• Journal of Food Hygiene and Safety
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• v.26 no.4
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• pp.398-402
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• 2011

Cruciferous vegetables including diindolylmethane (DIM) have been shown to have anticancer activity. Especially, DIM-pPhBr and DIM-pPhF used in this study was reported to have more effective and less toxic effects than DIM. However, there is no report presenting their anti-tumorigenic activity in oral cancer. In the present study, we examined the effects of DIM-pPhBr and DIM-pPhF on the cell proliferation and apoptosis in KB human oral cancer cells. DIM-pPhBr and DIM-pPhF decreased cell proliferation and induced apoptosis evidenced by western blot analysis, DAPI staining and sub-$G_1$ population. This provides the first evidence that DIM-pPhBr and DIM-pPhF originating from Cruciferous vegetables induce apoptotic cell death in human oral cancer cells to inhibit cancer cell proliferation.

• Food Science and Preservation
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• v.22 no.1
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• pp.19-26
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• 2015

Indole 3-carbinol (I3C), important component of cruciferous vegetables and its major acid-catalyzed metabolite, 3,3'-diindolylmethane (DIM) have been suggested to have an inhibitory effect on the tumor growth and metastasis. This study investigated the effect of DIM on the adhesion, migration and invasion of highly invasive PC3 and DU145 human prostate cancer cell lines. Cells were grown in Dulbecco's modified Eagle's medium (DMEM) supplemented with 3.0 g/L glucose, 3.7 g/L sodium bicarbonate and 10% fetal bovine and were incubated in a humidified incubator at $37^{\circ}C$ and 5% $CO_2$. DIM reduced the adhesion of PC3 and DU145 cells in a dose dependent manner. The pretreatment of PC3 cells with DIM reduced the adhesion dose dependantly, but inhibition was less effective than the treatment with DIM during the adhesion assay. The migration and invasion of PC3 and DU145 cells were reduced by DIM dose dependantly, and the inhibition of DIM was less effective in the DU145 cells than in the PC3 cells. The pretreatment of PC3 cells with DIM for 24 hr before the assay reduced invasion of PC3 cells by 37%. These results suggest that DIM inhibits adhesion, migration and invasion of the PC3 and DU145 cells and may be an effective antimetastatic therapy in addition to traditional chemotherapy.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.733-740
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• 2023

Let R be a commutative ring and M be an R-module. The dimension graph of M, denoted by DG(M), is a simple undirected graph whose vertex set is Z(M) ⧵ Ann(M) and two distinct vertices x and y are adjacent if and only if dim M/(x, y)M = min{dim M/xM, dim M/yM}. It is shown that DG(M) is a disconnected graph if and only if (i) Ass(M) = {𝖕, 𝖖}, Z(M) = 𝖕 ∪ 𝖖 and Ann(M) = 𝖕 ∩ 𝖖. (ii) dim M = dim R/𝖕 = dim R/𝖖. (iii) dim M/xM = dim M for all x ∈ Z(M) ⧵ Ann(M). Furthermore, it is shown that diam(DG(M)) ≤ 2 and gr(DG(M)) = 3, whenever M is Noetherian with |Z(M) ⧵ Ann(M)| ≥ 3 and DG(M) is a connected graph.

• Journal of the Korean Society of Food Science and Nutrition
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• v.41 no.12
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• pp.1701-1707
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• 2012

