• Proceedings of the KSRS Conference
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• v.2
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• pp.610-614
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• 2006

In this paper the advanced method of geodesic active contours was developed for the task of building detection from aerial and satellite images. Automatic extraction of man-made structures including buildings, building blocks or roads from remote sensing data is useful for land use mapping, scene understanding, robotic navigation, image retrieval, surveillance, emergency management procedures, cadastral etc. A level set method based on a region-driven segmentation model was implemented with which building boundaries were detected, through this curve propagation technique. The essence of this approach is to optimize the position and the geometric form of the curve by measuring information along that curve, and within the regions that compose the image partition. To this end, one can consider uniform intensities inside objects and the background. Thus, given an initial position of the curve, one can determine global, region-driven functions and provide a statistical description of the inside and outside object area. The calculus of variations and a gradient descent method was used to optimize the variational functional by an iterative steady state process. Experimental results demonstrate the potential of the proposed processing scheme.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• Steel and Composite Structures
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• v.39 no.5
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• Steel and Composite Structures
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• v.42 no.3
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• pp.375-388
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• 2022

In this work, limit elastic speed analysis of functionally graded porous rotating disks has been reported. The work proposes an effective approach for modeling the mechanical properties of a porous functionally graded rotating disk. Four different types of porosity models namely: uniform, symmetric, inner maximum, and outer maximum distribution are considered. The approach used is the variational principle, and the solution has been achieved using Galerkin's error minimization theory. The study aims to investigate the effect of grading indices, aspect ratio, porosity volume fraction, and porosity types on limit angular speed for uniform and variable disk geometries of constant mass. To validate the current study, finite element analysis has been used, and there is good agreement between the two methods. The study yielded a decrease in limit speed as grading indices and aspect ratio increase. The porosity volume fraction is found to be more significant than the aspect ratio effect. The research demonstrates a range of operable speeds for porous and non-porous disk profiles that can be used in industries as design data. The results show a significant increase in limit speed for an exponential disk when compared to other disk profiles, and thus, the study demonstrates a range of FG-based structures for applications in industries that will not only save material (lightweight structures) but also improve overall performance.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.827-838
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• 2023

Centrifugal pump is a key part of nuclear power plant systems, and its health status is critical to the safety and reliability of nuclear power plants. Therefore, fault diagnosis is required for centrifugal pump. Traditional fault diagnosis methods have difficulty extracting fault features from nonlinear and non-stationary signals, resulting in low diagnostic accuracy. In this paper, a new fault diagnosis method is proposed based on the improved particle swarm optimization (IPSO) algorithm-based variational modal decomposition (VMD) and relevance vector machine (RVM). Firstly, a simulation test bench for rotor faults is built, in which vibration displacement signals of the rotor are also collected by eddy current sensors. Then, the improved particle swarm algorithm is used to optimize the VMD to achieve adaptive decomposition of vibration displacement signals. Meanwhile, a screening criterion based on the minimum Kullback-Leibler (K-L) divergence value is established to extract the primary intrinsic modal function (IMF) component. Eventually, the factors are obtained from the primary IMF component to form a fault feature vector, and fault patterns are recognized using the RVM model. The results show that the extraction of the fault information and fault diagnosis classification have been improved, and the average accuracy could reach 97.87%.

• East Asian mathematical journal
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• v.27 no.1
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1269-1283
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• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.859-863
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• 2003

We report on the theoretical positron affinities of closed-shell atomic anions. The second-order many-body perturbation theory is applied taking the positron-electron interaction as a perturbation. The corrections for the complete basis set effects to the second order affinity are calculated based on the variational and nonvariational energy functionals of explicitly correlated geminals. It is shown that the explicitly correlated methods accelerate the convergence of the expansion significantly giving the account of the cusp behavior outside the orbital space.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.631-638
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• 1999

Sensitive testing has been widely employed for many years in connection with the development and evaluation explosives detonation devices and propellants. Perhaps its earliest and possibly most important implementation was in biological studies of dosage mortality and response to drugs. Recently sensitivity experiments has been employed in the evaluation of new materials subject to stress in various environments and in delineanation of unstable combustion regions in chemical propulsion systems. This paper discussed a sta-tistical development of sensitivity testing.