• Honam Mathematical Journal
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• v.22 no.1
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• pp.77-82
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• 2000

After considering an equivalence relation on a directed preordered set, we construct an isomorphism between derived limits of inverse systems indexed by the directed (pre)ordered sets.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.2
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• pp.68-78
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• 2007

D-class is defined as a set of equivalent $n{\times}n$ boolean matrices according to a given equivalence relation. The D-class computation requires the multiplication of three boolean matrices for each of all possible triples of $n{\times}n$ boolean matrices. However, almost all the researches on boolean matrices focused on the efficient multiplication of only two boolean matrices and a few researches have recently been shown to deal with the multiplication of all boolean matrices. The paper suggests a mathematical theory that enables the efficient multiplication for all possible boolean matrix triples and the efficient computation of all D-classes, and discusses algorithms designed with the theory and their execution results.

• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

• Computational Structural Engineering
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• v.10 no.4
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• pp.131-142
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• 1997

In this paper the kinematics of damage for finite elastoplastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. Unlike the approach of strain equivalence or energy equivalence, which is applicable only to small strains, the proposed kinematic description provides a relation between the effective strain and the damage elastoplastic strain in finite deformation. This is accomplished by directly considering the kinematics of the deformation field both real configuration. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence at finite strains. The damage effect tensor in this work is explicitly characterized in terms of a kinematic measure of damage in the elastoplastic domain through a second-order damage tensor.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.857-864
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• 2004

The change in the NO emission indices (EINO) in a two-dimensional plane has been investigated, which is due to the interaction between a vortex and methane-air flames established at different equivalence ratios, by solving the field equation. After solving the field equation, the spatial distribution of G-values is obtained. The NO emission index is calculated after applying the appropriate relation between the G-values and the NO production rate or the mass fraction of methane obtained from the library of freely propagating flames created from detailed simulations. When a vortex exists in a reacting flow field, in general EINO slightly increases, whereas ElNO is lowered in the vicinity of the vortex regardless of flow direction. A change in vortex size has negligible impact on EINO$\_$T/ but increasing the vortex strength slightly increases EINO$\_$T/ in the domain of this study.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.7
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• pp.1022-1029
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• 1998

The relation of the inlet fuel distribution, velocity, and overall equivalence ratio to the stability of a lean burning no-swirl dump combustor was examined. Premixed or partially premixed natural gas was introduced into the air stream, which flowed to the dump region through an annular inlet pipe. Inlet air was preheated upto 400 deg.C. Combustion instability was observed to occur at higher value of equivalence ratio (> 0.6) as the degree of unpremixedness was increased. Instabilities exhibited a dominant frequency of ~ 500 Hz, which corresponded to a half wave mode of combustor. CH chemiluminescence and pressure fluctuations were in-phase when combustion instabilities occurred. Acetone LIF images revealed that there was a strong fuel concentration gradient across the inlet annulus. Phase resolved OH LIF images showed that inlet fuel distribution was affected by the combustion instabilities.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.203-209
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• 1988

In this paper, we define a g-regular semigroup which is a generalization of a regular semigroup. And we want to find some properties of g-regular semigroup. G-regular semigroups contains the variety of all regular semigroup and the variety of all periodic semigroup. If a is an element of a semigroup S, the smallest left ideal containing a is Sa.cup.{a}, which we may conveniently write as $S^{I}$a, and which we shall call the principal left ideal generated by a. An equivalence relation l on S is then defined by the rule alb if and only if a and b generate the same principal left ideal, i.e. if and only if $S^{I}$a= $S^{I}$b. Similarly, we can define the relation R. The equivalence relation D is R.L and the principal two sided ideal generated by an element a of S is $S^{1}$a $S^{1}$. We write aqb if $S^{1}$a $S^{1}$= $S^{1}$b $S^{1}$, i.e. if there exist x,y,u,v in $S^{1}$ for which xay=b, ubv=a. It is immediate that D.contnd.q. A semigroup S is called periodic if all its elements are of finite order. A finite semigroup is necessarily periodic semigroup. It is well known that in a periodic semigroup, D=q. An element a of a semigroup S is called regular if there exists x in S such that axa=a. The semigroup S is called regular if all its elements are regular. The following is the property of D-classes of regular semigroup.group.

• Journal of the Korean Society of Propulsion Engineers
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• v.18 no.1
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• pp.73-84
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• 2014

The present paper includes recent research works on the estimation of physical properties like equivalence ratio and heat release rate of flame through chemiluminescence measurement. Modern combustion devices require a precise control to increase combustion stability as well as to suppress pollutant emissions. The determination of combustion characteristics from chemiluminescence provides practical advantages over other techniques. However, the technique is dependent on equivalence ratio, combustion pressure, inlet temperature, turbulent intensity and fuel type. The intensity ratio of $OH^*$ and $CH^*$ has a strong relation with an equivalence ratio for methane/air premixed flames. The global measurement of chemiluminescence is accepted as a good indicator for a global heat release rate.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.6
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• pp.3370-3375
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• 2014

MILD combustion is a highly favored technology for solving the trade-off relation between high thermal efficiency and low pollutant emissions. The system has low NOx concentration in high temperature combustion by recirculating the combustion gas, as well as improving the thermal efficiency by making the internal temperature in a combustion furnace uniform. This study describes the combustion characteristics of a conical MILD combustor in a laboratory-scale furnace by adjusting the equivalence ratio with the fuel gas flow rate while maintaining a constant air flow rate of the furnace. The MILD regime in the furnace is well characterized and the in-furnace temperature and emissions were predicted, respectively, for the range of equivalence of 0.69 - 0.83. For the range of equivalence ratios, this study confirmed the existence of a stable flame region that has an approximately $300^{\circ}C$ temperature difference between the maximum flame temperature region and main reaction region.