12 research outputs found
On ambiguous numbers of an invariant subset \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \end{document} of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \end{document} under the action of the modular group \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \end{document}
No full textProperties of real quadratic irrational numbers under the action of the group H = áx, y: x 2 = y 4 = 1ñ
No full textMagnetohydrodynamic mixed convection flow of Jeffery fluid with thermophoresis, Soret and Dufour effects and convective condition
No full textMagnetohydrodynamic mixed convection flow of Jeffery fluid with thermophoresis, Soret and Dufour effects and convective condition
No full textThe aim of this paper is to investigate heat and mass transfer of Jeffery fluid on a stretching sheet. Moreover, the influence of magnetic field with mixed convection, convective boundary condition and Soret and Dufour effects is also brought into the consideration along with chemical reaction and thermophoresis condition. The problem is modeled by system of partial differential equations and solutions are obtained by optimal homotopy analysis method. In addition, for comprehensive interpretation of the influence of the system parameters results are shown by graphs and tables
On the analytical solutions of conformable time-fractional extended Zakharov–Kuznetsov equation through ( G ′ / G 2 )-expansion method and the modified Kudryashov method
No full textAction of the mobius group ¨ M = hx, y : x 2 = y 6 = 1i on certain real quadratic fields
No full textLet C 0 = C ∪ {∞} be the extended complex plane and M = ­ x, y : x 2 = y 6 = 1® , where x(z) = −1 3z and y(z) = −1 3(z+1) are the linear fractional transformations from C 0 → C 0 . Let m be a squarefree positive integer. Then Q∗ ( √ n) = { a+ √ n c : a, c 6= 0, b = a 2−n c ∈ Z and (a, b, c) = 1} where n = k 2m, is a proper subset of Q( √ m) for all k ∈ N. For non-square n = 3h Qr i=1 p ki i , it was proved in an earlier paper by the same authors that the set Q 000 ( √ n) = { α t : α ∈ Q∗ ( √ n), t = 1, 3} is M-set ∀ h ≥ 0 whereas if h = 0 or 1, then Q∗∗∗√ n) = { a+ √ n c : a+ √ n c ∈ Q∗ ( √ n) and 3 | c} is an M-subset of Q 000 ( √ n) = Q∗ ( √ n) ∪ Q∗∗∗( √ 9n). In this paper we prove that if h ≥ 2, then Q 000 ( √ n) = (Q∗ ( pn 9 )\Q∗∗∗( pn 9 ))∪Q∗ ( √ n)∪Q∗∗∗( √ 9n) and also determine its proper M-subsets. In particular Q( √ m) \ Q = ∪Q 000 ( √ k 2m) for all k ∈ N
On the heights of power digraphs modulo
Get PDFsummary:A power digraph, denoted by , is a directed graph with as the set of vertices and as the edge set. In this paper we extend the work done by Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory, Czech. Math. J. 54 (2004), 465–485, and Lawrence Somer and Michal Křížek: Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), 2174–2185. The heights of the vertices and the components of for and are determined. We also find an expression for the number of vertices at a specific height. Finally, we obtain necessary and sufficient conditions on such that each vertex of indegree of a certain subdigraph of is at height
Symmetry of iteration graphs
Get PDFsummary:We examine iteration graphs of the squaring function on the rings when , for a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when and when and are symmetric when
On monogenity of certain pure number fields of degrees
No full textsummary:Let be a pure number field generated by a complex root of a monic irreducible polynomial , where , , are three positive natural integers. The purpose of this paper is to study the monogenity of . Our results are illustrated by some examples
On power integral bases for certain pure number fields defined by
Get PDFsummary:Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic
