• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.359-366
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• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.12
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• pp.2381-2388
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• 2015

It has been known that interference occurs between macrocell ans small-cell base stations in a heterogeneous network (HetNet) of LTE-A. For solving this problem, 3GPP suggested eICIC (Enhanced Inter Cell Interference Coordination) that includes ABS (Almost Blank Subframe) and power control. This paper proposes to use ABS with power control and derives an effective ABS ratio as a function of the number of users and HeNBs. Through simulation, we confirm that integration of ABS and power control can mitigate interference than using ABS only. Furthermore, we verify that an effective ABS ratio is different depending on the number of users and HeNBs.