• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.703-723
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• 2019

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.5
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• pp.957-964
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• 2011

New time schemes based on the FEM were developed and their performances were tested with 2D wave equation. The least-squares and weighted residual methods are used to construct new time schemes based on traditional residual minimization method. To overcome some drawbacks that time schemes based on the least-squares and weighted residual methods have, ad-hoc method is considered to minimize residuals multiplied by others residuals as a new approach. And variational method is used to get necessary conditions of ad-hoc minimization. A-stability was chosen to check the stability of newly developed time schemes. Specific values of new time schemes are presented along with their numerical solutions which were compared with analytic solution.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.4
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• pp.432-446
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• 1996

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.04a
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• pp.245-248
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• 1997

The dielectric resonators(DRs) with dielectric properties are widely used in microwave integrated circuit(MICs) and monolithic microwave integrated circuits(MMICS). The variational method as numerical simulation scheme would be applied to calculate the resonant frequencies(fr) and Q-factors of microwave dielectric resonators. The dielectric resonator with a cylindrical “puck” structure of high dielectric material is modeled in this simulation. The parameters, such as the diameter, the height, and the dielectric constant of dielectric resonator, would determine the resonant frequency and the Q-factor. The relationship between these parameters would effect each other to evaluate the approximate resonant frequency. This simulation method by the variational formula is very effective to calculate fr, and Q-factor. in high frequency microwave dielectric resonator The error rate of the simulation results and the measured results would be considered to design the microwave dielectric resonators.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.569-586
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• 1996

A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic 8-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious zero energy modes and Poisson's ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.

• ETRI Journal
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• v.41 no.3
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• pp.298-307
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• 2019

This paper investigates the use of the inverse-free sparse Bayesian learning (SBL) approach for peak-to-average power ratio (PAPR) reduction in orthogonal frequency-division multiplexing (OFDM)-based multiuser massive multiple-input multiple-output (MIMO) systems. The Bayesian inference method employs a truncated Gaussian mixture prior for the sought-after low-PAPR signal. To learn the prior signal, associated hyperparameters and underlying statistical parameters, we use the variational expectation-maximization (EM) iterative algorithm. The matrix inversion involved in the expectation step (E-step) is averted by invoking a relaxed evidence lower bound (relaxed-ELBO). The resulting inverse-free SBL algorithm has a much lower complexity than the standard SBL algorithm. Numerical experiments confirm the substantial improvement over existing methods in terms of PAPR reduction for different MIMO configurations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.908-928
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• 2022

Multiple target tracking mainly focuses on tracking unknown number of targets in the complex environment of clutter and missed detection. The generalized labeled multi-Bernoulli (GLMB) filter has been shown to be an effective approach and attracted extensive attention. However, in the scenarios where the clutter rate is high or measurement-outliers often occur, the performance of the GLMB filter will significantly decline due to the Gaussian-based likelihood function is sensitive to clutter. To solve this problem, this paper presents a robust GLMB filter and smoother to improve the tracking performance in the scenarios with high clutter rate, low detection probability, and measurement-outliers. Firstly, a Student-T distribution variational Bayesian (TDVB) filtering technology is employed to update targets' states. Then, The likelihood weight in the tracking process is deduced again. Finally, a trajectory smoothing method is proposed to improve the integrative tracking performance. The proposed method are compared with recent multiple target tracking filters, and the simulation results show that the proposed method can effectively improve tracking accuracy in the scenarios with high clutter rate, low detection rate and measurement-outliers. Code is published on GitHub.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.3
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• pp.91-97
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• 2023

Recent research shows that latent directions can be used to image process towards certain attributes. However, controlling the generation process of generative model is very difficult. Though the latent directions are used to image process for certain attributes, many restrictions are required to enhance the attributes received the latent vectors according to certain text and prompts and other attributes largely unaffected. This study presents a generative model having certain restriction to the latent vectors for image generation and manipulation. The suggested method requires only few minutes per manipulation, and the simulation results through Tensorflow Variational Auto-encoder show the effectiveness of the suggested approach with extensive results.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.