• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.585-590
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• 2016

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.

• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2479-2484
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• 2018

The filter bank multicarrier modulation (FBMC) technique is one of multicarrier modulation technique (MCM), which is mainly used to improve channel capacity of cognitive radio (CR) network and frequency spectrum access technique. The existing FBMC System contains serial to parallel converter, normal QAM modulation, Radix2 inverse FFT, parallel to serial converter and poly phase filter. It needs high area, delay and power consumption. To further reduce the area, delay and power of FBMC structure, a new clock gating technique is applied in the QAM modulation, radix2 multipath delay commutator (R2MDC) based inverse FFT and unified addition and subtraction (UAS) based FIR filter with parallel asynchronous self time adder (PASTA). The clock gating technique is mainly used to reduce the unwanted clock switching activity. The clock gating is nothing but clock signal of flip-flops is controlled by gate (i.e.) AND gate. Hence speed is high and power consumption is low. The comparison between existing QAM and proposed QAM with clock gating technique is carried out to analyze the results. Conversely, the proposed inverse R2MDC FFT with clock gating technique is compared with the existing radix2 inverse FFT. Also the comparison between existing poly phase filter and proposed UAS based FIR filter with PASTA adder is carried out to analyze the performance, area and power consumption individually. The proposed FBMC with clock gating technique offers low power and high speed than the existing FBMC structures.