• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.279-284
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• 1994

Let R = ($r_1$, $r_2$, …, $r_{m}$) and S = ($s_1$, $s_2$, …, $s_{n}$ ) be positive integral vectors satisfying $r_1$＋ $r_2$＋…＋ $r_{m}$ = $s_1$＋ $s_2$＋ㆍㆍㆍ＋ $s_{n}$ , and let U(R, S) denote the class of all m $\times$ n matrices A = [$_a{ij}$ ] where $a_{ij}$ = 0 or 1 such that (equation omitted) = $r_{i}$ , (equation omitted) = $s_{j}$ , i = 1, ㆍㆍㆍ, m, j = 1, ㆍㆍㆍ, n.(omitted)

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.1
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• pp.125-129
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• 2011

The aim was to determine the relationship between muscle structure and meat quality traits in neuromuscular compartments (NMCs: R1, R2, R3, R4) of pig semitendinosus muscle. Barrows from the INTA-MGC genetic line (Argentina) were slaughtered at 100 kg body weight. In each NMC the following parameters were determined: the fibre types I, IIA, IIX and IIB by immunohistochemistry, the fibre cross sectional area (FCSA), the pH of meat after 24 h post-mortem ($pH_{24}$), instrumental meat tenderness (WB) and colour ($L^*$, $a^*$, $b^*$). There were significant differences in the following: $L^*$ (R1 = R4$a^*$ (R1>R4>R2 = R3), $b^*$ (R1 = R4R1 = R3 = R4), $pH_{24}$ (R1 = R4>R2 = R3). The relative percentages of FCSA were as follows: I (R4>R1>R3>R2), IIA (R1>R4>R3>R2), IIX (R1 = R2 = R3 = R4) and IIB (R2>R3>R1>R4). The correlation values were statistically significant between IIB and WB (R1 and R4, $r_s$ = 0.66), (R2 and R3 $r_s$ = 0.74), IIB and $L^*$ (R1 and R4 $r_s$ = 0.84), IIX and $L^*$ without discriminating NMCs. Our data suggest that the NMC where the sampling takes place is important for determining meat quality traits because of the heterogeneity of the whole muscle.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.5
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• pp.1337-1348
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• 1990

Estimations of the thermodynamic properties are made for the selected binary non-azeotropic refrigerant mixtures including R13B1/R114, R22/R114, R12/R114, R152a/R114, R13B1/R152a and R13B1/R12 using the Peng-Robinson equation of state and mixing rules. In this study, we find that the binary interaction coefficients for the above mixtures have an effect upon the vapor-liquid equilibria and the thermodynamic properties. As the binary interaction coefficient becomes larger, the deviation from the idealized model, say, Raoult`s rule, is obvious. A correlation is proposed to relate the binary interaction coefficient to the difference between the dipole moments op each pure refrigerant. Vapor-liquid equilibrium are also accurately estimated using the binary interaction coefficient. Pressure-enthalpy and temperature-entropy relations are plotted for a certain composition ratio of each refrigerant mixture. Results show that the estimating method in this study can be applied to the investigation of the thermodynamic properties for the binary non-azeotropic refrigerant mixtures.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1341-1354
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• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.41-51
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• 2007

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

• Journal of Advanced Marine Engineering and Technology
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• v.31 no.1
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• pp.74-83
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• 2007

This paper presents the experimental results of evaporation heat transfer coefficients of HC refrigerants (e.g. R290 and R600a). R-22 as a HCFCs refrigerant and R-l34a as a HFCs refrigerant in horizontal double pipe heat exchangers, having four different inner diameters of 10.07, 7.73, 6.54 and 5.80 mm respectively. The experiments of the evaporation process were conducted at mass flux of $35.5{\sim}210.4 kg/m^2s$ and cooling capacity of $0.95{\sim}10.1 kW$. The main results were summarized as follows : The average evaporation heat transfer coefficient of hydrocarbon refrigerants(R-290 and R-600a) was higher than the refrigerants, R-22 and R-l34a. In comparison with R-22 the evaporation heat transfer coefficient of R-l34a is approximately $-11{\sim}8.1 %$ higher. R-290 is $56.7{\sim}70.1 %$ higher and R-600a is $46.9{\sim}59.7 %$ higher. respectively. In comparison with experimental data and some correlations, the evaporation heat transfer coefficients are well predicted with the Kandlikar's correlation regardless of a type of refrigerants and tube diameters.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.693-699
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• 2010

In this paper we show that the flat property of a left R-module does not imply (carry over) to the corresponding inverse polynomial module. Then we define an induced inverse polynomial module as an R[x]-module, i.e., given an R-linear map f : M $\rightarrow$ N of left R-modules, we define $N+x^{-1}M[x^{-1}]$ as a left R[x]-module. Given an exact sequence of left R-modules $$0\;{\rightarrow}\;N\;{\rightarrow}\;E^0\;{\rightarrow}\;E^1\;{\rightarrow}\;0$$, where $E^0$, $E^1$ injective, we show $E^1\;+\;x^{-1}E^0[[x^{-1}]]$ is not an injective left R[x]-module, while $E^0[[x^{-1}]]$ is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN = 0. We show inj $dim_R$ N = n implies inj $dim_{R[x]}$ N = n + 1 by using the induced inverse polynomial modules and their properties.

• Journal of Animal Science and Technology
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• v.63 no.4
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• pp.854-863
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• 2021

Weaning induces physiological changes in intestinal development that affect pigs' growth performance and susceptibility to disease. As a posttranscriptional regulator, microRNAs (miRNAs) regulate cellular homeostasis during intestinal development. We performed small RNA expression profiling in the small intestine of piglets before weaning (BW), 1 week after weaning (1W), and 2 weeks after weaning (2W) to identify weaning-associated differentially expressed miRNAs. We identified 38 differentially expressed miRNAs with varying expression levels among BW, 1W, and 2W. Then, we classified expression patterns of the identified miRNAs into four types. ssc-miR-196a and ssc-miR-451 represent pattern 1, which had an increased expression at 1W and a decreased expression at 2W. ssc-miR-499-5p represents pattern 2, which had an increased expression at 1W and a stable expression at 2W. ssc-miR-7135-3p and ssc-miR-144 represent pattern 3, which had a stable expression at 1W and a decreased expression at 2W. Eleven miRNAs (ssc-miR-542-3p, ssc-miR-214, ssc-miR-758, ssc-miR-4331, ssc-miR-105-1, ssc-miR-1285, ssc-miR-10a-5p, ssc-miR-4332, ssc-miR-503, ssc-miR-6782-3p, and ssc-miR-424-5p) represent pattern 4, which had a decreased expression at 1W and a stable expression at 2W. Moreover, we identified 133 candidate targets for miR-196a using a target prediction database. Gene ontology and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analyses revealed that the target genes were associated with 19 biological processes, 4 cellular components, 8 molecular functions, and 7 KEGG pathways, including anterior/posterior pattern specification as well as the cancer, PI3K-Akt, MAPK, GnRH, and neurotrophin signaling pathways. These findings suggest that miRNAs regulate the development of the small intestine during the weaning process in piglets by anterior/posterior pattern specification as well as the cancer, PI3K-Akt, MAPK, GnRH, and neurotrophin signaling pathways.