Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

این پژوهش با الهام گرفتن از نتایج یک طرح مطالعاتی کاربردی، رویکرد سلسله­‌مراتبی جهت پیگیری فرایند توسعه تأمین‌کنندگان و حمایت تصمیمات موجود در هر مراحل آن ارائه‌ می‌کند. ابتدا، زمینه‌های تأمین نیازمند سپس واجد شرایط هریک زمینه‌ها به کمک تصمیم‌گیری چندشاخصه بهترین-بدترین مشخص می‌گردند. معیارهای شناسایی نیز مرور مطالعات پیشین بهره‌گیری نظرات خبرگان حوزه‌ی خرید استخراج‌شده‌اند. درنهایت، مدل ریاضی ...

We consider the 2D J 1 −J 2 classical XY model on a square lattice. In the frustrated phase corresponding to J 2 > J 1 /2, an Ising order parameter emerges by an " order due to disorder " effect. This leads to a discrete symmetry plus the O(2) global one. We formulate the problem in a Coulomb gas language and show by a renormalization group analysis that only two phases are still possible: a lo...

Equation Basepoint Parameter Dimension Restrictions of Isotropy #1 W = XY + Z (0, 0, 0, 0) 4 #2 W 2 = XY + Z + 1 (1, 0, 0, 0) 3 #3 W = XY + Z +X (0, 0, 0, 0) 2 #4 W = XY + Z +XZ + αX (0, 0, 0, 0) α arbitrary 1 #5 W = XY + Z +XZ (0, 0, 0, 0) 1 #6 W 2 = XY +XY +XZ (1, 1, 0, 1) 1 #7 W = XY + Z (1, 0, 0, 1) α 6= 0, 1, 2 1 #8 W = XY + e (1, 0, 0, 0) 1 #9 W = XY + logZ (0, 0, 0, 1) 1 #10 W = XY + Z l...

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...