• Structural Engineering and Mechanics
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• v.24 no.2
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• pp.195-212
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• 2006

In seismic areas, ductility is an important factor in design of high strength concrete (HSC) members under flexure. A number of twelve HSC beams with different percentage of ${\rho}$ & ${\rho}^{\prime}$ were cast and incrementally loaded under bending. The effect of ${\rho}^{\prime}$ on ductility of members were investigated both qualitatively and quantitatively. During the test, the strain on the concrete middle faces, on the tension and compression bars, and also the deflection at different points of the span length were measured up to failure. Based on the obtained results, the serviceability and ultimate behavior, and especially the ductility of the HSC members are more deeply reviewed. Also a comparison between theoretical and experimental results are reported here.

• 전기의세계
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• v.28 no.12
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• pp.33-40
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• 1979

This mininzation of the multi-output switching function becomes a difficult task when the input varibles and the number of functions increase. This paper describes the optimal selection of prime inplicats for the multi-output switching function by using the Inter-section Table. This procedure is applicable to both manual and computhe programmed realization without complesith. The algorithm is implemented by a computer program in the standard FORTRAN iv language.

• KIPS Transactions on Computer and Communication Systems
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• v.4 no.10
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• pp.337-342
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• 2015

We develop a new parallelization method for Sieve of Eratosthenes algorithm, which enhances both computation speed and energy efficiency. A pipeline scheduling is included for better load balancing after proper workload partitioning. They run on multicore CPUs with hybrid parallel programming model which uses both message passing and multithreading computation. Experimental results performed on both small scale clusters and a PC with a mobile processor show significant improvement in execution time and energy consumptions.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.985-1000
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• 2019

Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1105-1115
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• 2019

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets {$x^k:1{\leq}x{\leq}n$, (x, n) = 1} and {$x^k:1{\leq}x{\leq}n/2$, (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.6
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• pp.221-228
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• 2013

It is impossible directly to find a prime number p,q of a large semiprime n = pq using Trial Division method. So the most of the factorization algorithms use the indirection method which finds a prime number of p = GCD(a-b, n), q=GCD(a+b, n); get with a congruence of squares of $a^2{\equiv}b^2$ (mod n). It is just known the fact which the area that selects p and q about n=pq is between $10{\cdots}00$ < p < $\sqrt{n}$ and $\sqrt{n}$ < q < $99{\cdots}9$ based on $\sqrt{n}$ in the range, [$10{\cdots}01$, $99{\cdots}9$] of $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$. This paper proposes the method that reduces the range of p using information obtained from n. The proposed method uses the method that sets to $p_{min}=n_{LR}$, $q_{min}=n_{RL}$; divide into $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$. The proposed method is more effective from minimum 17.79% to maxmimum 90.17% than the method that reduces using $\sqrt{n}$ information.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.147-155
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• 2014

Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.