• Korean Journal of Mathematics
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• 제20권3호
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.81-90
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• 2013

We investigate the bounded weak solutions for the Hamiltonian system with bounded nonlinearity decaying at the origin and periodic condition. We get a theorem which shows the existence of the bounded weak periodic solution for this system. We obtain this result by using variational method, critical point theory for indefinite functional.

• 충청수학회지
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• 제27권4호
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• pp.707-720
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• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• 호남수학학술지
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• 제30권3호
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• pp.443-468
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• 2008

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.399-410
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• 2019

In the manuscript, we concern with the existence of solutions of boundary value problems for fourth order nonlinear discrete systems. Some criteria for the existence of at least one nontrivial solution of the problem are obtained. The proof is mainly based upon the variational method and critical point theory. An example is presented to illustrate the main result.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.527-535
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집B
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• pp.404-409
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• 2000

Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder where the Taylor hypothesis does not hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV. For the analysis in a moving frame of reference, the convection velocity of the Karman vortices is evaluated from the trajectory of vortex center which is defined as the centroid of the vorticity field. Then, a saddle point is obtained by applying the critical point theory. Science the distributions of fluctuating Reynolds stresses defined by triple-decomposition are closely related with the existence of secondary vortices. the physical meaning of them is explained in conjunction with vortex center and saddle point trajectories. Finally, the temporal evolution of streamwise vortex is also discussed.

• Bulletin of the Korean Chemical Society
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• 제30권9호
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• pp.2001-2006
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• 2009

Temperature dependence of the critical micelle concentration (CMC), $x_{CMC}$, in micellization can be described by ln $x_{CMC}$ = A + BT + C lnT + D/T, which has been derived statistical-mechanically. Here A, B, C, and D are fitting parameters. The equation fits the CMC data better than conventionally used polynomial equations of temperature. Moreover, it yields the unique(exponent) value of 2 when the CMC is expressed in a power-law form. This finding is quite significant, because it may point to the universality of the thermal behavior of CMC. Hence, in this article, the nature of the equation ln $x_{CMC}$ = A + BT + C lnT + D/T is examined from a lattice-theory point of view through the Flory-Huggins model. It is found that a linear behavior of heat capacity change of micellization is responsible for the CMC equation of temperature.

• Monthly Notices of the Royal Astronomical Society
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• 제496권4호
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• pp.4787-4821
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• 2020

The merging rate of cosmic structures is computed, relying on the ansatz that they can be predicted in the initial linear density field from the coalescence of critical points with increasing smoothing scale, used here as a proxy for cosmic time. Beyond the mergers of peaks with saddle points (a proxy for halo mergers), we consider the coalescence and nucleation of all sets of critical points, including wall-saddle to filament-saddle and wall-saddle to minima (a proxy for filament and void mergers, respectively), as they impact the geometry of galactic infall, and in particular filament disconnection. Analytical predictions of the one-point statistics are validated against multiscale measurements in 2D and 3D realizations of Gaussian random fields (the corresponding code being available upon request) and compared qualitatively to cosmological N-body simulations at early times (z ≥ 10) and large scales (≥5 Mpc h^-1). The rate of filament coalescence is compared to the merger rate of haloes and the two-point clustering of these events is computed, along with their cross-correlations with critical points. These correlations are qualitatively consistent with the preservation of the connectivity of dark matter haloes, and the impact of the large-scale structures on assembly bias. The destruction rate of haloes and voids as a function of mass and redshift is quantified down to z = 0 for a Lambda cold dark matter cosmology. The one-point statistics in higher dimensions are also presented, together with consistency relations between critical point and critical event counts.