Arslan, Feza
Sahin, Mesut
In this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique for constructing large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has a non-decreasing Hilbert function.


Monomial curve families supporting Rossi's conjecture
Arslan, Feza; Sipahi, Neslihan; Sahin, Nil (Elsevier BV, 2013-08-01)
In this article, we give a constructive method to form infinitely many families of monomial curves in affine 4-space with corresponding Gorenstein local rings in embedding dimension 4 supporting Rossi's conjecture. Starting with any monomial curve in affine 2-space, we obtain large families of Gorenstein local rings with embedding dimension 4, having non-decreasing Hilbert functions, although their associated graded rings are not Cohen-Macaulay.
Asymptotic Behavior of Lotz-Rabiger and Martingale Nets
Emelyanov, Eduard (2010-09-01)
Using Theorem 1 (of convergence) in [1], we prove several results on LR- and M-nets by a unified approach to these nets that appear as the two extreme types of asymptotically abelian nets.
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
Symplectic and multi-symplectic methods for coupled nonlinear Schrodinger equations with periodic solutions
Aydin, A.; Karasoezen, B. (Elsevier BV, 2007-10-01)
We consider for the integration of coupled nonlinear Schrodinger equations with periodic plane wave solutions a splitting method from the class of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed according to the discretizations in time and space for both methods. Due to its local nat...
An improvement on the bounds of Weil exponential sums over Gallois rings with some applications
Ling, S; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2004-10-01)
We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum dista...
Citation Formats
F. Arslan, P. METE, and M. Sahin, “GLUING AND HILBERT FUNCTIONS OF MONOMIAL CURVES,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 2225–2232, 2009, Accessed: 00, 2020. [Online]. Available: