• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.347-351
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• 1993

The dichotomy of absolute continuity and singularity for a pair of stationary and ergodic measures (one of which need not be ergodic) is obtained using the ergodic decomposition theorem. The known fact that two different stationary and ergodic measures are mutually singular is obtained as a corollary of our result. An example of a pair of stationary-ergodic measures enjoying the dichotomy is presented.

• East Asian mathematical journal
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• 제15권2호
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• pp.301-312
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• 1999

In this paper, we study the nonlinear ergodic retraction theorems for an asymptotically nonexpansive semigroup with nonconvex and nonclosed domains in Hilbert spaces.

• 대한수학회지
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• 제59권3호
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• pp.549-570
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• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.929-942
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• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• 충청수학회지
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• 제37권2호
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• pp.75-80
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• 2024

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.17-30
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• 1996

In ergodic theory cutting and stacking constructions have been used to obtain a variety of important examples of transformations on the unit interval. We examine the example constructed by J. von Neumann and Kakutani and then apply the method used in the construction of Chacon's transformation to make examples that are weakly mixing but not mixing.

• ETRI Journal
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• 제40권3호
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• pp.330-336
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• 2018

Free-space optical (FSO) systems have attracted much attention from both research and application perspectives owing to their many benefits, such as license-free operation, low-cost, and high data rates. This paper investigates the ergodic capacity of FSO systems, which is an important metric of system performance. The stochastic temporary laser-beam blockage, pointing errors, and atmospheric turbulence are simultaneously considered. The results illustrate that the link blockage causes a decreased ergodic capacity. We show that to maximize the ergodic capacity, there is an optimal value of the laser-beam radius at the waist, which largely depends on pointing errors; however, it is independent of the atmospheric turbulence and the probability of link blockage.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권7호
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• pp.2992-3009
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• 2016

The performance of D-MIMO systems is not only affected by multipath fading but also from shadowing fading, as well as path loss. In this paper, we investigate the ergodic capacity of D-MIMO systems operating in non-correlated K fading (Rayleigh/Gamma) channels. With the aid of majorization and Minkowski theory, we derive analytical closed-form expressions of the upper and lower bounds on the ergodic capacity for D-MIMO systems over non-correlated K fading channels, which are quite general and applicable for arbitrary signal-to-noise ratio (SNR) and the number of transceiver antennas. To intuitively reveal the impacts of system and fading parameters on the ergodic capacity, we deduce asymptotic approximations in the high and low SNR regimes. Finally, we pursue the massive MIMO systems analysis for the lower bound and derive closed-form expressions when the number of antennas at BS grows large, and when the number of antennas at transceivers becomes large with a fixed and finite ratio. It is demonstrated that the proposed expressions on the ergodic capacity accurately match with the theoretical analysis.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권10호
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• pp.4231-4245
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• 2020

Non-orthogonal multiple access (NOMA) is widely studied in both academia and industry due to its high spectral efficiency over orthogonal multiple access (OMA). To effectively improve spectrum efficiency, an amplify-and-forward (AF) cooperative NOMA system is proposed as well as a novel detection scheme is proposed, in which we first perform successive interference cancellation (SIC) twice at U1 for the two signals received from two time slots to remove interference from symbol 2, then two new signals apply max ratio combining (MRC). In addition, a closed-form upper bound approximation for the ergodic capacity of our proposed system is derived. Monte-Carlo simulations and numerical analysis illustrate that our proposed system has better ergodic capacity performance than the conventional cooperative NOMA system with decode-forward (DF) relay, the conventional cooperative NOMA system with AF relay and the proposed AF cooperative NOMA system in [16]. In addition, we can see that ergodic capacity of all NOMA cooperative systems increase with the increase of transmit SNR. Finally, simulations display that power allocation coefficients have little effect on ergodic capacity of all NOMA cooperative systems. This is due to this fact that ergodic capacity of two symbols can be complementary with changing of power allocation coefficients.

• Journal of Information Processing Systems
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• 제17권2호
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• pp.306-317
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• 2021

The unbalance between system ergodic sum rate and high fairness is one of the key issues affecting the performance of non-orthogonal multiple access (NOMA) system. To solve the problem, this paper proposes a power allocation algorithm to realize the ergodic sum rate maximization of NOMA system. The scheme is mainly achieved by the construction algorithm of fair model based on α fair utility function and the optimal solution algorithm based on the interior point method of penalty function. Aiming at the construction of fair model, the fair target is added to the traditional power allocation model to set the reasonable target function. Simultaneously, the problem of ergodic sum rate and fairness in power allocation is weighed by adjusting the value of α. Aiming at the optimal solution algorithm, the interior point method of penalty function is used to transform the fair objective function with unequal constraints into the unconstrained problem in the feasible domain. Then the optimal solution of the original constrained optimization problem is gradually approximated within the feasible domain. The simulation results show that, compared with NOMA and time division multiple address (TDMA) schemes, the proposed method has larger ergodic sum rate and lower Fairness Index (FI) values.