• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1059-1066
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• 2011

We introduce the concept of fuzzy S-weakly r-M-continuous functions on fuzzy r-minimal spaces, and investigate some characterizations of such functions and the relations between the continuity and fuzzy r-minimal compactness on fuzzy r-minimal spaces.

• East Asian mathematical journal
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• 제25권4호
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• pp.441-447
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• 2009

Jat and Choudhari defined a near-ring R with left bipotent or right bipotent condition in 1979. Also, we can dene a near-ring R as subcommutative if aR = Ra for all a in R. From these above two concepts it is natural to investigate the near-ring R with the properties aR = $Ra^2$ (resp. $a^2R$ = Ra) for each a in R. We will say that such is a near-ring with (1,2)-potent condition (resp. a near-ring with (2,1)-potent condition). Thus, we can extend a general concept of a near-ring R with (m,n)-potent condition, that is, $a^mR\;=\;Ra^n$ for each a in R, where m, n are positive integers. We will derive properties of near-ring with (1,n) and (n,1)-potent conditions where n is a positive integer, any homomorphic image of (m,n)-potent near-ring is also (m,n)-potent, and we will obtain some characterization of regular near-rings with (m,n)-potent conditions.

• 대한수학회지
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• 제51권2호
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• pp.239-250
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• 2014

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

• 대한물리치료과학회지
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• 제9권2호
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• pp.67-75
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• 2002

The purpose of this study is to know the average of hip joint range of motion and difference according to the aging for the elderly. This study consisted of elder male(n=75) and elder female(n=109). The result of assessment and analysis in hip pint range of motion are as follows : 1) The average hip flexion(knee flexed) joint range of motion in 60-69(from sixty to sixty-nine)years old are $104.26^{\circ}$(Left-Male), $101.00^{\circ}$(Right-Male), $107.05^{\circ}$(Left-Female), $107.05^{\circ}$(Right-Female). 70-79years old are $104.59^{\circ}$(L-M), $102.05^{\circ}$(R-M), $105.73^{\circ}$(L-F), $108.75^{\circ}$(R-F). 80-89years old are $101.53^{\circ}$(L-M), $101.13^{\circ}$(R-M), $96.83^{\circ}$(L-F), $97.67^{\circ}$(R-F). There was significant difference in hip flexion(knee flexed) among female group(p<.01). The average hip flexion(knee extended) joint range of motion in 60-69(from sixty to sixty-nine)years old are $73.13^{\circ}$(Left-Male), $72.04^{\circ}$(Right-Male), $77.29^{\circ}$(Left-Female), $75.97^{\circ}$(Right-Female). 70-79years old are $74.95^{\circ}$(L-M), $72.19^{\circ}$(R-M), $76.73^{\circ}$(L-F), $76.65^{\circ}$(R-F). 80-89years old are $70.83^{\circ}$(L-M), $70.37^{\circ}$(R-M), $69.00^{\circ}$(L-F), $69.00^{\circ}$(R-F). There was significant difference in left hip flexion(knee extended) among female group(p<.05). 2) The average hip extension joint range of motion in 60-69years old are $13.09^{\circ}$(L-M), $12.78^{\circ}$(R-M), $10.97^{\circ}$(L-F), $10.68^{\circ}$(R-F). 70-79years old are $8.95^{\circ}$(L-M), $8.48^{\circ}$(R-M), $11.24^{\circ}$(L-F), $10.90^{\circ}$(R-F). 80-89 years old are $8.40^{\circ}$(L-M), $8.23^{\circ}$(R-M), $7.33^{\circ}$(L-F), $7.33^{\circ}$(R-F). There was significant difference in left(p<.01) and right(p<.05) hip extension among male group(p<.05). 3) The average hip abduction joint range of motion in 60-69 years old are $33.04^{\circ}$(L-M), $33.17^{\circ}$(R-M), $33.16^{\circ}$(L-F), $33.37^{\circ}$(R-F). 70-79 years old are $31.00^{\circ}$(L-M), $30.05^{\circ}$(R-M), $32.44^{\circ}$(L-F), $32.68^{\circ}$(R-F). 80-89 years old are $29.07^{\circ}$(L-M), $27.90^{\circ}$(R-M), $28.17^{\circ}$(L-F), $28.67^{\circ}$(R-F). There was no significant difference among group. 4) The average hip adduction pint range, of motion in 60-69years old are $29.57^{\circ}$(L-M), $29.35^{\circ}$(R-M), $31.87^{\circ}$(L-F), $31.89^{\circ}$(R-F). 70-79, years old are $27.41^{\circ}$(L-M), 27.00(R-M) $30.85^{\circ}$(L-F), $31.28^{\circ}$(R-F). 80-89 years old are $26.87^{\circ}$(L-M), $26.63^{\circ}$(R-M), $24.67^{\circ}$(L-F), $24.83^{\circ}$(R-F). There was significant difference in hip abduction among female group(p<01). 5) The average hip external rotation pint range of motion in 60-69years old are $32.26^{\circ}$(L-M), $31.17^{\circ}$(R-M), $33.53^{\circ}$(L-F), $34.42^{\circ}$(R-F). 70-79 years old are $31.64^{\circ}$(L-M), $28.62^{\circ}$(R-M) $31.29^{\circ}$(L-F), $31.45^{\circ}$(R-F). 80-89 years old are $26.40^{\circ}$(L-M), $26.07^{\circ}$(R-M), $24.77^{\circ}$(L-F), $24.27^{\circ}$(R-F). There was significant difference in left(male, female p<.01) and right(female p<.0l) hip external rotation among group. 6) The average hip internal rotation joint range of motion in 60-69years old are $30.30^{\circ}$(L-M), $28.13^{\circ}$(R-M), $34.27^{\circ}$(L-F), $36.03^{\circ}$(R-F). 70-79years old are $31.24^{\circ}$(L-M), $29.57^{\circ}$(R-M), $28.51^{\circ}$(L-F), $29.10^{\circ}$(R-F). 80-89 years old are $24.63^{\circ}$(L-M), $24.40^{\circ}$(R-M), $24.27^{\circ}$(L-F), $24.27^{\circ}$(R-F). There was significant difference in left(male p<.05, female p<.01) and right(female p<.01) hip internal rotation among group.

