• 대한수학회보
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• 제61권2호
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• pp.557-584
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• 2024

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tⁿ ≃ (S¹)ⁿ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χ_y-genus of M.

• 대한수학회지
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• 제44권5호
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• pp.1079-1092
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• 2007

This paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space X to a compact $K\"{a}hler$ manifold Y. We will show that when the target has non-negative Kodaira dimension, all deformations of surjective holomorphic maps $X{\rightarrow}Y$ come from automorphisms of an unramified covering of Y and the underlying reduced varieties of associated components of Hol(X, Y) are complex tori. Under the additional assumption that Y is projective algebraic, this was proved in [7]. The proof in [7] uses the algebraicity in an essential way and cannot be generalized directly to the $K\"{a}hler$ setting. A new ingredient here is a careful study of the infinitesimal deformation of orbits of an action of a complex torus. This study, combined with the result for the algebraic case, gives the proof for the $K\"{a}hler$ setting.

• Wind and Structures
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• 제30권1호
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• pp.15-27
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• 2020

This paper reports the study on development and verification of numerical models and analyzes of flow at high speed around structural elements in the shape of a curved pipe (e.g., a fragment of a water slide). Possibility of engineering estimation of wind forces acting on an object in the shape of a helix is presented, using relationships concerning toroidal and cylindrical elements. Determination of useful engineering parameters (such as aerodynamic forces, pressure distribution, and air velocity field) is presented, impossible to obtain from the existing standard EN 1991-1-4 (the so-called wind standard). For this purpose, flow at high speed around a torus and helix, arranged both near planar surface and high above it, was analyzed. Analyzes begin with the flow around a cylinder. This is the simplest object with a circular cross-section and at the same time the most studied in the literature. Based on this model, more complex models are analyzed: first in the shape of half of a torus, next in the shape of a helix.