• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.143-153
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• 2021

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1069-1091
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• 2022

We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.671-683
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• 2022

The aim of this paper is to deal with the realization problem of a given Lagrangian submanifold of a symplectic manifold as the fixed point set of an anti-symplectic involution. To be more precise, let (X, ω, µ) be a toric Hamiltonian T-space, and let ∆ = µ(X) denote the moment polytope. Let τ be an anti-symplectic involution of X such that τ maps the fibers of µ to (possibly different) fibers of µ, and let p₀ be a point in the interior of ∆. If the toric fiber µ^-1(p₀) is real Lagrangian with respect to τ, then we show that p₀ should be the origin and, furthermore, ∆ should be centrally symmetric.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.491-502
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• 2023

As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.511-517
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• 2024

Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In [7], Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane M_m in such a way that if M_m satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of M_m with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when M_m satisfies certain conditions, then M is homeomorphic to ℝⁿ.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.11
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• pp.775-784
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• 2017

The purpose of this study was to analyse the basic data of the engine tuning inspection by confirming the working possibility of effective engine tuning and identifying the characteristics of tuned engine that are no problem with the safety operation and environment in a driving gasoline car. The effects of tuned engine on the characteristics of air/fuel ratio and performance at a wide range of engine speeds were experimentally investigated by the actual driving car with a four-cycle, four-cylinder DOHC, turbo-intercooler, water-cooled gasoline engine operating under four types of non-tuning, and tuning 2-1, 2-2 and 2-3. The tuned parts of engine in a driving gasoline car include the intake manifold, intake pipe, air filter, exhaust manifold, exhaust pipe and silencer. In this experiment, the air-fuel ratio and torque of both non-tuned and tuned engines that one person took on board in the car with a five-speed automatic transmission were measured by the chassis dynamometer(Dynojet 224xLC). It was found that the maximum torque of tuned engine in a driving gasoline car was increased by 103.68% on average, while the maximum output was increased by 119.68% on average in comparison to the non-tuned engine.

• The KIPS Transactions:PartB
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• v.15B no.3
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• pp.205-210
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• 2008

A new approach is proposed for restoration of corrupted regions and segmentation in natural text images. The challenge is to fill in the corrupted regions on the basis of color feature analysis by second order symmetric stick tensor. It is show how feature analysis can benefit from analyzing features using tensor voting with chromatic and achromatic components. The proposed method is applied to text images corrupted by manifold types of various noises. Firstly, we decompose an image into chromatic and achromatic components to analyze images. Secondly, selected feature vectors are analyzed by second-order symmetric stick tensor. And tensors are redefined by voting information with neighbor voters, while restore the corrupted regions. Lastly, mode estimation and segmentation are performed by adaptive mean shift and separated clustering method respectively. This approach is automatically done, thereby allowing to easily fill-in corrupted regions containing completely different structures and surrounding backgrounds. Applications of proposed method include the restoration of damaged text images; removal of superimposed noises or streaks. We so can see that proposed approach is efficient and robust in terms of restoring and segmenting text images corrupted.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.1
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• pp.116-127
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• 1994

A method using the linear matrix algebra is developed in order to determine unknown external forces in linear structural analyses. The method defines a matrix which represents the linearity of the vibrational analysis for a structural system. The unknown external forces are determined by the operations of the matrix. The method is applied to find an engine motion in an automobile system. For a simulation process, an exhaust system is modeled and analyzed by the finite element method. The validity of the simulation is verified by comparing with the experimental results the free vibration. Also, an experiment on the forced vibration is performed to determine the damping ratio of the exhaust sysetm. Estimated model parameters(natural frequency, mode shape) are in accord with the experimental results. Because the method merely repeats the transpose and inverse operations of a matrix, the solution is extremely easy and simple. Moreover, it is more accurate than the existing methods in that there is no artificial assumptions in the calculation processes. Therefore, the method is found to be reliable for the analysis of the exhaust system considering the characteristics of vibrations. Although the suggested method is tested by only the exhaust system here, it can be applied to general structures.