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.255-263
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• 2009

For an endomorphism ${\alpha}$ of R, in [1], a module $M_R$ is called ${\alpha}$-compatible if, for any $m{\in}M$ and $a{\in}R$, ma = 0 iff $m{\alpha}(a)$ = 0, which are a generalization of ${\alpha}$-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an ${\alpha}$-compatible module $M_R$ (1) $M_R$ is p.q.-Baer module iff $M[x;{\alpha}]_{R[x;{\alpha}]}$ is p.q.-Baer module. (2) for an automorphism ${\alpha}$ of R, $M_R$ is p.q.-Baer module iff $M[x,x^{-1};{\alpha}]_{R[x,x^{-1};{\alpha}]}$ is p.q.-Baer module.

• 대한수학회논문집
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• 제36권1호
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• 호남수학학술지
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• 제28권3호
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• pp.377-386
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• 2006

For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, $ann_R(a)$, for each $a{\in}R$ is a pure ideal in R. Also it is proved that the polynomial ring, R[x], is a PF-ring if and only if R is a PF-ring. Finally, we prove that M as an R-module is PF-module if and only if M[x] is a PF R[x]-module. Also M is a PP R-module if and only if M[x] is a PP R[x]-module.

• 대한토목학회논문집
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• 제14권4호
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• pp.941-951
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• 1994

본 연구에서는 국내에서 사용되고 있는 보조기층재료에 대해 변형측정정치의 위치 및 포화도에 따른 $M_R$값의 변화양상을 파악하고, 시료내의 입자크기(particle size)에 따른 치수효과(size effect)를 파악하여 적절한 $M_R$ 관계식을 제시하였다. 외부변형측정장치를 사용한 경우의 $M_R$값은 회복변형율을 과대평가 하기 때문에 내부변형측정장치를 사용한 경우보다 작았고, 포화도에 따른 $M_R$값은 wet 상태($S_r$=70%)가 damp 상태 ($S_r$=40%)보다 10% 정도 작게 나타났으며 시편을 구성하는 입자의 치수효과는 과대 입자(oversize particle)를 제거함에 따른 간극비의 변화와 직접적인 관계가 있음을 알 수 있었다. 이와같은 결과를 종합하여 보조기층의 $M_R$ 관계식은 damp 상태의 포화도에서, $M_R=3960{\cdot}{\theta}^{0.60}$ psi.로 제안할 수 있다.

• 대한수학회보
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• 제56권1호
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• pp.57-71
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• 2019

Let R be an associative ring with identity, M a t.u.p. monoid with only one unit and ${\omega}:M{\rightarrow}End(R)$ a monoid homomorphism. Let R be a reversible, M-compatible ring and ${\alpha}=a_1g_1+{\cdots}+a_ng_n$ a non-zero element in skew monoid ring $R{\ast}M$. It is proved that if there exists a non-zero element ${\beta}=b_1h_1+{\cdots}+b_mh_m$ in $R{\ast}M$ with ${\alpha}{\beta}=c$ is a constant, then there exist $1{\leq}i_0{\leq}n$, $1{\leq}j_0{\leq}m$ such that $g_{i_0}=e=h_{j_0}$ and $a_{i_0}b_{j_0}=c$ and there exist elements a, $0{\neq}r$ in R with ${\alpha}r=ca$. As a consequence, it is proved that ${\alpha}{\in}R*M$ is unit if and only if there exists $1{\leq}i_0{\leq}n$ such that $g_{i_0}=e$, $a_{i_0}$ is unit and aj is nilpotent for each $j{\neq}i_0$, where R is a reversible or right duo ring. Furthermore, we determine the relation between clean and nil clean elements of R and those elements in skew monoid ring $R{\ast}M$, where R is a reversible or right duo ring.

• 호남수학학술지
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• 제23권1호
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• pp.15-20
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• 2001

Reduced Von Neumann Regular ring is pseudo symmetric and N(R) is reduced. Thus N(R) is pseudo symmetric and M(R) is reduced if and only if M(R) = N(R).