• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.229-241
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• 2007

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• Journal of Korean Academy of Nursing
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• v.40 no.3
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• pp.411-422
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• 2010

Purpose: In the present study, an analysis of the life of adolescents with complex congenital heart disease (CHD) was done using grounded theory. Consideration was given to the socio-cultural context of Korea. Methods: After approval from the institutional review board of Y hospital, 12 patients ranging in age from 14 to 35 were recruited. Data were gathered using in-depth interviews. Theoretical sampling was performed until the concepts were saturated. Results: The results confirmed the life of adolescents with complex CHD as a 'journey to finding uniqueness of oneself as a person with CHD'. The life consisted of 3 stages. In the crisis stage, participants had a feeling of threat to self-existence, and made an effort to be the same as others. In the self-recognition stage, participants who had sufficient role-performance built self-esteem while those who did not fell into self-accusation. In the self-establishment stage, participants who reached sufficiency in independence and knowledge planned the future, whereas those who did not conformed to the realities of life. Conclusion: The results of present study provide help in understanding the experiences of adolescents with CHD and provide a basis for developing nursing intervention strategies for these patients.

• ETRI Journal
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• v.36 no.1
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• pp.31-41
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• 2014

The heterogeneous network (HetNet) has been discussed in detail in the Long-Term Evolution (LTE) and LTE Advanced standards. However, the standardization of High-Speed Packet Access HetNet (HSPA HetNet) launched by 3GPP is pushing at full steam. Interference coordination (IC), which is responsible for dealing with the interference in the system, remains a subject worthy of investigation in regard to HSPA HetNet. In this paper, considering the network framework of HSPA HetNet, we propose a quasi-distributed IC (QDIC) scheme to lower the interference level in the co-channel HSPA HetNet. Our QDIC scheme is constructed as slightly different energy-efficient non-cooperative games in the downlink (DL) and uplink (UL) scenarios, respectively. The existence and uniqueness of the equilibrium for these games are first revealed. Then, we derive the closed-form best responses of these games. A feasible implementation is finally developed to achieve our QDIC scheme in the practical DL and UL. Simulation results show the notable benefits of our scheme, which can indeed control the interference level and enhance the system performance.

• Journal of Communications and Networks
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• v.16 no.2
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• pp.121-129
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• 2014

The trend of an increasing demand for a high-quality user experience, coupled with a shortage of radio resources, has necessitated more advanced wireless techniques to cooperatively achieve the required quality-of-experience enhancement. In this study, we investigate the critical problem of rate splitting in heterogeneous cellular networks, where concurrent transmission, for instance, the coordinated multipoint transmission and reception of LTE-A systems, shows promise for improvement of network-wide capacity and the user experience. Unlike most current studies, which only deal with spectral efficiency enhancement, we implement an optimal rate splitting strategy to improve both spectral efficiency and energy efficiency by exploring and exploiting cooperation diversity. First, we introduce the motivation for our proposed algorithm, and then employ the typical cooperative bargaining game to formulate the problem. Next, we derive the best response function by analyzing the dual problem of the defined primal problem. The existence and uniqueness of the proposed cooperative bargaining equilibrium are proved, and more importantly, a distributed algorithm is designed to approach the optimal unique solution under mild conditions. Finally, numerical results show a performance improvement for our proposed distributed cooperative rate splitting algorithm.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.197-214
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• 2021

In this paper, we have studied dynamics of fractional order mathematical model of malaria transmission for two groups of human population say semi-immune and non-immune along with growing stages of mosquito vector. The present fractional order mathematical model is the extension of integer order mathematical model proposed by Ousmane Koutou et al. For this study, Atangana-Baleanu fractional order derivative in Caputo sense has been implemented. In the view of memory effect of fractional derivative, this model has been found more realistic than integer order model of malaria and helps to understand dynamical behaviour of malaria epidemic in depth. We have analysed the proposed model for two precisely defined set of parameters and initial value conditions. The uniqueness and existence of present model has been proved by Lipschitz conditions and fixed point theorem. Generalised Euler method is used to analyse numerical results. It is observed that this model is more dynamic as we have considered all classes of human population and mosquito vector to analyse the dynamics of malaria.

• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.219-232
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• 2002

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.107-116
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• 2005

A suspension bridge is an example of a nonlinear dynamical system, especially systems with the so called jumping nonlinearity. The fact that we deal with a serious and topical problem is demonstrated for example by the collapse of the Tacoma Narrow suspension bridge. So it would be very contributive to determine under what conditions a similar situation cannot occur and find out safe parameters of the bridge construction. In this paper, we show various possibilities how to model the behaviour of suspension bridge. Then we introduce our own results concerning existence and uniqueness of time-periodic solutions.

• Journal of Distribution Science
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• v.16 no.8
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• pp.79-89
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• 2018

Purpose - This research aims to investigate the factors that influence consumer's overseas online shopping behavior. Consumers adopt overseas online shopping as a new buying way and more and more consumers prefer overseas online shopping than traditional shopping ways. Consumers' behaviors in this shopping experience can be different from other shopping experiences. With the increase of overseas online shopping, we need to find antecedents and results of overseas online shopping. Especially there would be positive or negative factors which influence overseas online shopping motivation. To find the relationship, this study examines self-efficacy and impulsivity as major factors which influence overseas online shopping. We also suggest that several attitude factors increase self-efficacy and it is positively related to customer satisfaction. On the other hand, we assume that overseas online shopping factors influence impulsivity of buying and it will decrease customer satisfaction. Research design, data, and methodology - This empirical study data were collected from Korean people who experience overseas online shopping. The subjects for this study were confined to shoppers who used overseas online shopping within the past six months. A total of 267 responses were gathered. SPSS 23.0, PLS 2.0 software were used in the data analysis. Descriptive statistics were used to show sample characteristics. We examined reliability, validity test for constructs. All measurement items used seven-point scales(1= very strong disagree, 7 = very strongly agree) drawn from previously published papers. Partial Least Square method was applied to find the relationship between antecedent factors and dependent factors and hypotheses were estimated. Results - Results show that perceived superiority, perceived ease of use, perceived transaction safety, perceived behavioral control positively affect self-efficacy. Self-efficacy influences positively to consumer's post purchase satisfaction. Perceived monetary benefit and perceived uniqueness motivated impulse buying. This can make consumer's post purchase dissatisfaction. Conclusions - This paper attempted to confirm the existence of both the positive and negative faces of overseas online shopping. The result reveals that self-efficacy is a major factor which may increase satisfaction in the overseas online shopping. Usually, we can think monetary benefit and uniqueness of products motivate overseas online shopping. But it can also intrigue impulse buying and negatively affect customer relationship. Therefore companies should provide enough products information to their potential customers and they might apply adequate processes such as recommendation, comparing systems to build long term relationship with their customers.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.9
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• pp.4188-4206
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• 2016

Power control is widely used to reduce co-channel interference in wireless networks and guarantee the signal-to-interference plus noise ratio (SINR) of ongoing connections. This technique is also effective for wireless body area networks (WBANs). Although achieving satisfactory SINR is important for WBAN users, they may not be willing to achieve it at arbitrarily high power levels since power is a scarce resource in WBANs. Besides, for WBANs with different purposes, the QoS requirements and concern about the power consumption may be different. This motivates us to formulate the power control problem using the concepts from microeconomics and game theory. In this paper, the QoS objective is viewed as a utility function, which represents the degree of user satisfaction, while the power consumption is viewed as a cost function. The power control problem consequently becomes a non-cooperative multiplayer game, in which each player tries to maximize its net utility, i.e., the utility minus the cost. Within this framework, we investigate the Nash equilibrium existence and uniqueness in the game and derive the best response solution to reach the Nash equilibrium. To obtain the optimal transmission power in a distributed way, we further propose a utility-based and QoS-aware power control algorithm (UQoS-PCA). Tunable cost coefficient in UQoS-PCA enables this scheme to be flexible to satisfy diverse service requirements. Simulation results show the convergence and effectiveness of the proposed scheme as well as improvements over existing algorithm.