• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.989-1004
• /
• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.2
• /
• pp.393-418
• /
• 2024

In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.32 no.4
• /
• pp.241-247
• /
• 2019

A band gap refers to a certain frequency range where the propagation of mechanical waves is prohibited. This work focuses on engineering three-dimensional Kelvin lattices having external band gaps at low audible frequency ranges using a gradient-based design optimization method. Elastic wave propagation in an infinite periodic lattice is investigated by employing the Bloch theorem. We model the ligaments using a shear-deformable beam model obtained by consistent linearization in a geometrically exact beam theory. For a given lattice topology, we enlarge band gap sizes by controlling the configuration of the beam neutral axis and cross-section thickness that are smoothly parameterized by B-spline basis functions within the isogeometric analysis framework.

• Korean Journal of Logic
• /
• v.8 no.1
• /
• pp.23-46
• /
• 2005

The purpose of the paper Is to discuss and estimate early Popper's theory of probability, which is presented in his book, The Logic of of Scientific Discovery. For this, Von Mises' frequency theory shall be discussed in detail, which is regarded as the most systematic and sophisticated frequency theory among others. Von Mises developed his theory to response to various critical questions such as how finite and empirical collectives can be represented in terms of infinite and mathematical collectives, and how the axiom of randomness can be mathematically formulated. But his theory still has another difficulty, which is concerned with the inconsistency between the axiom of convergence and the axiom of randomness. Defending the objective theory of probability, Popper tries to present his own frequency theory, solving the difficulty. He suggests that the axiom of convergence be given up and that the axiom of randomness be modified to solve Von Mises' problem. That is, Popper introduces the notion of ordinal selection and neighborhood selection to modify the axiom of randomness. He then shows that Bernoulli's theorem is derived from the modified axiom. Consequently, it can be said that Popper solves the problem of inconsistency which is regarded as crucial to Von Mises' theory. However, Popper's suggestion has not drawn much attention. I think it is because his theory seems anti-intuitive in the sense that it gives up the axiom of convergence which is the basis of the frequency theory So for more persuasive frequency theory, it is necessary to formulate the axiom of randomness to be consistent with the axiom of convergence.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.7 no.2
• /
• pp.1-7
• /
• 2003

Mode superposition method(MSM) is the most commonly used for solving linear response problems of structural dynamics. The major advantage of MSM is that usually a small number of lower mode is sufficient to analysis the response. However, the convergence is slow and many modes would be needed to give an accurate MSM in large structure with many degrees of freedom. The inaccuracies of MSM are caused by mode truncation in the solution. These demerits can be overcome by use of the mode acceleration method(MAM). Example analyses are carried out in simple beam subjected to harmonic loadings and compared the convergence of the joint displacements by the two methods. For relatively low frequency loadings, a good results was obtained by the lowest one mode in MAM, so the method is more economic in numerical analysis on an accurate solution.

• Journal of the Korea Convergence Society
• /
• v.10 no.1
• /
• pp.205-214
• /
• 2019

In Korea, the first-price sealed bid auction and the constrained mean-price sealed bid auction(buchal-je in Korean) have been used alternatively as procurement auctions. In this paper, we characterize the constrained mean-price sealed bid auction in the context of mechanism design. We consider the general ?-bidder case in which each bidder has private information. Under the assumptions of uniformly distributed valuations and linear strategies, we derive the equilibrium of the constrained mean-price sealed bid auction. Furthermore, we analyze the efficiency and the expected revenue of this auction mechanism in comparison with the first-price sealed bid auction. Finally, we conclude with the critical remarks on the practical intention of the government which uses this auction.

• Convergence Security Journal
• /
• v.18 no.4
• /
• pp.27-33
• /
• 2018

Stream cipher is an one-time-pad type encryption algorithm that encrypt plaintext using simple operation such as XOR with random stream of bits (or characters) as symmetric key and its security depends on the randomness of used stream. Therefore we can design more secure stream cipher algorithm by using mathematical analysis of the stream such as period, linear complexity, non-linearity, correlation-immunity, etc. The key stream in stream cipher is generated in linear feedback shift register(LFSR) having characteristic polynomial. The primitive polynomial is the characteristic polynomial which has the best security property. It is used widely not only in stream cipher but also in SEED, a block cipher using 8-degree primitive polynomial, and in Chor-Rivest(CR) cipher, a public-key cryptosystem using 24-degree primitive polynomial. In this paper we present the concept and various properties of primitive polynomials in Galois field and prove the theorem finding the number of irreducible polynomials and primitive polynomials over $F_p$ when p is larger than 2. This kind of research can be the foundation of finding primitive polynomials of higher security and developing new cipher algorithms using them.

• Smart Structures and Systems
• /
• v.16 no.5
• /
• pp.781-806
• /
• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• Journal of Power Electronics
• /
• v.18 no.5
• /
• pp.1409-1423
• /
• 2018

Compared with classical linear controllers, a nonlinear controller can result in better control performance for the nonlinear uncertainties of continuously variable transmission (CVT) systems that are driven by a synchronous reluctance motor (SynRM). Improved control performance can be seen in the nonlinear uncertainties behavior of CVT systems by using the proposed mingled revised recurrent Hermite polynomial neural network (MRRHPNN) control with mend ant colony optimization (ACO). The MRRHPNN control with mend ACO can carry out the overlooker control system, reformed recurrent Hermite polynomial neural network (RRHPNN) control with an adaptive law, and reimbursed control with an appraised law. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the RRHPNN and the appraised law of the reimbursed control are established. Furthermore, to help improve convergence and to obtain better learning performance, the mend ACO is utilized for adjusting the two varied learning rates of the two parameters in the RRHPNN. Finally, comparative examples are illustrated by experimental results to confirm that the proposed control system can achieve better control performance.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.23 no.1
• /
• pp.46-50
• /
• 2013

This paper proposes an adaptive fault accommodation control approach for flexible-joint (FJ) robots with multiple actuator faults. It is assumed that the value and occurrence time of multiple actuator faults are unknown. An adaptive fault accommodation control scheme with prescribed performance bounds, which characterize the convergence rate and maximum overshoot of tracking errors, is designed to accommodate the actuator faults. From the Lyapunov stability theorem, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and tracking errors are preserved within prescribed performance bounds regardless of actuator faults.