In this note we extend an irreducibility criterion of polynomial over finite fields. Weprove the irreducibility of the polynomial P(Y ) = Yn + λn−1Y n−1 + λn−2Y n−2 + · · · + λ1Y + λ0, such that λ0 6= 0, deg λn−2 = 2 deg λn−1 + l deg λi, for all i 6= n − 2 and odd integer l.
Aims: The aim of this article is to propose a boundary integral equation algorithm for modeling and optimization of magneto-thermoelastic problems in multilayered functionally graded anisotropic (MFGA) structures.
Study Design: Original research paper.
Place and Duration of Study: Jamoum laboratory, January 2018.
Methodology: a new dual reciprocity boundary element algorithm was implemented for solving the governing equations of magneto-thermoelastic problems in MFGA structures.
Results: A numerical results demonstrate validity, accuracy, and efficiency of the presented technique.
Conclusion: Our results thus confirm the validity, accuracy, and efficiency of the proposed technique. It is noted that the obtained dual reciprocity boundary element method (DRBEM) results are more accurate than the FEM results, the DRBEM is more efficient and easy to use than FEM because it only needs the boundary of the domain needs to be discretized.
In this paper, we generalize the concept of infra-\(\alpha\)-open (closed) and supra-\(\alpha\)-open (closed) sets to fuzzy topological spaces and basic properties of these new concepts have been introduced. Some applications on fuzzy (supra-) infra-\(\alpha\)-open (closed) sets, likely, fuzzy (supra-) infra-\(\alpha\)-continuous mappings, fuzzy (supra-) infra-\(\alpha\)-open (closed) mappings, fuzzy supra-\(\alpha\)- irresolute mapping and fuzzy supra-\(\alpha\)-connected space are introduced. The relations and converse relations between these new concepts and others kinds of fuzzy open sets and fuzzy continuous mappings are discussed. Special results about these new concepts are investigated and studied.
A simple system is a system who has no proper ideals. We prove that every simple system $\mathcal{J}$ have one of the following assertion:
\begin{description}
\item[$(1)$] $\mathcal{J}$ is $\mathfrak{h}-$irreducible.
\item[$(2)$] $\mathcal{J}=\mathcal{J}_1\bigoplus\widetilde{\mathcal{J}_1}$ is the direct summation of two $\mathfrak{h}-$invariant and $\mathfrak{h}-$irreducible subsystems.
\end{description}
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