• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.721-734
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• 2014

Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({\Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{\in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({\Gamma}(M))$ and $T_0({\Gamma}(M))$ of $T({\Gamma}(M))$, with vertices $T(M){\backslash}\{0\}$ and $M{\backslash}\{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.6
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• pp.513-518
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• 2007

In this paper, we propose a fault diagnosis scheme tor induction motor by adopting a hierarchical classifier consisting of k-Nearest Neighbors(k-NN) and Support Vector Machine(SVM). First, some motor conditions are classified by a simple k-NN classifier in advance. And then, more complicated classes are distinguished by SVM. To obtain the normal and fault data, we established an experimental unit with induction motor system and data acquisition module. Feature extraction is performed by Principal Component Analysis(PCA). To show its effectiveness, the proposed fault diagnostic system has been intensively tested with various data acquired under the different electrical and mechanical faults with varying load.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.35-44
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• 1994

In this paper we study exponential growth of Betti numbers over artinian local rings. By the Change of Tor Formula the results in the paper extend to the asymptotic behavior of Betti numbers over Cohen-Macaulay local rings. Using the length function of an artinian ring we calculate an upper bound for the number of generators of modules, this is then used to maximize the number of generators of sygyzy modules. Finally, applying a filtration of an ideal, which we call a Loewy series of an ideal, we derive an invariant B(R) of an artinian local ring R, such that if B(R)>1, then the sequence $b^{R}$$_{i}$ (M) of Betti numbers is strictly increasing and has strong exponential growth for any finitely generated non-free R-module M (Theorem 2.7).).

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.21-38
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• 2023

Let R be a commutative ring with identity. Let R be an integral domain and M a torsion-free R-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari [1], and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor T or and Ext, and study some properties of them.

• Journal of Microbiology and Biotechnology
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• v.32 no.3
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• pp.365-377
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• 2022

Mammalian target of rapamycin (mTOR) is a serine-threonine kinase member of the cellular phosphatidylinositol 3-kinase (PI3K) pathway, which is involved in multiple biological functions by transcriptional and translational control. mTOR is a downstream mediator in the PI3K/Akt signaling pathway and plays a critical role in cell survival. In cancer, this pathway can be activated by membrane receptors, including the HER (or ErbB) family of growth factor receptors, the insulin-like growth factor receptor, and the estrogen receptor. In the present work, we congregated an electronic network of mTORC1 built on an assembly of data using natural language processing, consisting of 470 edges (activations/interactions and/or inhibitions) and 206 nodes representing genes/proteins, using the Cytoscape 3.6.0 editor and its plugins for analysis. The experimental design included the extraction of gene expression data related to five distinct types of cancers, namely, pancreatic ductal adenocarcinoma, hepatic cirrhosis, cervical cancer, glioblastoma, and anaplastic thyroid cancer from Gene Expression Omnibus (NCBI GEO) followed by pre-processing and normalization of the data using R & Bioconductor. ExprEssence plugin was used for network condensation to identify differentially expressed genes across the gene expression samples. Gene Ontology (GO) analysis was performed to find out the over-represented GO terms in the network. In addition, pathway enrichment and functional module analysis of the protein-protein interaction (PPI) network were also conducted. Our results indicated NOTCH1, NOTCH3, FLCN, SOD1, SOD2, NF1, and TLR4 as upregulated proteins in different cancer types highlighting their role in cancer progression. The MCODE analysis identified gene clusters for each cancer type with MYC, PCNA, PARP1, IDH1, FGF10, PTEN, and CCND1 as hub genes with high connectivity. MYC for cervical cancer, IDH1 for hepatic cirrhosis, MGMT for glioblastoma and CCND1 for anaplastic thyroid cancer were identified as genes with prognostic importance using survival analysis.