• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.31-35
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• 2022

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.133-144
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• 2020

In this paper, we discuss generalized q-poly-Euler numbers and polynomials. To do so, we define generalized q-poly-Euler polynomials with variable a and investigate its identities. We also represent generalized q-poly-Euler polynomials E^(k)_n,q(x; a) using Stirling numbers of the second kind. So we explore the relation between generalized q-poly-Euler polynomials and Stirling numbers of the second kind through it. At the end, we provide symmetric properties related to generalized q-poly-Euler polynomials using alternating power sum.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.3887-3907
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• 2015

This paper introduces a full duplex single secondary user multiple-input multiple-output (FD-SSU-MIMO) cognitive radio network, where secondary user (SU) opportunistically accesses the authorized spectrum unoccupied by primary user (PU) and transmits data based on FD-MIMO mode. Then we study the network achievable average sum-rate maximization problem under sum transmit power budget constraint at SU communication nodes. In order to solve the trade-off problem between SU's sensing time and data transmission time based on opportunistic spectrum access (OSA) and the power allocation problem based on FD-MIMO transmit mode, we propose a simple trisection algorithm to obtain the optimal sensing time and apply an alternating optimization (AO) algorithm to tackle the FD-MIMO based network achievable sum-rate maximization problem. Simulation results show that our proposed sensing time optimization and AO-based optimal power allocation strategies obtain a higher achievable average sum-rate than sequential convex approximations for matrix-variable programming (SCAMP)-based power allocation for the FD transmission mode, as well as equal power allocation for the half duplex (HD) transmission mode.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.591-600
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• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.6
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• pp.1379-1397
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• 2013

We consider a system where a licensed radio spectrum is shared by multiple primary users(PUs) and secondary users(SUs). As the spectrum of interest is licensed to primary network, power and channel allocation must be carried out within the cognitive radio network so that no excessive interference is caused to PUs. For this system, we study the joint beamforming and power allocation problem via game theory in this paper. The problem is formulated as a non-cooperative beamforming and power allocation game, subject to the interference constraints of PUs as well as the peak transmission power constraints of SUs. We design a joint beamforming and power allocation algorithm for maximizing the total throughput of SUs, which is implemented by alternating iteration of minimum mean square error based decision feedback beamforming and a best response based iterative power allocation algorithm. Simulation results show that the algorithm has better performance than an existing algorithm and can converge to a locally optimal sum utility.

• Journal of Platform Technology
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• v.11 no.1
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• pp.3-10
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• 2023

Unmanned Aerial Vehicles (UAVs) have gained significant attention in 5G and 6G wireless networks due to their high flexibility and low hardware costs. However, UAV communication is still challenged by blockage and energy consumption issues. Reconfigurable Intelligent Surfaces (RISs) have emerged as a promising solution to these challenges, enabling improved spectral efficiency and reduced energy consumption by transmitting signals to users who cannot receive signals because of the obstacles. Many previous studies have focused on minimizing power consumption and data transmission delay through phase shift and power optimization. This paper proposes an algorithm that maximizes the sum rate by including bandwidth optimization. Simulation results demonstrate the effectiveness of the proposed algorithm.

• Korean System Dynamics Review
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• v.2 no.2
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• pp.25-40
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• 2001

This paper describes the forecast of power plant construction in a competitive korean electricity market. In Korea, KEPCO (Korea Electric Power Corporation, fully controlled by government) was responsible for from the production of the electricity to the sale of electricity to customer. However, the generation part is separated from KEPCO and six generation companies were established for whole sale competition from April 1st, 2001. The generation companies consist of five fossil power companies and one nuclear power company in Korea at present time. Fossil power companies are scheduled to be sold to private companies including foreign investors. Nuclear power company is owned and controlled by government. The competition in generation market will start from 2003. ISO (Independence System Operator will purchase the electricity from the power exchange market. The market price is determined by the SMP(System Marginal Price) which is decided by the balance between demand and supply of electricity in power exchange market. Under this uncertain circumstance, the energy policy planners such as government are interested to the construction of the power plant in the future. These interests are accelerated due to the recent shortage of electricity supply in California. In the competitive market, investors are no longer interested in the investment for the capital intensive, long lead time generating technologies such as nuclear and coal plants. Large unclear and coal plants were no longer the top choices. Instead, investors in the competitive market are interested in smaller, more efficient, cheaper, cleaner technologies such as CCGT(Combined Cycle Gas Turbine). Electricity is treated as commodity in the competitive market. The investors behavior in the commodity market shows that the new investment decision is made when the market price exceeds the sum of capital cost and variable cost of the new facility and the existing facility utilization depends on the marginal cost of the facility. This investors behavior can be applied to the new investments for the power plant. Under these postulations, there is the potential for power plant construction to appear in waves causing alternating periods of over and under supply of electricity like commodity production or real estate production. A computer model was developed to sturdy the possibility that construction will appear in waves of boom and bust in Korean electricity market. This model was constructed using System Dynamics method pioneered by Forrester(MIT, 1961) and explained in recent text by Sternman (Business Dynamics, MIT, 2000) and the recent work by Andrew Ford(Energy Policy, 1999). This model was designed based on the Energy Policy results(Ford, 1999) with parameters for loads and resources in Korea. This Korea Market Model was developed and tested in a small scale project to demonstrate the usefulness of the System Dynamics approach. Korea electricity market is isolated and not allowed to import electricity from outsides. In this model, the base load such as unclear and large coal power plant are assumed to be user specified investment and only CCGT is selected for new investment by investors in the market. This model may be used to learn if government investment in new unclear plants could compensate for the unstable actions of private developers. This model can be used to test the policy focused on the role of unclear investments over time. This model also can be used to test whether the future power plant construction can meet the government targets for the mix of generating resources and to test whether to maintain stable price in the spot market.

• Journal of The Korean Astronomical Society
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• v.46 no.3
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• pp.125-131
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• 2013

We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; ${\beta}_0$ is the number of connected regions, ${\beta}_1$ is the number of circular holes (i.e., complement of solid tori), and ${\beta}_2$ is the number of three-dimensional voids (i.e., complement of three-dimensional excursion regions). Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. ${\beta}_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). ${\beta}_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-density surfaces, and ${\beta}_2$ corresponds to the low-threshold part measuring the void abundance. We average the Betti number curves (the Betti numbers as a function of the threshold level) over many realizations of Gaussian fields and find that both the amplitude and shape of the Betti number curves depend on the slope of the power spectrum n in such a way that their shape becomes broader and their amplitude drops less steeply than the genus as n decreases. This behaviour contrasts with the fact that the shape of the genus curve is fixed for all Gaussian fields regardless of the power spectrum. Even though the Gaussian Betti number curves should be calculated for each given power spectrum, we propose to use the Betti numbers for better specification of the topology of large scale structures in the universe.