In this paper, we study some ring theoretic properties of the amalgamated duplication ring $Rbowtie I$ of a commutative Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$ satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a normal ring, a generalized Cohen-Macaulay ring and finally a filter ring.

In this paper we prove that the Benjamin–Ono equation admits an analytic Birkhoff normal form in open neighborhood of zero H0s(T,R) for any s>−1/2 where denotes subspace Sobolev space Hs(T,R) elements with mean 0. As application show −1/2<s<0, flow map S0t:H0s(T,R)→H0s(T,R) is nowhere locally uniformly continuous a H0s(T,R).

thirty seven randomly selected patients suffering from multiple s c l e r os i s (ms) (17 males and 20 females)and 30 healthy control subjects were studied for the lymphocyte subpopulations and ce l l -medi a t e d immunity.we obs e r ved a decrease of the total t-cells and an increase of a ctive t-lymphocytes and b ce l l s , in ms p at i ent s as compared t o normal controls. the inability of...

We prove that every projectively normal Fano manifold in Pn+r of index 1, codimension r, and dimension n≥10r is birationally superrigid K-stable. This result was previously proved by Zhuang under the complete intersection assumption.