• Journal of KIISE:Computer Systems and Theory
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• v.37 no.3
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• pp.138-146
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• 2010

It is well known that many biological networks are very robust against various types of perturbations, but we still do not know the mechanism of robustness. In this paper, we find that there exist a number of feedback loops in a real biological network compared to randomly generated networks. Moreover, we investigate how the topological property affects network robustness. To this end, we properly define the notion of robustness based on a Boolean network model. Through extensive simulations, we show that the Boolean networks create a nearly constant number of fixed-point attractors, while they create a smaller number of limit-cycle attractors as they contain a larger number of feedback loops. In addition, we elucidate that a considerably large basin of a fixed-point attractor is generated in the networks with a large number of feedback loops. All these results imply that the existence of a large number of feedback loops in biological networks can be a critical factor for their robust behaviors.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.99-110
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• 2019

In this paper, we prove some common fixed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized ${\phi}-weak$ contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al.. Also we provide an example for validity of our results.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11b
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• pp.181-184
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• 2001

Chemical Mechanical Polishing(CMP) of Shallow Trench Isolation(STD structure in 0.18 m semiconductor device fabrication is studied. CMP process is applied for the STI structure with and without reverse moat pattern and End Point Detection (EPD) method is tested. To optimize the transistor properties related metal 1 parameters. we studied the correlation between CMP thickness of STI using high selectivity slurry. DOE of gate etch recipe, and 1st metal DC values. Remaining thickness of STI CMP is proportional to the thickness of gate-etch process and this can affect to gate profile. As CMP thickness increased. the N-poly foot is deteriorated. and the P-Poly Noth is getting better. If CD (Critical Dimension) value is fixed at some point,, all IDSN/P values are in inverse proportional to CMP thickness by reason of so called Profile Effect. Weve found out this phenomenon in all around DOE conditions of Gate etch process and we also could understand that it would not have any correlation effects between VT and CMP thickness in the range of POE 120 sec conditions. As CMP thickness increased by $100\AA$. 3.2 $u\AA$ of IDSN is getting better in base 1 condition. In POE 50% condition. 1.7 $u\AA$ is improved. and 0.7 $u\AA$ is improved in step 2 condition. Wed like to set the control target of CD (critical dimension) in gate etch process which can affect Idsat, VT property versus STI topology decided by CMP thickness. We also would like to decide optimized thickness target of STI CMP throughout property comparison between conventional STI CMP with reverse moat process and newly introduced STI CMP using high selectivity slurry. And we studied the process conditions to reduce Gate Profile Skew of which source known as STI topology by evaluation of gate etch recipe versus STI CMP thickness.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11a
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• pp.181-184
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• 2001

Chemical Mechanical Polishing(CMP) of Shallow Trench Isolation(STI) structure in 0.18 m semiconductor device fabrication is studied. CMP process is applied for the STI structure with and without reverse moat pattern and End Point Detection (EPD) method is tested. To optimize the transistor properties related metal 1 parameters, we studied the correlation between CMP thickness of STI using high selectivity slurry, DOE of gate etch recipe, and 1st metal DC values. Remaining thickness of STI CMP is proportional to the thickness of gate-etch process and this can affect to gate profile. As CMP thickness increased, the N-poly foot is deteriorated, and the P-Poly Noth is getting better. If CD (Critical Dimension) value is fixed at some point, all IDSN/P values are in inverse proportional to CMP thickness by reason of so called Profile Effect. Weve found out this phenomenon in all around DOE conditions of Gate etch process and we also could understand that it would not have any correlation effects between VT and CMP thickness in the range of POE 120 sec conditions. As CMP thickness increased by 100 ${\AA}$, 3.2 u${\AA}$ of IDSN is getting better in base 1 condition. In POE 50% condition, 1.7 u${\AA}$ is improved, and 0.7 u${\AA}$ is improved in step 2 condition. Wed like to set the control target of CD (critical dimension) in gate etch process which can affect Idsat, VT property versus STI topology decided by CMP thickness. We also would like to decide optimized thickness target of STI CMP throughout property comparison between conventional STI CMP with reverse moat process and newly introduced STI CMP using high selectivity slurry. And we studied the process conditions to reduce Gate Profile Skew of which source known as STI topology by evaluation of gate etch recipe versus STI CMP thickness.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.251-263
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• 1993

