• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.29-40
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• 2001

In this note, we get the conditions such that strong continuity ${\Rightarrow}$ weak continuity plus interiority condition( wc+ic), and continuity ${\Rightarrow}$ wc+ic are true. And we investigate some equivalent conditions with weak continuity, some properties of weak continuity. And we show that almost compactness is preserved by weakly continuous function, and we improve some known results with respect to strong continuity.

• East Asian mathematical journal
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• v.17 no.1
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• pp.1-17
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• 2001

In this paper, fuzzy D-continuous function is defined. Some basic properties of this continuity are summarized; and sufficient conditions on domain and/or ranges implying fuzzy D-continuity of fuzzy D-continuous functions are given. Also fuzzy D-regular space is defined and by using fuzzy D-continuity, the condition which is equivalent to fuzzy D-regular space, is given.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.347-365
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• 1996

Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.557-562
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• 2006

We consider the relationship between absolute continuity for functions of a real variable and absolute continuity of functions of generalized bounded variation. Here, we obtain necessary and sufficient conditions between these two functions.

• Structural Engineering and Mechanics
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• v.3 no.2
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• pp.121-133
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• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.1-8
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• 2006

In this paper, we obtain some unique common fixed point theorems for four self-maps and pair of maps in D-metric space using orbitally lower semi continuity conditions.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.117-123
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• 2012

We provide a convergence analysis of Newton's method for set valued maps under center H$\ddot{o}$lder continuity conditions on the Fr$\acute{e}$chet derivative of the operator involved. This approach extends the applicability of earlier works [4,5,7].

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1261-1270
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• 2011

In this note we give conditions for continuity of spectrum, approximative point spectrum and defect spectrum on the set $\{T\}+\mathcal{K}(X)$, where $T{\in}\mathcal{B}(X)$ and $\mathcal{K}(X)$ is the set of compact operators.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.71-78
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• 2018

This paper presents the assembling of multiple patches based on the single patch isogeometric formulation for the shear deformable shell element given in the previous study. The geometrically exact shell formulation has been accomplished with the shell theory based formulation and the generalized curvilinear coordinate system directly derived from the given NURBS geometry. For the knot elements matching across adjacent surfaces, the zero-th and first parametric continuity conditions are considered and the corresponding coupling constraints are implemented by a master-slave formulation between adjacent patches. The constraints are then enforced by a substitution method for condensation of the slave variables, thereby reducing the model size. Through numerical investigations, the important features of the first parametric continuity condition are confirmed. The performance of the multi-patch shell models is also examined comparing the rate of convergence of response coefficients for the zero and first order continuity conditions and continuity in coupling boundary between two patches is confirmed.