• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.151-167
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• 2014

Let M, N be modules over a ring R and $[M,N]=Hom_R(M,N)$. The concern is study of: (1) Some fundamental properties of [M, N] when [M, N] is regular or semipotent. (2) The substructures of [M, N] such as radical, the singular and co-singular ideals, the total and others has raised new questions for research in this area. New results obtained include necessary and sufficient conditions for [M, N] to be regular or semipotent. New substructures of [M, N] are studied and its relationship with the Tot of [M, N]. In this paper we show that, the endomorphism ring of a module M is regular if and only if the module M is semi-injective (projective) and the kernel (image) of every endomorphism is a direct summand.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.891-906
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• 2020

In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 𝑙¹(S) into a reflexive module is inner.

• Smart Structures and Systems
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• v.23 no.4
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• pp.359-371
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• 2019

As part of a structural health monitoring system, the relative geometric relationship between a ship and bridge has been recognized as important for bridge authorities and ship owners to avoid ship-bridge collision. This study proposes a novel computer vision method for the real-time geometric parameter identification of moving ships based on a single shot multibox detector (SSD) by using transfer learning techniques and monocular vision. The identification framework consists of ship detection (coarse scale) and geometric parameter calculation (fine scale) modules. For the ship detection, the SSD, which is a deep learning algorithm, was employed and fine-tuned by ship image samples downloaded from the Internet to obtain the rectangle regions of interest in the coarse scale. Subsequently, for the geometric parameter calculation, an accurate ship contour is created using morphological operations within the saturation channel in hue, saturation, and value color space. Furthermore, a local coordinate system was constructed using projective geometry transformation to calculate the geometric parameters of ships, such as width, length, height, localization, and velocity. The application of the proposed method to in situ video images, obtained from cameras set on the girder of the Wuhan Yangtze River Bridge above the shipping channel, confirmed the efficiency, accuracy, and effectiveness of the proposed method.