• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.76-107
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• 2022

In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded mollification technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.141-154
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• 2022

Let R be a commutative ring with identity. Denote by w𝒫_w the class of weak w-projective R-modules and by w𝒫_w^⊥ the right orthogonal complement of w𝒫_w. It is shown that (w𝒫_w, w𝒫_w^⊥) is a hereditary and complete cotorsion theory, and so every R-module has a special weak w-projective precover. We also give some necessary and sufficient conditions for weak w-projective modules to be w-projective. Finally it is shown that when we discuss the existence of a weak w-projective cover of a module, it is enough to consider the w-envelope of the module.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• Journal of the Chungcheong Mathematical Society
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• v.2 no.1
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• pp.45-49
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• 1989

The main goal of the present paper is to characterize the $weak^*$-integral, which is a $weak^*$ analogy of Geitz[4].

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.167-187
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• 2006

We introduce the concepts of intuitionistic fuzzy submodules and intuitionistic fuzzy weak congruences on an R-module (Near-ring module). And we obtain the correspondence between intuitionistic fuzzy weak congruences and intuitionistic fuzzy submodules of an R-module. Also, we define intuitionistic fuzzy quotient R-module of an R-module over an intuitionistic fuzzy submodule and obtain the correspondence between intuitionistic fuzzy weak congruences on an R-module and intuitionistic fuzzy weak congruences on intuitionistic fuzzy quotient R-module over an intuitionistic fuzzy submodule of an R-module.

• Structural Engineering and Mechanics
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• v.89 no.3
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• pp.253-263
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• 2024

Slope stability is generally paid more attention to in slope protection works, especially for slope containing weak layers. Two indexes of safety factor and failure model are selected to perform slope stability. Moreover, the finite element limit analysis method comprehensively combines the advantage of the limit analysis method and the finite element method obtaining the upper and lower bounds of the safety factor and the failure mode under the slope stability limit state. In this study, taking a waste dump containing a weak layer as an engineering background, the finite element limit analysis method is adopted to explore the potential failure mode. Meanwhile, the sensitivity analysis of slope stability is performed on geometrical and geotechnical parameters of the waste dump. The results show that the failure mode of the waste dump slope is two wedges if the weak layer is located on the ground surface (Model A), while the slope can be observed as three wedges failure if the weak layer is below the ground surface (Model B). In addition, both failure modes are highly sensitive to the friction angle of the weak layer and the shear strength of waste disposal, and moderately sensitive to the heap height, the dip angle and cohesion of the weak layer, while the toe cutting has limited effect on the slope stability. Moreover, the sensitivity to the excavation of the ground depends on the location of the weak layer and failure mode.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.325-330
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• 2013

In this paper, we prove Trotter-Kato theorem in the weak topology if $X^*$ is a uniformly convex Banach space.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.899-912
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• 2002

In this paper, the boundedness of some commutators related to linear operators on weak Herz spaces are obtained.

• East Asian mathematical journal
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• v.26 no.3
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• pp.441-446
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• 2010

We characterize the main types of anti fuzzy ideals in weak BCC-algebras.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.54-54
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• 2014

We use dense redshift surveys of nine galaxy clusters at z ~ 0.2 to compare the galaxy distribution in each system with the projected matter distribution from weak lensing. By combining 2087 new MMT/Hectospec redshifts and the data in the literature, we construct spectroscopic samples within the region of weak-lensing maps of high (70-89%) and uniform completeness. With these dense redshift surveys, we construct galaxy number density maps using several galaxy subsamples. The shape of the main cluster concentration in the weak-lensing maps is similar to the global morphology of the number density maps based on cluster members alone, mainly dominated by red members. We cross correlate the galaxy number density maps with the weak-lensing maps. The cross correlation signal when we include foreground and background galaxies at 0.5zcl < z < 2 zcl is 10 - 23% larger than for cluster members alone at the cluster virial radius. The excess can be as high as 30% depending on the cluster. Cross correlating the galaxy number density and weak-lensing maps suggests that superimposed structures close to the cluster in redshift space contribute more significantly to the excess cross correlation signal than unrelated large-scale structure along the line of sight. Interestingly, the weak-lensing mass profiles are not well constrained for the clusters with the largest cross correlation signal excesses (>20% for A383, A689 and A750). The fractional excess in the cross correlation signal including foreground and background structures could be a useful proxy for assessing the reliability of weak-lensing cluster mass estimates.