• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1125-1128
• /
• 2011

Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules $H^j_a(M)$ are a-cominimax; that is, $Ext^i_R$(R/a, $H^j_a(M)$) is minimax for all i and j in the following cases: (a) dim R/a = 1; (b) cd(a) = 1, where cd is the cohomological dimension of a in R; (c) dim $R{\leq}2$. In these cases we also prove that the Bass numbers and the Betti numbers of $H^j_a(M)$ are finite.

• Journal of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.249-271
• /
• 2008

We prove the Hyers-Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital $C^*-algebra$ and of linear isometries in Banach modules over a unital $C^*-algebra$. The main purpose of this paper is to investigate d-isometric $C^*-algebra$ isomor-phisms between linear d-normed $C^*-algebras$ and isometric $C^*-algebra$ isomorphisms between $C^*-algebras$, and d-isometric Poisson $C^*-algebra$ isomorphisms between linear d-normed Poisson $C^*-algebras$ and isometric Poisson $C^*-algebra$ isomorphisms between Poisson $C^*-algebras$. We moreover prove the Hyers-Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms.

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

• 한국태양에너지학회:학술대회논문집
• /
• 2008.04a
• /
• pp.252-256
• /
• 2008

Photovoltaic (PV) modules output changes noticeable with variations in temperature and irradiance. In general it is has been shown that a $1^{\circ}C$ increase in temperature results in a 0.5% drop in output. In this paper, seven PV module types are analyzed for variation in temperature and irradiance, and the resulting output characteristics examined. The 7 modules types utilized are as follows; 3 poly crystalline modules, 2 single crystalline modules, 1 back contact single crystalline module and 1 HIT module. 3 groups of experiments are then conducted on the modules; tests with varying irradiance values, tests with module temperature varying under $25^{\circ}C$ and tests with module temperature varying over $25^{\circ}C$. The experiments results show that as temperature rises the follow is observed; Pmax decreases by 0.6%, Voc decreases by about 0.4%, and Isc increasing by between 0.03%${\sim}$0.08%. In addition, an irradiance decrease of 100 w/m2 translates into a 10% drop in Pmax.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.289-298
• /
• 2017

Let R denote a commutative Noetherian (not necessarily local) ring and let I be an ideal of R of dimension one. The main purpose of this note is to show that the category ${\mathfrak{M}}(R,\;I)_{com}$ of I-cominimax R-modules forms an Abelian subcategory of the category of all R-modules. This assertion is a generalization of the main result of Melkersson in [15]. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category ${\mathcal{C}}^1_B(R)$ of all R-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all R-modules.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.649-661
• /
• 2023

Let 𝓜 be a stable Serre subcategory of the category of R-modules. We introduce the concept of 𝓜-minimax R-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the 𝓜-minimaxness. We also provide the 𝓜-finiteness dimension f^𝓜_I (M, N) of M, N relative to I which is an extension the finiteness dimension f_I (N) of a finitely generated R-module N relative to I.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.157-167
• /
• 2008

A mapping f : $M{\rightarrow}N$ between Hilbert $C^*$-modules approximately preserves the inner product if $$\parallel<f(x),\;f(y)>-<x,y>\parallel\leq\varphi(x,y)$$ for an appropriate control function $\varphi(x,y)$ and all x, y $\in$ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert $C^*$-modules on more general restricted domains. In particular, we investigate some asymptotic behavior and the Hyers-Ulam-Rassias stability of the orthogonality equation.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.503-511
• /
• 1994

In this paper, the ring A will mean a commutative Noetherian ring with non-zero multiplicative identity, it is understood that the ring homomorphisms respect identity elements and M will denote an A-module. Throughout this paper A and B will denote rings, $f : A \to B$ a ring homomorphism. C(A) (resp. C(B)) presents the category of all A-modules (resp. B-modules) and A-homomorphisms (resp. B-homorphisms) between them. The following ideas will be used without further explanation. B can be regarded as an A-module by means of f and $M\otimesB$ can be regarded as a B-module in the natural way. Furthermore the restriction of scalars provides a functor from C(B) to C(A).

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.12 no.2
• /
• pp.155-161
• /
• 1994

Accurate positioning method using low cost GPS modules is proposed, which use the technique of differential GPS. DGPS experiments have been made using two coarse-acquisition (C/A) code GPS modules. Position accuracy of better than 5 m was obtained for position dilution of precision (PDOP) of 2-3 and that of better than 10 m after filtering was obtained for PDOP of about 9 in a local area. Static DGPS experiments were performed at Kookmin university with the DGPS correction data of KRISS reference station at Taejon. The distance between two stations is about 140 km. The results show that precision of the position is about 10 m (2 drms), which is ten times better than the results with the GPS module alone. Accuracy of about 10 meters can be obtained in near real time by the DGPS service with a reference station in our country.

• Kyungpook Mathematical Journal
• /
• v.61 no.2
• /
• pp.239-248
• /
• 2021

In this paper we study modules with the W F I⁺-extending property. We prove that if M satisfies the W F I⁺-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I⁺-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M₁ ⊕ M₂ for some semisimple submodule M₁ and Noetherian (respectively, Artinian) submodule M₂. Moreover, we show that if M is a W F I-extending module with pseudo duo, C₂ and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.