• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.305-320
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• 2024

We consider a mathematical model which describes the quasistatic contact of electro-viscoelastic rod with an obstacle. We use a modified Kelvin-Voigt viscoelastic constitutive law in which the elasticity operator is nonlinear and locally Lipschitz continuous, taking into account the piezoelectric effect of the material. We model the contact with a general damped response condition. We establish a local existence and uniqueness result of the solution by using arguments of time-dependent nonlinear equations and Schauder's fixed-point theorem and obtain a global existence for small enough data.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

• 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 the Korean Society of Industry Convergence
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• v.23 no.3
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• pp.463-471
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• 2020

Recently, various tries to apply ROV (Remotely Operated Vehicle) into underwater are being developed. However, due to underwater environment uniqueness, the additional problem must be taken into account when designing an ROV for the inspection of the underwater structure. This is because a GPS-based information method cannot be applied, and the obtainable image is also dependent on the turbidity. Also, it is necessary to be able to satisfy waterproof and operating speeds in consideration of most practical application environments. This paper describes the design results of the ROV system for underwater structure inspection considering the above problems. The designed system applied INS / DVL for location recognition and was configured to support 3D mapping and stereo camera-based image information using sonar depending on visibility. To satisfy the waterproof, a pressure vessel using a composite material was applied. And over-actuated system using eight thrusters to maintain a stable posture and operating speed was applied also. The designed system was verified by structural analysis and flow analysis also.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1003-1031
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• 2020

We consider the following Dirichlet initial boundary value problem with a gradient absorption and a nonlocal source $$\frac{{\partial}u}{{\partial}t}-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)={\lambda}u^k{\displaystyle\smashmargin{2}{\int\nolimits_{\Omega}}}u^sdx-{\mu}u^l{\mid}{\nabla}u{\mid}^q$$ in a bounded domain Ω ⊂ ℝ^N, where p > 1, the parameters k, s, l, q, λ > 0 and µ ≥ 0. Firstly, we establish local existence for weak solutions; the aim of this part is to prove a crucial priori estimate on |∇u|. Then, we give appropriate conditions in order to have existence and uniqueness or nonexistence of a global solution in time. Finally, depending on the choices of the initial data, ranges of the coefficients and exponents and measure of the domain, we show that the non-negative global weak solution, when it exists, must extinct after a finite time.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.12
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• pp.4967-4986
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• 2015

Multi-hop relaying communications have great potentials in improving transmission performance by deploying relay nodes. The benefit is critically dependent on the accuracy of the channel state information (CSI) of all the transmitting links. However, the CSI has to be estimated. In this paper, we investigate the channel estimation problem in one-way multi-hop MIMO amplify-and-forward (AF) relay system, where both the two-hop and three-hop communication link exist. Traditional point-to-point MIMO channel estimation methods will result in error propagation in estimating relay links, and separately tackling the channel estimation issue of each link will lose the gain as part of channel matrices involved in multiple communication links. In order to exploit all the available gains, we develop a novel channel estimation model by structuring different communication links using the PARAFAC and PARATUCK2 tensor analysis. Furthermore, a two-stage fitting algorithm is derived to estimate all the channel matrices involved in the communication process. In particular, essential uniqueness is further discussed. Simulation results demonstrate the advantage and effectiveness of the proposed channel estimator.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.7
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• pp.1217-1233
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• 2015

The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.

• The Journal of the Acoustical Society of Korea
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• v.27 no.8
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• pp.411-417
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• 2008

An alternative formulation of the Helmholtz integral equation derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface is used to solve acoustic radiation and fluid/structure interaction problems. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the surface pressure field is expressed explicitly as a surface integral of the surface velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use BEM to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• 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.