in Primitive variable formulations. The methods applied in this study can be carried out in different types of Laminar and Turbulent flows raised in our real life situations.
This short paper continues to discuss randomness of the Euler’s number e digits in decimal expansion. To analyze such randomness statistically, we exploit fixed-effects and random-effects Poisson panel-data models. The results of the regression models reveal the presence of some structure in the distribution of e decimals.
In this paper we introduce a weighted retro Banach frame for a discrete signal space. Necessary and sufficient condition for the existence of weighted retro Banach frames is obtained. Construction of weighted retro Banach frames from bounded linear operator is discussed. A Paley-Wiener type perturbation result for weighted retro Banach frame in Banach space setting is given.
In this paper, an algorithm for solving high-order non-singular Sturm-Liouville eigenvalue problems is proposed. A modified form of Adomian decomposition method is implemented to provide a semianalytical solution in the form of a rapidly convergent series. Convergent analysis and error estimate based on the Banach fixed-point is discussed. Five high-order Sturm-Liouville problems are solved numerically. Numerical results demonstrate reliability and efficiency of the proposed scheme.
In this paper, a SEIV epidemic model with saturated incidence rate that incorporates polynomial information on current and past states of the disease is investigated. The model exhibits two equilibria, disease-free equilibrium (DFE) and the endemic equilibrium (EE). It is shown that if the basic reproduction number, R0< 1, the DFE is locally asymptotically stable and by the use of Lyapunov function, DFE is globally asymptotically stable and in such a case, the EE is unstable. Moreover, if R0>1, the endemic equilibrium is locally asymptotically stable. The effects of the rate at which vaccine wanes (ω) are investigated through numerical stimulations.