# NONTRANSITIVE DICE SETS REALIZING THE PALEY TOURNAMENTS FOR SOLVING SCHÃœTTE'S TOURNAMENT PROBLEM

## Related Articles

- PERIODIC ORBITS OF QUADRATIC POLYNOMIALS. TIMO ERKAMA // Bulletin of the London Mathematical Society;Oct2006, Vol. 38 Issue 5, p804
It is known that quadratic polynomials do not have real rational orbits of period four. By using a two-dimensional model for the quadratic family, this result is generalized for complex rational orbits.

- Stability of Pexiderized quadratic functional equation on a set of measure zero. EL-Fassi, Iz-iddine; Chahbi, Abdellatif; Kabbaj, Samir; Park, Choonkil // Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 6, p4554
Let R be the set of real numbers and Y a Banach space. We prove the Hyers-Ulam stability theorem when f; h : R â†’ Y satisfy the following Pexider quadratic inequality â€–f(x + y) + f(x - y) - 2f(x) - 2h(y)â€– â‰¤ Îµ, in a set Î© âŠ‚ R2 of Lebesgue measure m(Î©) = 0.

- ON THE LOCAL AND GLOBAL PRINCIPLE FOR SYSTEMS OF RATIONAL HOMOGENEOUS FORMS IN A FINITE NUMBER OF VARIABLES. Nguyen, Lan // JP Journal of Algebra, Number Theory & Applications;Feb2016, Vol. 38 Issue 1, p79
In this paper, we prove that the Hasse principle for any system of rational cubic forms, any system of rational homogeneous forms of degree at least 3 in an arbitrary number of variables is equivalent to the Hasse principle of certain systems of rational quadratic forms. This shows, in...

- Fuzzy Stability of Jensen-Type Quadratic Functional Equations. Sun-Young Jang; Jung Rye Lee; Choonkil Park; Dong Yun Shin // Abstract & Applied Analysis;2009, Special section p1
We prove the generalized Hyers-Ulam stability of the following quadratic functional equations 2f((x + y)/2) + 2f((x - y)/2) = f(x) + f(y) and f(ax + ay) = (ax - ay) = 2a2f(x) + 2a2f(y) in fuzzy Banach spaces for a nonzero real number a with aâ‰ Â± 1/2.

- Inequalities for certain means in two arguments. Yang, Zhen-Hang; Chu, Yu-Ming // Journal of Inequalities & Applications;9/26/2015, Vol. 2015 Issue 1, p1
In this paper, we present the sharp bounds of the ratios $U(a,b)/L_{4}(a,b)$, $P_{2}(a,b)/U(a,b)$, $NS(a,b)/P_{2}(a,b)$ and $B(a,b)/NS(a,b)$ for all $a, b>0$ with $a\neq b$, where $L_{4}(a,b)=[(b^{4}-a^{4})/(4(\log b-\log a))]^{1/4}$, $U(a,b)=(b-a)/[\sqrt{2}\arctan((b-a)/\sqrt{2ab})]$,...

- QUADRATIC FUNCTIONAL EQUATION AND ITS STABILITY IN FELBIN'S TYPE SPACES. Ravi, K.; Sabarinathan, S. // Far East Journal of Mathematical Sciences;Dec2015, Vol. 98 Issue 8, p977
In this paper, we introduce a new quadratic functional equation, obtain the general solution and investigate the Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability for the quadratic functional equations in Felbin's type fuzzy normed linear spaces. A...

- Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24. Lam, Ching Hung; Shimakura, Hiroki // Proceedings of the London Mathematical Society;Mar2012, Vol. 104 Issue 3, p540
In 1993, Schellekens [â€˜Meromorphic c=24 conformal field theoriesâ€™, Comm. Math. Phys. 153 (1993) 159â€“185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this...

- Koszul Duality for Multigraded Algebras. Hawwa, F. T.; William Hoffman, J.; Wang, Haohao // European Journal of Pure & Applied Mathematics;2012, Vol. 5 Issue 4, p511
Classical Koszul duality sets up an adjoint pair of functors, establishing an equivalence F : Db(A) â‡† Db(A!) : G, where A is a quadratic algebra, A! is the quadratic dual, and Db refers to the bounded derived category of complexes of graded modules over the graded algebra (i.e., A or A!)....

- Relations between simplicial groups, 3-crossed modules and 2-quadratic modules. Atik, Hasan; Ulualan, Erdal // Acta Mathematica Sinica;Jun2014, Vol. 30 Issue 6, p968
In this paper, we define two-quadratic module and explore the relations among twoquadratic modules, three-crossed modules and simplicial groups.