• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.177-185
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• 2011

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${\neq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${\rightarrow}$ M for every principally small right ideal aR can be extended to R ${\rightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.57-64
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• 2020

Let R ⊆ T be an ascending chain of commutative rings with identity and H(R, T) (resp., h(R, T)) the composite Hurwitz series ring (resp., composite Hurwitz polynomial ring). In this article, we give some conditions for the rings H(R, T) and h(R, T) to be PS-rings.

• Polymer(Korea)
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• v.33 no.5
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• pp.458-462
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• 2009

We have synthesized ABC linear triblock copolymers, i.e., polystyrene-b-poly(ethylene oxide)-b-polylactide, via sequential anionic and ring-opening polymerizations. In the first anionic polymerization step, styrene was polymerized in cyclohexane using sec-butyllithium as the initiator. Poly (styryl) lithium was hydroxylated by the addition of ethylene oxide, and the subsequent protonation with methanolic HCl. In the second anionic polymerization step, potassium naphthalenide was used to deprotonate the hydroxyl group of the PS to generate the macroinitiator of PS-$O^-K^+$. Polymerization of ethylene oxide was performed in THF and terminated with methanolic HCl. In the ring-opening polymerization step, the PS-b-PEO-$AlEt_2$ macroinitiator was prepared from an $AlEt_3$/pyridine system in THF, and the polymerization of lactide was performed at $90^{\circ}C$. The resulting block copolymers showed well-defined molecular weights and narrow molecular weight distributions as revealed by $^1H$- NMR spectroscopy and gel permeation chromatography (GPC).

• Korean Journal of Optics and Photonics
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• v.10 no.1
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• pp.58-63
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• 1999

A 10 GHz harmonically mode-locked semiconductor-fiber ring laser was implemented using a semiconductor optical amplifier at $1.5\mu\textrm{m}$ The laser pulse has 13~18 ps pulse duration, 0.4~0.6 nm spectral width and was positively chirped. The output pulse with an average power of 4 dBm was compressed to 6.8 ps using 2 km long standard single mode optical fiber.

• Journal of Photoscience
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• v.7 no.4
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• pp.153-154
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• 2000

No Abstract. See full-text

• Journal of the Optical Society of Korea
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• v.18 no.6
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• pp.766-771
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• 2014

Single-ring all-pass filters with various coupling ratios are designed, fabricated, and characterized to assess the validity of the split-step time-domain modeling approach, which is considered for direct simulation of time-domain characteristics, such as optical delay, of various ring resonator devices. When the coupling ratio of the single-ring all-pass filter is 0.4 and 0.8, the delay time is measured to be about 145 and 42 ps respectively, which is comparable to the time-domain modeling results of 151 and 47 ps respectively. The measurements for two- and three-ring all-pass filters are also found to agree quite well with the simulation results. With these results it is confirmed that the split-step time-domain model could be efficiently incorporated into an optical-communication simulation module for ring resonator delay components in an all-optical packet switching system.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.471-476
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• 2014

Let R be a ring. A right R-module M is PS-injective if every R-homomorphism $f:aR{\rightarrow}M$ for every principally small right ideal aR can be extended to $R{\rightarrow}M$. We investigate, in this paper, rings whose simple singular modules are PS-injective. New characterizations of semiprimitive rings and semisimple Artinian rings are given.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.479-481
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• 2006

This paper describes a 2.5V, 320MHz low-noise and low-power Phase Locked Loop(PLL) using a noise-rejected Voltage Controlled ring Oscillator(VCO) fabricated in a TSMC 0.25um CMOS technology. In order to improve the power consumption and oscillation frequency of the PLL, The VCO consist of three-stage fully differential delay cells that can obtain the characteristic of high speed, low power and low phase noise. The VCO operates at 7MHz -670MHz. The oscillator consumes l.58mA from a 320MHz frequency and 2.5V supply. When the PLL with fully-differential ring VCO is locked 320MHz, the jitter and phase noise measured 26ps (rms), 157ps (p-p) and -97.09dB at 100kHz offset. We introduce and analysis the conditions in which ring VCO can oscillate for low-power operation.

• Korean Journal of Optics and Photonics
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• v.7 no.4
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• pp.386-389
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• 1996

We report on comparative results obtained from harmonically mode-locked laser operations of ring-type and figure-of-eight(F8) type erbium-doped fiber lasers by using a directional-coupler type electro-optic modulator as an active mode-locker. The mode-locked and transform-limited pulses of 10.6 ps width were obtained at harmonics of the fundamental cavity frequency with the F8 type laser while mode-locked laser pulses greater than 15 ps were achieved with the ring type laser.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.6
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• pp.741-746
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• 1986

A novel n-p-n bipolar transistor of which emitter is self-aligned with base contact by polyilicon is developed for using in high speed and high packing density LSI circuits. The emitter of this transistor is separated less than 0.4 \ulcorner with base contact by self-aligh technology, and the emitter feature size is less than 3x5 \ulcorner\ulcorner Because the active region of this transistor is not damaged through all the process, it has excellent electric properties. Using the n-p-n transistors by 3.0\ulcorner design rules, a NTL ring oscillator has 380 ps, a CML ring oscillator has 390ps, and a I\ulcorner ring oscillator has 5.6ns of per-gate minimum propagation delay time.