• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Honam Mathematical Journal
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• v.13 no.1
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• pp.29-45
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• 1991

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1447-1455
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• 2016

In this note, we mainly discuss the Gorenstein $Pr{\ddot{u}}fer$ domains. It is shown that a domain is a Gorenstein $Pr{\ddot{u}}fer$ domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, $B{\acute{e}}zout$ domain) if and only if it is a Gorenstein $Pr{\ddot{u}}fer$ UFD (resp., Krull domain, GCD domain).

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.335-351
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• 2016

Spherical convexity may be defined in different ways. It depends on which statement we take as a definition among several statements that can be all used as a definition of convexity of subsets in an affine space. In this article, we consider this question from various perspectives. We compare several different definitions of spherical convexity which are found in mathematical papers. In particular, we focus our discussion on the definitions of J. P. $Benz{\acute{e}}cri$ and N. H. Kuiper who built a solid foundation for theory of convex bodies and convex affine(projective) structures on manifolds.

• Physical Therapy Rehabilitation Science
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• v.8 no.2
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• pp.93-98
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• 2019

Objective: The purpose of this study was to investigate the effect of robot arm reach training on upper extremity functional movement in chronic stroke survivors. Design: One group pretest-posttest design. Methods: Thirteen chronic stroke survivors participated in this study. Robot arm reach training was performed with a Whole Arm Manipulator (WAM) and a 120-inch projective display to provide visual and auditory feedback. During the robotic arm reach training, WAM provided gravity compensation and assist-as-needed (AAN) force according to the robot control mode. When a participant could not move the arm toward the target for more than 2 seconds, WAM provided AAN force to reach the desired targets. All patients participated in the training for 40 minutes per day, 3 times a week, for 4 weeks. Main outcome measures were the Fugl-Meyer Assessment (FMA), Action Research Arm Test (ARAT) and Box and Block Test (BBT) to assess upper extremity functional movement. Results: After 4 weeks, significant improvement was observed in upper extremity functional movement (FMA: 42.15 to 46.23, BBT: 12.23 to 14.00, p<0.05). In the subscore analysis of the FMA upper extremity motor function domains, significant improvement was observed in upper extremity and coordination/speed units (p<0.05). However, there were no significant differences in the ARAT. Conclusions: This study showed the positive effects of robot arm reach training on upper extremity functional movement in chronic stroke survivors. In particular, we confirmed that robot arm reach training could have a positive influence by leading to improvement of motor recovery of the proximal upper extremity.