3,3'-Diindolylmethane (DIM) is a major in vivo derivative of the putative anticancer agent indole-3-carbinol, which is present in cruciferous vegetables and has been reported to have anti-carcinogenic properties. An abnorrmally elevated level of cyclooxygenase-2 (COX-2) has been implicated in the pathogenesis of carcinogenesis. To investigate the mechanism by which DIM exhibits anti-carcinogenic effects, we investigated the effects of DIM on COX-2 expression in MCF-10A human mammary epithelial cells treated with the tumor promoter 12-O-tetradecanoylphorbol 13-acetate (TPA). DIM inhibited TPA-induced COX-2 expression and suppressed the synthesis of prostaglandin $E_2$, one of the major products of COX-2. Nuclear factor-kappa B ($NF-{\kappa}B$) is a transcription factor known to play a role in regulation of COX-2 expression. Treatment of MCF-10A cells with TPA increased nuclear translocation of phospho-p65, with the maximal levels being reached at 1 hour, while DIM inhibited the TPA-induced nuclear translocation of phospho-p65. Overall, we demonstrated that DIM suppresses phorbol ester-induced $PGE_2$ production and COX-2 expression in MCF-10A cells. The reduction in COX-2 levels by DIM maybe mediated through inhibition of $NF-{\kappa}B$ signaling.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.637-647
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• 2023

Let R be a commutative Noetherian ring, 𝔞 an ideal of R, M an arbitrary R-module and X a finite R-module. We prove a characterization for Hⁱ_𝔞(M) and Hⁱ_𝔞(X, M) to be 𝔞-weakly cofinite for all i, whenever one of the following cases holds: (a) ara(𝔞) ≤ 1, (b) dim R/𝔞 ≤ 1 or (c) dim R ≤ 2. We also prove that, if M is a weakly Laskerian R-module, then Hⁱ_𝔞(X, M) is 𝔞-weakly cofinite for all i, whenever dim X ≤ 2 or dim M ≤ 2 (resp. (R, m) a local ring and dim X ≤ 3 or dim M ≤ 3). Let d = dim M < ∞, we prove an equivalent condition for top local cohomology module H^d_𝔞(M) to be weakly Artinian.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.633-648
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• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.45-49
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• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

• Journal of Animal Science and Technology
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• v.62 no.4
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• pp.565-576
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• 2020

Recently, Jersey cattle was introduced and produced by embryo transfer to Korea. This study was conducted to investigate the differences of milk compositions between Jersey and Holstein cows and the relationship between days in milk (DIM) and milk compositions during early lactation. Data were collected from twelve lactating cows from Department of Animal Resources Development at National Institute of Animal Science. Cows in parity 1 were used, and calved at spring from April to March of 2017. All cows were housed in two sections within a free-stall barn, which divided into six from each breed, and received a basal total mixed ration. Milk samples of each cow were collected at 3 DIM and 30 DIM for analyzing the milk compositions, including fatty acids (FA), amino acids and minerals. Total solids, citrate, and milk urea nitrogen level were differed between the breeds (p < 0.05). As DIM went from 3 to 30, milk protein, total solids, and somatic cell count decreased (p < 0.05), but lactose increased in all breed milk (p < 0.05). Citrate and free fatty acid (FFA) elevated in Jersey milk (p < 0.05), whereas reduced in Holstein milk (p < 0.05). Proportions of some individual FA varied from the breeds. Myristic (C14:0), palmitic (C16:0), and arachidonic acid (C20:4) in milk from all cows were higher at 3 DIM than at 30 DIM (p < 0.05). Also, stearic (C18:0) and oleic acid (C18:1) were lower at 3 DIM than at 30 DIM (p < 0.05), and the C18:1 to C18:0 ratio was significantly differed in DIM × breed interactions (p < 0.05). The contents of the individual amino acids did not differ from the breeds. Calcium, phosphorous, magnesium, and zinc (Zn) contents was significantly increased in Holstein milk than Jersey milk at 3 DIM. Also, K and Zn concentrations were higher in Holstein milk than in Jersey milk at 30 DIM (p < 0.05). It was concluded that Jersey cows would produce more effective milk in processing dairy products and more proper energy status compared with Holstein cows in early lactation under the same environmental and nutritional conditions.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.15-36
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• 1999

In this paper, we determine the dimension of the rectangular product of certain finite lattices. In face, if L1 and a L2 be finite lattices which satisfy the some conditions, then we have dim (L1$\square$L2) = dim(L1) + dim(L2) - 1.