• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.617-626
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• 2000

We study the vectors related tro states on the Cuntz algebra Ο(sub)n and prove hat, for tow states $\omega$ and $\rho$ on Ο(sub)n with $\omega$│UHF(sub)n = $\rho$│UHF(sub)n, if ($\omega$(s$_1$), …, $\omega$(s(sub)n)) and ($\rho$(s$_1$),…, $\rho$(s(sub)n)) are unit vectors, then they and linearly dependent. We also study the linear functional on Ο(sub)n associated to a sequence of unit vectors in C(sup)n which is the generalization of the Cuntz state. We show that if the linear functional associated to a sequence of unit vectors with a certain condition is a state, then it is just the Cuntz state.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.471-478
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• 2002

Let $Let\eta={\eta m}m$ be an eventually constant sequence of unit vectors $\eta m$ in $C^{n}$ and let $\rho$η be the pure state on $UHF_{n}$ algebra which is defined by $\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}$. We find infinitely many state extensions of $\rho\eta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.

• Investigative Magnetic Resonance Imaging
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• v.24 no.3
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• pp.95-122
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• 2020

In this article, we evaluated the performance of radiofrequency (RF) coils in terms of the signal-to-noise ratio (S/N) and homogeneity of magnetic resonance images when used for ultrahigh-frequency (UHF) 7T magnetic resonance imaging (MRI). High-quality MRI can be obtained when these two basic requirements are met. However, because of the dielectric effect, 7T magnetic resonance imaging still produces essentially a non-uniform magnetic flux (|B₁|) density distribution. In general, heterogeneous and homogeneous RF coils may be designed using electromagnetic (EM) modeling. Heterogeneous coils, which are surface coils, are used in consideration of scalability in the |B₁| region with a high S/N as multichannel loop coils rather than selecting a single loop. Loop coils are considered state of the art for their simplicity yet effective |B₁|-field distribution and intensity. In addition, combining multiple loop coils allows phase arrays (PA). PA coils have gained great interest for use in receiving signals because of parallel imaging (PI) techniques, such as sensitivity encoding (SENSE) and generalized autocalibrating partial parallel acquisition (GRAPPA), which drastically reduce the acquisition time. With the introduction of a parallel transmit coil (pTx) system, a form of transceiver loop arrays has also been proposed. In this article, we discussed the applications and proposed designs of loop coils. RF homogeneous coils for volume imaging include Alderman-Grant resonators, birdcage coils, saddle coils, traveling wave coils, transmission line arrays, composite right-/left-handed arrays, and fusion coils. In this article, we also discussed the basic operation, design, and applications of these coils.