The purpose of this paper is to study the solvability of the equation (E). In Section 2, we give preliminary definitions. In Section 3, we prove related two results (Theorem 1 and Corollary 1) concerning the closedness property of accretive operators in the class of spaces whose nonempty bounded closed convex subsets have the fixed point property for nonexpansive self-mapping. Using therem 1, we derive a result (Theorem 2) on the range of accetive operators in (.pi.)$_{1}$ spaces with a view to establishing a new result, which improves a result of Kartsatos [8] and Webb [15]. Further, we give an interesting consequence (Corollary 3) of Theorem 2. In section 4, we apply Corollary 1 to obtain two results (Theorem 3 and 4) for the range of sums of two accretive operators, which generalize two results of Reich [12].

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.99-113
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• 2011

In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.219-224
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• 2015

In this paper it is investigated as to when a nonempty invariant closed subset A of a $S^1$-space X containing the set of stationary points (S) can be the fixed point set of an equivariant continuous selfmap on X and such space X is said to possess the S-equivariant complete invariance property (S-ECIP). It is also shown that if X is a metric space and $S^1$ acts on $X{\times}S^1$ by the action $(x,p){\cdot}q=(x,p{\cdot}q)$, where p, $q{\in}S^1$ and $x{\in}X$, then the hyperspace $2^{X{\times}S^1}$ of all nonempty compact subsets of $X{\times}S^1$ has the S-ECIP.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.9
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• pp.130-138
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• 1997

In this study, to improve the ride and handling characteristics of the vehicle whose hard points have been already fixed, a tuning method of load spring, damper and stabilizer bar is described. For the suspension system of vehicle, optimized design is necessary to satisfy the incompatible two dynamic characteristics which are the ride isolation property between unsprung mass and sprung mass to reduce the excitation from the road and the accurate correring response property to specific steering inputs. To accomplish above aims, we may approach by experimental method, but it requires to sacrifice much time and cost. This paper, therefore, provides a process of suspension development to improve the ride and handling properties by using computer simulation with saving time and cost, and as results, comparaes the dynamic characteristics of the tuned vehicle with the base vehicle not tuned.

• Journal of the Korean Geosynthetics Society
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• v.3 no.2
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• pp.31-38
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• 2004

Long-term stability of two type geogrids were evaluated. Membrane drawn type geogrid showed the exponential type tensile property and textile type geogrid showed the rapid increase of tensile property closer toward the break point. Accelerated creep test was done for textile type geogrid but not done for membrane drawn type geogrid because of its thermal property. Creep strain for membrane drawn type geogrid was larger than the ultimate tensile strain by tensile test and reduction factor by creep deformation of textile type geogrid was smaller than that of membrane type geogrid.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.765-780
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• 2015

We consider the problem of characterizing the palindromic sequences ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$, $c_{d-1}{\neq}0$, having the property that for any $K{\in}\mathbb{N}$ there exists a number that is a palindrome simultaneously in K different bases, with ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$ being its digit sequence in one of those bases. Since each number is trivially a palindrome in all bases greater than itself, we impose the restriction that only palindromes with at least two digits are taken into account. We further consider a related problem, where we count only palindromes with a fixed number of digits (that is, d). The first problem turns out not to be very hard; we show that all the palindromic sequences have the required property, even with the additional point that we can actually restrict the counted palindromes to have at least d digits. The second one is quite tougher; we show that all the palindromic sequences of length d = 3 have the required property (and the same holds for d = 2, based on some earlier results), while for larger values of d we present some arguments showing that this tendency is quite likely to change.