we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

Within the context of predicting and mitigating flood hazards, this paper motivates the development of innovative ideas in three engineering research areas: (a) spatially-distributed quantitative rainfall prediction, (b) spatially-distributed flow prediction, and (c) long-term flow prediction for water resources management. Design, operational implementation, real-time testing, and training of ...

this paper intends to offer a new iterative method based on articial neural networks for finding solution of a fuzzy equations system. our proposed fuzzied neural network is a ve-layer feedback neural network that corresponding connection weights to output layer are fuzzy numbers. this architecture of articial neural networks, can get a real input vector and calculates its corresponding fu...

it seems using the maxwell-stefan (m-s) diffusion model in combination with the vacancy solutiontheory (vst) and the single-component adsorption data provides a superior, qualitative, andquantitative prediction of diffusion in zeolites. in the m-s formulation, thermodynamic factor (г) isan essential parameter which must be estimated by an adsorption isotherm. researchers usually utilizethe simp...