• Journal of the Korean Society of Safety
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• v.12 no.3
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• pp.155-160
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• 1997

The conventional fault tree and reliability analysis gives in many cases insufficient information concerning the relative frequencies of hazard events. This stems from that the basic events are not stationary and ergodic, and therefore the tolerances of the induced and top events cannot be calculated reliably based on the classical probability theory. To overcome this difficulty, the paper considers the relative frequencies of the basic events as fuzzy numbers and uses instead of probability, possible considerations for evaluating the mean values and tolerances of the top events. The possibility distribution of the basic events can be approximated based on heuristic considerations. This paper shows the use of these operators for constructing fault trees. The use of the method for numerical calculation is demonstrated on a field safety problem.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.167-170
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• 1988

Versions of Tannaka duality in operator algebraic context have been obtained in [6], [8] etc. Suppose .sigma.is an automorphism of a von Neumann algebra M, on which there is an action .alpha. of a compact group G such that .sigma. vertical bar $M^{\alpha}$=id, where $M^{\tau}$is the fixed point algebra under the action .alpha.. Then it is shown that if there is an action .tau. of a group H which commutes with .alpha., and which is ergodic in the sense that the fixed point algebra $M^{\tau}$ is trivial, then there exists g.mem.G such that .sigma.=.alpha.(g). Recently Evans and Kishimoto ([4]) showed the versions of Tannaka duality in $C^{*}$-settings under some conditions.s.

• International Journal of Contents
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• v.12 no.1
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• pp.70-75
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• 2016

In this paper, we considered heterogeneous spectrum sharing system where the number of subcarriers of the primary user (PU) was twice as much as that of the secondary user (SU). In this case, due to non-orthogonality and inter-carrier interference (ICI) from SU to PU, it is difficult to satisfy the interference constraint of PU. In order to mitigate ICI and satisfy the interference constraint, we proposed a new transmission scheme of the SU with power allocation scheme. The proposed scheme will only generate subcarrier-by-subcarrier interference. Therefore, it can easily satisfy the interference constraint of the PR and enhance the capacity of the SU. In addition, we derived the ergodic capacity of the SU. Based on numerical results, we confirmed that the proposed schemes could guarantee SU with a reliable capacity while satisfying the interference constraint of the PU. In addition, the derived capacity well matched the numerical results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.4
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• pp.1889-1910
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• 2017

This paper investigates a protocol so-called Adaptive Harvest Then Transmit (AHTT) for wireless powered communication networks (WPCNs) in multiple-input single-output (MISO) downlink systems, which assists in transmitting signals from a multi-antenna transmitter to a single-antenna receiver. Particularly, the power constrained relay is supplied with power by utilizing radio frequency (RF) signals from the source. In order to take advantage of multiple antennas, two different linear processing schemes, including Maximum Ratio Combining (MRC) and Selection Combination (SC) are studied. The system outage capacity and ergodic capacity are evaluated for performance analysis. Furthermore, the optimal power allocation is also considered. Our numerical and simulation results prove that the implementation of multiple antennas helps boost the energy harvesting capability. Therefore, this paper puts forward a new way to the energy efficiency (EE) enhancement, which contributes to better system performance.

• Journal of Communications and Networks
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• v.16 no.3
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• pp.293-300
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• 2014

As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.171-194
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• 2020

For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.11
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• pp.3731-3750
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• 2014

This paper considers a wideband cognitive radio network (WCRN) which can simultaneously sense multiple narrowband channels and thus aggregate the detected available channels for transmission and studies the ergodic throughput of the WCRN that operated under: the wideband sensing-based spectrum sharing (WSSS) scheme and the wideband opportunistic spectrum access (WOSA) scheme. In our analysis, besides the average interference power constraint at PU, the average transmit power constraint of SU is also considered for the two schemes and a novel cognitive radio sensing frame that allows data transmission and spectrum sensing at the same time is utilized, and then the maximization throughput problem is solved by developing a gradient projection method. Finally, numerical simulations are presented to verify the performance of the two proposed schemes.