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SHARP ORE-TYPE CONDITIONS FOR THE EXISTENCE OF AN EVEN [4, b]-FACTOR IN A GRAPH

  • Cho, Eun-Kyung;Kwon, Su-Ah;O, Suil
    • Journal of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.757-774
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    • 2022
  • Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ2(G) = minuv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ2(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ2(G) is sharp.

Design and Implementation of $\pi/4$ QPSK Satellite IP Modem Part ($\pi/4$ QPSK 위성 IP 모뎀부 설계 및 구현)

  • Kang, Jung-Mo;Jung, Jae-Wook;Kim, Myung-Sik;Oh, Woo-Jin
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.10
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    • pp.1858-1865
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    • 2007
  • In this paper, we introduce the design and implementation of satellite IP modem. The designed satellite IP modem shows the performance of 0.2% overhead, BER=10-5 when Eb/No=6dB, frequency offset of 8KHz, data rate up to 1536Kbps, $F_{if}=140MHz$. The designed system is verified through software simulation and then implemented with MPC86x communication processor, TMS320C6416 DSP, and Altera FPGA. Since each hardware unit is implemented in daughter board for modularity, we can reduce the development time and easily improve the performance with using better processor. Linux is used for embedded OS because it shows better performance in IP manipulation multitask processing, and hardware control through device driver. The implemented system is tested and verified with channel simulator. Since the proposed IP modem shows small size and light weight, that can be used anywhere with easy if you need IP environment.

STRUCTURE OF IDEMPOTENTS IN POLYNOMIAL RINGS AND MATRIX RINGS

  • Juan Huang;Tai Keun Kwak;Yang Lee;Zhelin Piao
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.1321-1334
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    • 2023
  • An idempotent e of a ring R is called right (resp., left) semicentral if er = ere (resp., re = ere) for any r ∈ R, and an idempotent e of R∖{0, 1} will be called right (resp., left) quasicentral provided that for any r ∈ R, there exists an idempotent f = f(e, r) ∈ R∖{0, 1} such that er = erf (resp., re = fre). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the n by n full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.

Characterization of $ET_B$ Receptor-mediated Relaxation in Precontracted Mesenteric Artery from Streptozotocin-induced Diabetic Rats

  • Eom, Yang-Ki;Kim, Koan-Hoi;Rhim, Byung-Yong
    • The Korean Journal of Physiology and Pharmacology
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    • v.9 no.5
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    • pp.305-314
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    • 2005
  • Diabetes mellitus is associated with vascular complications, including an impairment of vascular function and alterations in the reactivity of blood vessels to vasoactive substances in various vasculature. In the present study, the authors have observed endothelin-B ($ET_B$) receptor agonist-induced relaxation in precontracted mesenteric arterial segments from streptozotocin (STZ)-induced diabetic rats, which was not shown from control rats or in other arterial segments from diabetic rats. Accordingly, the goal of this study was to investigate in what way STZ-induced diabetes altered reactivity of the mesenteric arterial bed and to examine the causal relaxation, if any, between this $ET_B$ receptor-mediated relaxation and endothelial paracrine function, especially nitric oxide (NO) production. The relaxation induced by $ET_B$ agonists was not observed in mesenteric arteries without endothelium. The relaxation to $ET_B$ agonists was completely abolished by pretreatment with BQ788, but not by BQ610. $N_{\omega}-nitro-L-arginine$ methyl ester and soluble guanylate cyclase inhibitors, methylene blue or LY83583 significantly attenuated the relaxant responses to $ET_B$ agonists, respectively. When the expression of eNOS and iNOS was evaluated on agarose gel stained with ethidium bromide, the expression of eNOS mRNA in diabetic rats was significantly decreased, but the expression of iNOS was increased compared with control rats. Furthermore, the iNOS-like immunostaining was densely detected in the endothelium and slightly in the arterial smooth muscle of diabetic rats, but not in control rats. These observations suggest that $ET_B$ receptor may not play a role in maintaining mesenteric vascular tone in normal situation. However, the alterations in $ET_B$ receptor sensitivity were found in diabetic rats and lead to the $ET_B$ agonist-induced vasorelaxation, which is closely related to NO production. In the state of increased vascular resistance of diabetic mesenteric vascular bed, enhanced NO production by activation of iNOS could lead to compensatory vasorelaxation to modulate adequate perfusion pressure to splanchnic area.

16-QAM-Based Highly Spectral-Efficient E-band Communication System with Bit Rate up to 10 Gbps

  • Kang, Min-Soo;Kim, Bong-Su;Kim, Kwang Seon;Byun, Woo-Jin;Park, Hyung Chul
    • ETRI Journal
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    • v.34 no.5
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    • pp.649-654
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    • 2012
  • This paper presents a novel 16-quadrature-amplitude-modulation (QAM) E-band communication system. The system can deliver 10 Gbps through eight channels with a bandwidth of 5 GHz (71-76 GHz/81-86 GHz). Each channel occupies 390 MHz and delivers 1.25 Gbps using a 16-QAM. Thus, this system can achieve a bandwidth efficiency of 3.2 bit/s/Hz. To implement the system, a driver amplifier and an RF up-/down-conversion mixer are implemented using a $0.1{\mu}m$ gallium arsenide pseudomorphic high-electron-mobility transistor (GaAs pHEMT) process. A single-IF architecture is chosen for the RF receiver. In the digital modem, 24 square root raised cosine filters and four (255, 239) Reed-Solomon forward error correction codecs are used in parallel. The modem can compensate for a carrier-frequency offset of up to 50 ppm and a symbol rate offset of up to 1 ppm. Experiment results show that the system can achieve a bit error rate of $10^{-5}$ at a signal-to-noise ratio of about 21.5 dB.

