• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1341-1352
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• 2016

Let R be a commutative Noetherian ring, ${\Phi}$ a system of ideals of R and $I{\in}{\Phi}$. In this paper among other things we prove that if M is finitely generated and $t{\in}\mathbb{N}$ such that the R-module $H^i_{\Phi}(M)$ is $FD_{{\leq}1}$ (or weakly Laskerian) for all i < t, then $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all i < t and for any $FD_{{\leq}0}$ (or minimax) submodule N of $H^t_{\Phi}(M)$, the R-modules $Hom_R(R/I,H^t_{\Phi}(M)/N)$ and $Ext^1_R(R/I,H^t_{\Phi}(M)/N)$ are finitely generated. Also it is shown that if cd I = 1 or $dimM/IM{\leq}1$ (e.g., $dim\;R/I{\leq}1$) for all $I{\in}{\Phi}$, then the local cohomology module $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all $i{\geq}0$. These generalize the main results of Aghapournahr and Bahmanpour [2], Bahmanpour and Naghipour [6, 7]. Also we study cominimaxness and weakly cofiniteness of local cohomology modules with respect to a system of ideals.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.653-662
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• 2005

In this paper we shall give the relationships among $T_R,\;End_{R}(M),\;SEnd_{R}(M)\;and\;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M {\times}N){\cong}SAut_{R}(M){\times}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.917-928
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• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.

• Journal of information and communication convergence engineering
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• v.17 no.3
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• pp.221-226
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• 2019

In this work, a transmitter/receiver front-end module (T/R FEM) with an automatic Tx/Rx switching scheme for a 2.4 GHz microwave power transfer is developed for a retro-reflective beamforming scheme. Recently, research on wireless power transfer techniques has moved to wireless charging systems for mobile devices. Retro-reflective beamforming is a good candidate for tracking the spatial position of a mobile device to be charged. In Tx mode, the T/R FEM generates a minimum of 1 W. It also comprises an amplitude and phase monitoring port for transmitting RF power. In Rx mode, it passes an Rx pilot signal from a mobile device to a digital baseband subsystem to recognize the position of the mobile device. The insertion loss of the Rx signal path is 4.5 dB. The Tx and Rx modes are automatically switched by detecting the Tx input power. This T/R FEM is a design example of T/R FEMs for wireless charging systems based on a retro-reflective beamforming scheme.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.653-657
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• 2014

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.2
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• pp.172-182
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• 2014

In this paper, is is presented the result of design and fabrication for X band T/R module using in active array radar. The high power RF circuit was fabricated using GaN element, so that high power and high efficiency was fulfilled comparing with the previous T/R module that have under 50 W output power for X band. Designed X band T/R module demonstrated 200 W(53 dBm) peak power, 20 us pulse width with 0.4 dB pulse droop and 20 % duty cycle. And it has characteristics of 26 dB receive gain and 4.5 dB noise figure. The structure was applied to prevent serious damage of receive path and GaN HPA by transmitting power during trasmit time of a pulse radar.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.21 no.12
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• pp.1380-1393
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• 2010

This paper presents a design, fabrication and the test results of planar active electronically scanned array(AESA) radar prototype for airborne fighter applications using transmit/receive(T/R) module hybrid technology. LIG Nex1 developed a AESA radar prototype to obtain key technologies for airborne fighter's radar. The AESA radar prototype consists of a radiating array, T/R modules, a RF manifold, distributed power supplies, beam controllers, compact receivers with ADC(Analog-to-Digital Converter), a liquid-cooling unit, and an appropriate structure. The AESA antenna has a 590 mm-diameter, active-element area capable of containing 536 T/R modules. Each module is located to provide a triangle grid with $14.7\;mm{\times}19.5\;mm$ spacing among T/R modules. The array dissipates 1,554 watts, with a DC input of 2,310 watts when operated at the maximum transmit duty factor. The AESA radar prototype was tested on near-field chamber and the results become equal in expected beam pattern, providing the accurate and flexible control of antenna beam steering and beam shaping.

• 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 the Korean Society of Safety
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• v.33 no.1
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• pp.28-34
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• 2018

The purpose of this study is to fabricate a sensor module to detect the resistive leakage current (Igr) in real time that occurs to low voltage electric lines and to verify its reliability. In the case of the developed sensor module, wires are inserted into the zero current transformer (ZCT) and current transformer (CT) in advance and then the branch line is connected to the circuit breaker. The measurement result of the resistance of the distribution panel equipped with the developed sensor module shows that the resistance is $0.151m{\Omega}$ between the R and R phases, $0.169m{\Omega}$ between the S and S phases, and $0.178m{\Omega}$ between the T and T phases, respectively. The insulation resistance measured at AC 500 V and 1,000 V is $0.08m{\Omega}$ between the R, S, T and N phases, respectively. Then, the insulation resistance measured at DC 500 V is $83.3G{\Omega}$ between the R, S, T and G terminal, respectively. In addition, the applied withstanding voltage is AC 220 V/380 V/440 V and it was found that characteristics between all phases are good. This study measured the standby power by installing the developed sensor module at the rear of the MCCB and switching the circuit breaker on sequentially. The standby power is 1.350 W when one circuit breaker is turned on, 1.690 W when 2 circuit breakers are turned on, and 4.371 W when 10 circuit breakers are turned on. This study also verified the reliability of the standby power of the distribution panel equipped with the developed sensor module using the Minitab Program (Minitab PGM). Since the analysis shows the statistical average of 1.34627 in the reliable range of normal distribution, standard deviation of 0.001874, AD of 0.554, and P value of 0.140, it is found that the distribution panel equipped with the developed sensor module has high reliability.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.