• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.435-447
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• 2012

Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.413-439
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• 2010

W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.329-336
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• 2010

In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M=N(Q) is essentially independent of choice of Q. 2) If f : M ${\rightarrow}$ M' is a maximal R-semimodule homomorphism, then $M/kerf_{(Q)}\;\cong\;M'$. 3) Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with $N{\subseteq}A$ if and only if $A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}$ is a subtractive subsemimodule of $M/N_{(Q)}$.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.7
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• pp.17-21
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• 2008

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• The Korean Journal of Ecology
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• v.9 no.4
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• pp.185-192
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• 1986

The production and decomposition rate of litters from the three different locations, Quercus acutissium forest at 630 m, Q. mongolica forests at 1, 005m and 1, 490 m of Mt. Dokyoo, were estimated by Olson model. The contents of N, P, K, Ca and Na in soils were measured and the relationships among them were elucidated. The amounts of litter production in Q. mangolica were the lowest, 378.96g/$m^2$ at 1, 490 m and the highest, 876.12g/$m^2$ at 1, 005 m. And the amounts of litter production in Q. acutissima at 630 m was 686.16 g/$m^2$. The decay rate of litters in Q. mongolica was the smallest, 0.123 at 1, 490 m, and the largest, 0.222 at 1, 005 m. And that in Q. acutissima was 0.169 at 630 m which was the medium rate. The production and decay rate of litters decreased with the ascending altitude. The values at 630 m were maller than those at 1, 005 m. This might be due to the fact that the tree species at 630 m was Q. acutissima was 0.169 at 630 m which was the medium rate. The production and decay rate of litters decreased with the ascending altitude. The values at 630 m was Q. acutissima which was different from Q. mongolica at 1, 005 m and 1, 490 m. The half-0life of litter decay in Q. monglica was 5, 634 years at 1, 490 m and 3.134 years at 1, 005 m. And that in Q. acutissima was 4.132 years at 630 m. The decay rates of litters were tend to be inversely proportional to the ascending altitude. The annual standing stocks of mineral and their amounts returned to the soil were proportional to the decay rate of organic matters.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.3C
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• pp.237-244
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• 2006

I/Q phase unbalance caused by non-ideal circuit components is inevitable physical phenomenons and leads to performance degradation when we implement a practical coherent M-ary phase shift keying(M-PSK) demodulator. In this paper, we present an exact and general expression involving two-dimensional Gaussian Q-functions for the bit error rate(BER) of uniform M-PSK with I/Q phase unbalance over an additive white Gaussian noise(AWGN) channel. First we derive a BER expression for the k-th bit of 8, 16-PSK signal constellations when Gray code bit mapping is employed. Then, from the derived k-th bit BER expression, we present the exact and general average BER expression for M-PSK with I/Q phase unbalance. This result can readily be applied to numerical evaluation for various cases of practical interest in an I/Q unbalanced M-PSK system, because the one- and two-dimensional Gaussian Q-functions can be easily and directly computed using commonly available mathematical software tools.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.579-582
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• 2003

In this paper, we propose a 4-step inference method needed for constructing a natural language communication system. The method is used to obtain fuzzy quantifier Q′when QA is Fisr τ⇔ Q′(m′A) is mF is m"is τ is inferred (Q, Q′: quantifiers, A: fuzzy subject, m′, m": modifiers, y: fuzzy predicate, τ: truth qualifier). We show that Q′is resolved step by step for two types of Q, including a non-increasing type (few,...) and a non-decreasing type(most,...).