We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m + 3m+ 9 and non-isomorphic simplest cubic fields. By applying R. Okazaki’s result for non-isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m+ 9.

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m+3m+9 and isomorphic simplest cubic fields. By applying R. Okazaki’s result for isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m + 9.

We study the space of binary cubic and quadratic forms over the ring of integers O of an algebraic number field k. By applying the theory of prehomogeneous vector spaces founded by M. Sato and T. Shintani, we can associate the zeta functions for these spaces. Applying these zeta functions, we derive some density theorems on the distributions of discriminants of cubic algebras of O. In the case ...

We study the space of binary cubic and quadratic forms over the ring of integers O of an algebraic number field k. By applying the theory of prehomogeneous vector spaces founded by M. Sato and T. Shintani, we can associate the zeta functions for these spaces. Applying these zeta functions, we derive some density theorems on the distributions of discriminants of cubic algebras of O. In the case ...

If each edge (u, v) of a graph G = (V,E) is decorated with a permutation πu,v of k objects, we say that it has a permuted k-coloring if there is a coloring σ : V → {1, . . . , k} such that σ(v) 6= πu,v(σ(u)) for all (u, v) ∈ E. Based on arguments from statistical physics, we conjecture that the threshold dk for permuted k-colorability in random graphs G(n,m = dn/2), where the permutations on th...

results with respect to the inter-reliability testing, there was a high level of agreement between reviewers applying the instrument in the admissions criteria and days of stay. overall agreement was > 77%; also specific inappropriate agreement and specific appropriate agreement were > 61%, and > 72%, respectively. regarding the validity of the testing, the instrument had a sensitivity of > 0.7...

Let $k'/k$ be a finite purely inseparable field extension and let $G'$ reductive $k'$-group. We denote by $G=\R_{k'/k}(G')$ the Weil restriction of across $k'/k$, pseudo-reductive group. This article gives bounds for exponent geometric unipotent radical $\RR_{u}(G_{\bar{k}})$ in terms invariants starting with case $G'=\GL_n$ applying these results to where is simple

data mining is a powerful tool for firms to extract knowledge from their customers’ transaction data. one of the useful applications of data mining is segmentation. segmentation is an effective tool for managers to make right marketing strategies for right customer segments. in this study we have segmented retailers of a hygienic manufacture. nowadays all manufactures do understand that for sta...