• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.135-146
• /
• 2005

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.961-977
• /
• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Computational Structural Engineering
• /
• v.7 no.4
• /
• pp.85-101
• /
• 1994

A family of variational principles governing the dynamics of laminated plate has been derived using a variationally consistent shear deformable discrete laminated plate theory with particular reference to finite element procedures. The theoretical basis for the derivation is Sandhu's generalized procedure for the variational formulation of linear coupled boundary value problem. As the bilinear mapping to write the operator matrix of the field equations in self-adjoint form, convolution product was employed. Boundary conditions, initial conditions and probable internal discontinuity were explicitly included in the governing functionals. Some interesting extensions and specializations of the general variational principle were presented, which can provide many different finite element formulations for the problem.

• Korean Journal of Oriental Medicine
• /
• v.2 no.1
• /
• pp.337-380
• /
• 1996

'Nei Jing(內徑)' first defined the interrelationship of the true and tile false between evil factor affecting health(雅氣) and vital essence energy(精氣). According to 「'Nei Jing(內徑)', the above interrelationship is explained as 'If state of evil domination is considered as sthenia-syndrome(雅氣盛則實), if the consumption of healthy energy Is considered as asenia-syndrome(精氣尊則虛): 'Nei Jing(內徑)', proposed major features of the medicall treatment by 'regluate the vatal energy of asthenia and sthenia, treat the sthenia-syndrome by purgation, and treat the asenia-syndrome by therapy of invigoration(調其氣之虛實, 實則瀉之, 虛則補之): The above interrelationship was interpreted as 'treat the asthenia-syndrome of child organ by invigorating the mother organ(虛者補其母)'in the 69th of 'The Classic on Difficulty',(難經 六十九難). Go-Mu(高武) of Myung-dynasty describe therapy for invigoration and purgation of itself-meridian(自經 補瀉法), which locating acupuncture points according to the Therorr of Five Element in the five shu points of itself-meridian(自經 五유穴), based on the generation in the ${\ulcorner}$A Synthetical Book of Acupuncture and Moxibustion(針灸聚英)${\lrcorner}$, Sae-hyun Jang(張世賢) further extended location acupuncture points of the five shu points to the other-meridian in the ${\ulcorner}$Gyeo Jung Do Ju Nan Gyung(校正圖註難經)${\lrcorner}$ Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) was originated in 1644, the middle of the Yi-dynasty. It linked the reinforcing and reducing in acupuncture therapy which incorporated tlle asthenia-syndrome and sthenia-syndrome of the hollow organs, based on principle of the Yin Yang 5 Element Theory(陰陽五行學說), not only to the generation in the 5 element(相生關係) but also to the restriction in the 5 element(相剋關係). Furthermore it was devised for the medical treatment by comning therapy for invigoration and purgation of itself-meridian(自經 補瀉法) with that of the other-meridian. Even though many original forms(正形) of the therapy for invigoration and purgation of the Yin Yang 5 Element Theory comply with the principle of the generation and the restriction based on the principle of the Yin Yang 5 Element Theory are abailable, variational forms(變形) are also recognized by examining the nature of the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法), For this reason, it is very difficult to understand the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) thoroughly. therefore, those variational forms are obstacles for the beginners to study the Sa-Ahm's 5 Element Acupuncture Method. In order to understand the principle of the practical clinical application of the Sa-Ahm's 5 Element Acupuncture Method, this study investigated which principle was based on the variations of the locating acupuncture points' method for the acupuncture prescription.

• Korean Journal of Mathematics
• /
• v.24 no.1
• /
• pp.51-63
• /
• 2016

In this works, we consider a class of regularized equilibrium problems in Banach spaces. By using the auxiliary principle techniques to suggest some iterative schemes for regularized equilibrium problems and proved the convergence of these iterative methods required either pseudoaccretivity or partially relaxed strongly accretivity.

• Journal of Ocean Engineering and Technology
• /
• v.10 no.3
• /
• pp.96-104
• /
• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
• /
• v.3 no.2
• /
• pp.105-112
• /
• 1999

Density and temeprature fronts are common features of the ocean. However, frontal dynamics are not quasi-geostrophic because the isopycnal deflections associated with fronts are large compared with the scale height of the hydrostatic geopotential. The frontal geostrophic model, developed by Cushman-Roisin et al.(1992) is generally used fro describing the dynamics of surface-density ocean fronts, whereas the two-layer frontal geostrophic model is used for fronts on a sloping continental shelf. This paper investigates the baroclinic nonlinear stability of surface-density ocean fronts and fronts on a sloping continental shelf using the two-layer frontal geostrophic model mentioned above. Nonlinear stability criteria for the two kinds of fronts are obtained using Arnol'd's (1965; 1969) variational principle and a prior estimate method. This is the first time a nonlinear stability criterion for surface ocean fronts has been established, furthermore, the results obtained for fronts on a sloping bottom are superior to any previous ones.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.23 no.7 s.166
• /
• pp.1205-1214
• /
• 1999

A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.

• Interaction and multiscale mechanics
• /
• v.2 no.3
• /
• pp.223-233
• /
• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.163-171
• /
• 1996

For the effective analysis of two dimensional plane problems, Treffiz finite elements and cavity elements have been proposed. These element matrix equaitons were formulated on the basis of hybrid variational principle and Treffiz function sets derived consitstently from the complex theoy of plane elasticity. In order to suggest the accuracy chatacteristics of the proposed Treffiz elements typical plane problems were analyzed and these results were compared with ones obtained by using the conveintional displacement type elements. The accuracy of the proposed elements is less sensitive to the element size and shape than the conventional displacement type elements. These elements, being able to be formed with multi-nodes, give the convenient modeling of an analytic domain. The cavity elements give the comparatively exact values of stress concentration factors of stress intensity factors and can be effectively used for the analysis of mechanical stuctures containing various cavities.