• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.10a
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• pp.918-919
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• 2012

This paper present a method of function decomposition and input variable manipulation method based on modular design techniques. We obtain the column multiplicity of decomposition function according to row decomposition method. Also, the proposed partial decomposition function have advantage which is able to omit control function using t-Gate. We find the advantage for internal connection decrement 12% and T-gate number 16%, therefore we find the simple design circuit.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.57-65
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• 1998

In this paper, we consider properties of Dedekind eta-function, modular discrimiant, thata-series and Weierstrass ${\wp}$-function. We prove the integrablities of ${\Delta}({\tau})$ and ${\eta}({\tau})$. Also, we give explicit formulae about ${\Delta}({\tau})$ and ${\tau}(n)$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.115-118
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• 2000

In order to approximate a nonlinear function, modular wavelet networks combining wavelet theory and modular concept based on single layer neural network have been proposed as an alternative to conventional wavelet neural networks and kind of modular network. Modular wavelet networks provide better approximating performance than conventional one. In this paper, we propose an effective method to construct an optimal modualr wavelet network using genetic algorithm. This is verified through experimental results.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.847-864
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• 2013

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.277-295
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• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.183-200
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• 2017

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.987-1028
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• 2014

In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.247-250
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• 2001

In this paper, we propose an growing and pruning algorithm to design the adaptive structure of modular wavelet neural network(MWNN) with F-projection and geometric growing criterion. Geometric growing criterion consists of estimated error criterion considering local error and angle criterion which attempts to assign wavelet function that is nearly orthogonal to all other existing wavelet functions. These criteria provide a methodology that a network designer can constructs wavelet neural network according to one's intention. The proposed growing algorithm grows the module and the size of modules. Also, the pruning algorithm eliminates unnecessary node of module or module from constructed MWNN to overcome the problem due to localized characteristic of wavelet neural network which is used to modules of MWNN. We apply the proposed constructing algorithm of the adaptive structure of MWNN to approximation problems of 1-D function and 2-D function, and evaluate the effectiveness of the proposed algorithm.