• The Pure and Applied Mathematics
• /
• v.10 no.1
• /
• pp.49-56
• /
• 2003

For (equation omitted) be an ordered $\ell$(t)-tuple of numbers in｛1,2, …,$\ell$｝and let Tt be chosen from a finite composition of orthogonal projections (equation omitted) acting on the normed linear space $C_1$(X) to closed convex subset $S(fi_{j}\;^{t})$ respectively. In this paper, we study the convergence of the sequence (equation omitted) where (equation omitted).

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.39-47
• /
• 2010

Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.415-425
• /
• 1995

• Kyungpook Mathematical Journal
• /
• v.34 no.2
• /
• pp.137-143
• /
• 1994

• East Asian mathematical journal
• /
• v.33 no.3
• /
• pp.271-289
• /
• 2017

It is our purpose in this paper to introduce the concept of best random proximity pair for subsets A and B of a separable Banach space E. We prove some best random approximation and best random proximity pair theorems of certain classes of random operators, which is the stochastic verse of the deterministic results of Eldred et al. [22], Eldred et al. [18] and Eldred and Veeramani [19]. Furthermore, our results generalize and extend recent results of Okeke and Abbas [42] and Okeke and Kim [43]. Moreover, we shall apply our results to study nonlinear stochastic integral equations of the Hammerstein type.

• Journal of KIISE:Computer Systems and Theory
• /
• v.31 no.10
• /
• pp.562-574
• /
• 2004

We address the problem of energy-optimal voltage scheduling for fixed-priority hard real-time systems. First, we prove that the problem is NP-hard. Then, we present a fully polynomial time approximation scheme (FPTAS) for the problem. for any $\varepsilon$>0, the proposed approximation scheme computes a voltage schedule whose energy consumption is at most (1+$\varepsilon$) times that of the optimal voltage schedule. Furthermore, the running time of the proposed approximation scheme is bounded by a polynomial function of the number of input jobs and 1/$\varepsilon$. Experimental results show that the approximation scheme finds more efficient voltage schedules faster than the best existing heuristic.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1882-1887
• /
• 2003

The response surface method (RSM) became one of famous meta modeling techniques, however its approximation errors give designers several restrictions. Classical RSM uses the least squares method (LSM) to find the best fitting approximation models from the all given data. This paper discusses how to construct RSM efficiently and accurately using moving least squares method (MLSM) with sensitivity information. In this method, several parameters should be determined during the construction of RSM. Parametric study and optimization for these parameters are performed. Several difficulties during approximation processes are described and numerical examples are demonstrated to verify the efficiency of this method.

• Geomechanics and Engineering
• /
• v.13 no.5
• /
• pp.845-860
• /
• 2017

It is very important to study displacement prediction in geotechnical engineering. Nowadays, the grey system method, time series analysis method and artificial neural network method are three main methods. Based on the brief introduction, the three methods are analyzed comprehensively. Their merits and demerits, applied ranges are revealed. To solve the shortcomings of the artificial neural network method, a new prediction method based on new evolutionary neural network is proposed. Finally, through two real engineering applications, the analysis of three main methods and the new evolutionary neural network method all have been verified. The results show that, the grey system method is a kind of exponential approximation to displacement sequence, and time series analysis is linear autoregression approximation, while artificial neural network is nonlinear autoregression approximation. Thus, the grey system method can suitably analyze the sequence, which has the exponential law, the time series method can suitably analyze the random sequence and the neural network method almostly can be applied in any sequences. Moreover, the prediction results of new evolutionary neural network method is the best, and its approximation sequence and the generalization prediction sequence are all coincided with the real displacement sequence well. Thus, the new evolutionary neural network method is an acceptable method to predict the measurement displacements of geotechnical engineering.

• Journal of Korea Society of Industrial Information Systems
• /
• v.27 no.2
• /
• pp.61-69
• /
• 2022

A multi-agent system is a system that aims at achieving the best-coordinated decision based on each agent's local decision. In this paper, we consider a multi agent-multi task assignment problem. Each agent is assigned to only one task and there is a completion probability for performing. The objective is to determine an assignment that maximizes the sum of the completion probabilities for all tasks. The problem, expressed as a non-linear objective function and combinatorial optimization, is NP-hard. It is necessary to design an effective and efficient solution methodology. This paper presents an approximation algorithm using submodularity, which means a marginal gain diminishing, and demonstrates the scalability and robustness of the algorithm in theoretical and experimental ways.

• Structural Engineering and Mechanics
• /
• v.69 no.6
• /
• pp.615-626
• /
• 2019

The 3-noded metric Timoshenko beam element with an offset of the internal node from the element centre is used here to demonstrate the best-fit paradigm using function space formulation under locking and mesh distortion. The best-fit paradigm follows from the projection theorem describing finite element analysis which shows that the stresses computed by the displacement finite element procedure are the best approximation of the true stresses at an element level as well as global level. In this paper, closed form best-fit solutions are arrived for the 3-noded Timoshenko beam element through function space formulation by combining field consistency requirements and distortion effects for the element modelled in metric Cartesian coordinates. It is demonstrated through projection theorems how lock-free best-fit solutions are arrived even under mesh distortion by using a consistent definition for the shear strain field. It is shown how the field consistency enforced finite element solution differ from the best-fit solution by an extraneous response resulting from an additional spurious force vector. However, it can be observed that when the extraneous forces vanish fortuitously, the field consistent solution coincides with the best-fit strain solution.