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SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES

  • Lee, Sang-Cheol;Varmazyar, Rezvan
    • 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.

GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS

  • Jun, Y.B.;Dudek, W.A.;Shabir, M.;Kang, Min-Su
    • 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.

On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings

  • Chaudhari, Jaiprakash Ninu;Bond, Dipak Ravindra
    • 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 $M/N_{(Q)}$.

Construction of Jacket Matrices Based on q-ary M-sequences (q-ary M-sequences에 근거한 재킷 행렬 설계)

  • S.P., Balakannan;Kim, Jeong-Ki;Borissov, Yuri;Lee, Moon-Ho
    • 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.

MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE

  • Li, Songxiao;Lou, Zengjian;Shen, Conghui
    • 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 𝓓αp, M(𝓓p-1p, 𝓓q-1q) = {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(𝓓p-2+sp, 𝓓q-2+sq) = {0}. However, X ∩ 𝓓p-1p ⊆ X ∩ 𝓓q-1q and X ∩ 𝓓p-2+sp ⊆ X ∩ 𝓓q-2+sp 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+sp, X∩𝓓q-2+sq) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓p-2+sp, X ∩ 𝓓q-2+sq) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗.

WEIGHTED VECTOR-VALUED BOUNDS FOR A CLASS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS AND APPLICATIONS

  • Chen, Jiecheng;Hu, Guoen
    • 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.

A Study on the Production and Decomposition of Litters along Altitude of Mt. Dokyoo (덕유산의 고도에 따른 낙엽의 생산과 분해에 관한 연구)

  • Chang, Nam-Kee;Mi-Ae Chung
    • 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.

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Generalized BER Performance Analysis for Uniform M-PSK with I/Q Phase Unbalance (I/Q 위상 불균형을 고려한 Uniform M-PSK의 일반화된 BER 성능 분석)

  • Lee Jae-Yoon;Yoon Dong-Weon;Hyun Kwang-Min;Park Sang-Kyu
    • 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.

SELF-RECIPROCAL POLYNOMIALS WITH RELATED MAXIMAL ZEROS

  • Bae, Jaegug;Kim, Seon-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.983-991
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    • 2013
  • For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

A 4-step Inference Method for Natural Language Propositions Involving Fuzzy Quantifiers and Truth Qualifiers

  • Okamoto, Wataru
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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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,...).

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