• Journal of the Korean Society of Combustion
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• v.10 no.3
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• pp.25-33
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• 2005

Fast-time instability is investigated for diffusion flames with Lewis numbers greater than unity by employing the numerical technique called the Evans function method. Since the time and length scales are those of the inner reactive-diffusive layer, the problem is equivalent to the instability problem for the $Li\tilde{n}\acute{a}n#s$ diffusion flame regime. The instability is primarily oscillatory, as seen from complex solution branches and can emerge prior to reaching the upper turning point of the S-curve, known as the $Li\tilde{n}\acute{a}n#s$ extinction condition. Depending on the Lewis number, the instability characteristics is found to be somewhat different. Below the critical Lewis number, $L_C$, the instability possesses primarily a pulsating nature in that the two real solution branches, existing for small wave numbers, merges at a finite wave number, at which a pair of complex conjugate solution branches bifurcate. For Lewis numbers greater than $L_C$, the solution branch for small reactant leakage is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a traveling nature. As the reactant leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for L < $L_C$.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.733-748
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• 2017

We give Hodge structures on quasitoric orbifolds. We define orbifold Hodge numbers and show a correspondence of orbifold Hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend Hodge structures to a non almost complex setting.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.3
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• pp.150-158
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• 1998

This paper describes the classification of remotely sensed image data using fuzzy neural network, whose algorithm was obtained by replacing real numbers used for inputs and outputs in the standard back propagation algorithm with fuzzy numbers. In the proposed method, fuzzy patterns, generated based on the histogram ofeach category for the training data, are put into the fuzzy neural network with real numbers. The results show that the generalization and appoximation are better than that ofthe conventional network in determining the complex boundary of patterns.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.805-811
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• 2010

It is the aim of this paper to observe an interesting phenomenon of 'scattering' of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ for -1 < q < 0 in complex plane. Observe that the structure of the zeros of the Genocchi polynomials $G_n(x)$ resembles the structure of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ as q $\rightarrow$ -1.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.765-773
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• 2004

In this paper we define the notion of asymptotically quadrant independent random field and derive the strong laws of large numbers for this random field.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2543-2554
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• 1993

In this paper, the kinematic and dynamic analyses of spatial complex kinematic chain are studied. Through the new method both using the set of identification numbers and applying the DenavitHartenberg link representation method to the spatial complex kinematic chain, the kinematic configuration of the chain is represented. Some link in the part of closed chain being fictitiously cutted, the complex kinematic chain is transformed to the branched chain. The kinematic constraint equations are derived from the constraint conditions which the cutted sections of the link have to satisfy. And the joint variables being partitioned in the independent joint variables and the dependent joint variables, the dependent variables are calculated from the independent variables by using the Newton-Raphson iterative method and the pseudoinverse matrix. The equations of motion are derived under the independent joint variables by using the principle of virtual work. Algorithms for dynamic analysis are presented and simulations are done to verify accuracy and efficiency of the algorithms.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.399-412
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• 2001

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.

• Water for future
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• v.24 no.2
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• pp.97-108
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• 1991

A number of different curve numbers are estimated, and three of them are the basin or composite curve numbers (CN-II and CN-III) evaluated from hydrologic soil cover complex, the observed curve numbers computed from rainfal1-runoff observations and the basin median curve numbers as a median of the observed curve numbers. Based on the observed runoff, CM-II underestimates the effective rainfall meanwhile CN-III overestimates. Hence, for the improvement in estimating effective rainfall, a modulating curve number may be defined as a value in between CN-II and CN-III. Basin median curve numbers produces the closest result to the observed runoff and therefore it can be adopted as a representative curve number for gaged basin.

• The Mathematical Education
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• v.51 no.1
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• pp.1-19
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• 2012

In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.353-356
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• 2000

This paper proposes a 16-bit $\times$ 16-bit multiplier for 2 twos-complement binary numbers with complex structure and implements it on a FPGA.