• East Asian mathematical journal
• /
• v.16 no.1
• /
• pp.89-96
• /
• 2000

In this paper, a differential polynomial ring $R[x;\delta]$ of ring R with a derivation $\delta$ are investigated as follows: For a reduced ring R, a ring R is Baer(resp. quasi-Baer, p.q.-Baer, p.p.-ring) if and only if the differential polynomial ring $R[x;\delta]$ is Baer(resp. quasi-Baer, p.q.-Baer, p.p.-ring).

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.147-158
• /
• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.

• East Asian mathematical journal
• /
• v.27 no.4
• /
• pp.471-483
• /
• 2011

The purpose of this study is to introduce the Common Core State Standards (CCSS) for mathematics which is released on June 2, 2010 in the U.S.A. The common core state standards are aligned with college and work expectations, and include rigorous content and application of knowledge through high-order skills. The most distinguishable differences between the CCSS standards and the NCTM standards are that the CCSS standards considers the mathematical modeling as one of the mathematical content domains such as algebra, geometry, ets, and the standards are designed by working together with school leaders of all states.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.617-630
• /
• 2012

In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

• East Asian mathematical journal
• /
• v.27 no.1
• /
• pp.11-21
• /
• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• East Asian mathematical journal
• /
• v.30 no.1
• /
• pp.31-50
• /
• 2014

In this paper we establish limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random sequences.

• East Asian mathematical journal
• /
• v.30 no.1
• /
• pp.69-77
• /
• 2014

In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.527-531
• /
• 2017

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.

• East Asian mathematical journal
• /
• v.34 no.1
• /
• pp.39-46
• /
• 2018

In this article we consider rings whose Jacobson radical contains all the nilpotent elements, and call such a ring an NJ-ring. The class of NJ-rings contains NI-rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

• East Asian mathematical journal
• /
• v.36 no.3
• /
• pp.417-424
• /
• 2020

Huang et al. proved that the n by n upper triangular matrix ring over a domain is weakly reversible-over-center by using the property of regular matrices. In this article we provide a concrete proof which is able to be available in the related study of centers. Next we extend an example of weakly reversible-over-center, which was argued by Huang et al., to the general case.