A ring is called strongly clean if every element is the sum of an idempotent and a unit which commute. In 1999 Nicholson asked whether every semiperfect ring is strongly clean and whether the matrix ring of a strongly clean ring is strongly clean. In this paper, we prove that if R = {m/n 6 Q : n is odd}, then M 2 (R) is a semiperfect ring but not strongly clean. Thus, we give negative answers to both questions. It is also proved that every upper triangular matrix ring over the ring R is strongly clean.Throughout this paper all rings are associative with unit. For a ring R, let U(R) be the group of units of R, M n (R) the nxn matrix ring over R, and T n (R) the nxn upper triangular matrix ring over R, respectively. The identity matrix of M n (R) is denoted by / . Q means the field of rational numbers. A ring R is called clean if every element of R is a sum of an idempotent and a unit. The ring is called strongly clean if every element is the sum of an idempotent and a unit which commute. It is shown by Camillo and Yu [2, Theorem 9] that every semiperfect ring is clean. Han and Nicholson [4, Corollary 1] showed that every matrix ring M n (R) over a clean ring is again clean.Nicholson asked whether every semiperfect ring is strongly clean [5, Question 5] and whether the matrix ring of a strongly clean ring is strongly clean [5, Question 3]. In this paper, we prove that if R -{m/n € Q : n is odd}, then M 2 (/2) is a semiperfect ring but not strongly clean. Thus, we answer the two questions above, both in the negative. Also we prove that every upper triangular matrix ring over the ring R is strongly clean. Thus, we obtain a new class of strongly clean rings. EXAMPLE 1. Let R -{m/n e Q : n is odd}. Then M 2 {R) is a semiperfect ring but it is not strongly clean.PROOF: Since R is a commutative local ring, it is semiperfect and strongly clean. Since semiperfect rings are Morita invariant, M 2 {R) is semiperfect. By direct computation, we find all nontrivial idempotents in the matrix ring M 2 (i?) are of the following types:I I , where a,b,c€ R and bc = a-a 2 . \c 1-a

BACKGROUND-U19/Eaf2 is an androgen-response gene and its downregulation is frequently observed in advanced human prostate cancer. U19/Eaf2 interacts with ELL, a fusion partner of MLL in the (11;19) (q23;p13.1) translocation in acute myeloid leukemia. U19/Eaf2 overexpression induces apoptosis and suppresses xenograft tumor growth.

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We show that in a ring of stable range 1, any (von Neumann) regular element is clean. Our main results also imply that any unit-regular ring has idempotent stable range 1 (and is therefore clean), and that a semilocal ring has idempotent stable range 1 if and only if it is semiperfect.

In order to investigate the non-linear fatigue cumulative damage of joints in ocean structural parts, one type of low carbon steel Q345D was employed to prepare designed T-type specimens, and a series of fatigue experiments were carried out on the specimens under two-step repeating variable amplitude loading condition. The chosen high cyclic loads were larger than the constant amplitude fatigue limit (CAFL) and the chosen low cyclic loads were below the CAFL. Firstly, the S-N curve of designed T-type specimen was obtained via different constant amplitude fatigue tests. Then, a series of two-step repeating variable load were carried out on designed T-type specimens with the aim of calculating the cumulative damage of specimen under the variable fatigue load. The discussions about non-linear fatigue cumulative damage of designed T-type specimens and the interaction effect between the high and low amplitude loadings on the fatigue life were carried out, and some meaningful conclusions were obtained according to the series of fatigue tests. The results show that fatigue cumulative damage of designed T-type specimens calculated based on Miner’s rule ranges from 0.513 to 1.756. Under the same cycle ratio, the cumulative damage increases with the increase of high cyclic stress, and at the same stress ratio, the cumulative damage increases linearly with the increase of cycle ratio. Based on the non-linear damage evaluation method, it is found that the load interaction effect between high and low stress loads exhibits different damage or strengthening effects with the change of stress ratio and cycle ratio.