A NOTE ON LINEAR COMBINATIONS OF AN IDEMPOTENT MATRIX AND A TRIPOTENT MATRIX

  • Yao, Hongmei;Sun, Yanling;Xu, Chuang;Bu, Changjiang
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1493-1499
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    • 2009
  • Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.

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The Design of Ku-Band Cavity BPF (Ku-Band Cavity BPF설계)

  • Jeon, Hyung-Joon;Kang, Chang-Soo
    • Journal of the Institute of Electronics Engineers of Korea TE
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    • v.42 no.4
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    • pp.69-76
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    • 2005
  • In this paper, a 2 stage 6-pole bandpass filter(BPF) is designed and implemented by using triple-mode cavity for satellite payload system. The BPF has a 100MHz bandwidth at the center frequency of 14.5GHz(Ku-band) and the response of the filter is the Chebyshev function. The cavity filter uses two orthogonal $TM_{113}$ modes and one $TM_{012}$ mode. The coupling between the adjacent cavityes(intercavity coupling) results in a Chebyshev response and is accomplished by only H-filed component of If modes. The size and location of intercavity slot is determined by the coupling equation from E-and H-field of TE and TM resonant modes in circular cavity. The 2-stage 6-pole triple-mode cavity BPF has the insertion loss of 2.4dB and the reflection loss of 15dB in the passband. The triple-mode BPF proposed in this thesis can be used as channel filters for satellite payload system and can minimize filter assembly in general wireless communication system.

Effect of the Corrosive Solution Conditions and Scan Rate to the Electrochemical Corrosion on the AISI 304 Stainless Steel (부식액의 조건 및 주사 속도가 AISI 304 스테인리스강의 전기화학적 부식에 미치는 영향)

  • 나은영;백신영
    • Journal of Advanced Marine Engineering and Technology
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    • v.21 no.5
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    • pp.535-541
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    • 1997
  • The effect of concentration of each solution( HCI, $H_2SO_4$ and $HNO_3$), scan rate and polished surface condition on the corrosion of AISI 304 Stainless Steel were investigated, utilizing the Method ASTM G5 - 87. It can be concluded that: 1) For the same concentration(i.e. 1N) of each solution the corrosion rate is the highest in HCI and lowest in $HNO_3$. Also, the difference of values of $i_{cirt}$ generated for each solution is significant. 2) As the concentration of the solution $H_2SO_4$ is increased (O.5N, 1N, 2N) the values of $E_{cor}$ $i_{crit}$ and $i_{p}$ are increased. 3) In case of existence of SCN ion of O.OlN, the values of iCTIt and ip generated are approximately 100 times and 1.4 times higher respectively, than in the case of non - existence of $SCN^{-}$. However the existence of $SCN^{-}$ doesn't affect the value of $E_{cor}$ and $E_{p}$. 4) The values of $i_{crit}$ and $i_{p}$ are increased due to the increase of scan rate. But the values of $E_{cor}$ and $E_{p}$ do not depend on the scan rate. 5) The $i_{p}$ value depends greatly on oxygen in the solution, but the changes in values of $E_{cor}$ $i_{crit}$ and $E_{b}$ due to the oxygen are insignificant. 6) If a component is polished using #400, #600 and #800 wet polish paper, the effect of surface condition on variations of values of $i_{crit}$ and $i_{p}$ is slightly significant.

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Marine Terrace of Daebo-Guryongpo-Gampo, SE Korea(II) (대보-구룡포-감포 지역의 해안단구(II))

  • 최성자
    • Economic and Environmental Geology
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    • v.37 no.2
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    • pp.245-253
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    • 2004
  • The 36km-long Daebo-Campo coast has a well-developed marine terraces divided to six steps by elevation of paleoshoreline : 0.5 m(T1), 10 m(T2), 30 m(T3), 40 m(T4), 60 m(T5) and 75 m(T6). The 2$^{nd}$ and 3$^{nd}$ platforms in Daebo to Guryongpo are wider and more distinctive than those of Guryongpo to Gampo. The 3$^{nd}$ terrace of 30 m high is subdivided to two flights as lower(T3b) and upper(T3a) by old sea cliff. Platform age is unclear because of coral fossil free. However, the terrace age could be determined with convergent OSL ages from beach sediments on 2$^{nd}$ step(T2). OSL ages of the terrace of 10 m high range in 60-70 ka. It reveals that the 2$^{nd}$ -step platform correlates to Oxygen Isotope Time scale, substage 5a(ca. 80 ka), and that uplift rate is ca. 0.19 m/ka for 2$^{nd}$ terrace at Daebo-Campo coast. If considering equivalent uplift rate for all terraces since the Late Pleistocene, the 3$^{rd}$ and 4$^{th}$ terraces would be 5e substage and 7 stage. The 30 m-high terrace provides a good indicator for uplift at Daebo-Gampo coast since 125,000 yrs(MIS 5e). It suggests that the local neotectonic deformation might cause an optional uplift rate of ca. 0.19 m/ka along the SE coast of Korea.

THE FINITE DIMENSIONAL PRIME RINGS

  • Koh, Kwangil
    • 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.

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