• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.303-323
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• 1994

In this paper, distribution of Votaw's $\lambda_1$(mvc) criterion has been obtained using inverse Mellin transform, residue theorem and properties of special functions.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.4
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• pp.57-66
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• 2004

This paper proposes the design of a 2,048-bit RSA based on RNS(residue number systems) Montgomery modular multiplier As the systems that RNS processes a fast parallel modular multiplication for a large word partitioned into small words, we introduce Montgomery reduction method(MRM)［1］based on Wallace tree modular multiplier and 33 RNS bases with 64-bit size for RNS Montgomery modular multiplication in this paper. Also, for fast RNS modular multiplication, a modified method based on Chinese remainder theorem(CRT)［2］ is presented. We have verified 2,048-bit RSA based on RNS using Samsung 0.35${\mu}{\textrm}{m}$ technology and the 2,048-bit RSA is performed in 2.54㎳ at 100MHz.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.1
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• pp.8-15
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• 1998

An analysis of the microstripline is started as an assumption of the axial & transveral current distribution. Applying the boundary conditions to the scalar wave equations of a electric & magnetic potential, the two simultaneous coupled integral equations are produced. The electronmagnetic fields in microstrip line can be obtained by solving these two coupled integral equaltion. In general, either a numerical analysis method or a Galerkin method was used to solve them. In this paper, a residue theorem is proposed to solve them. The electromagnetic fields are expressed as integral equations for LSE and LSM mode in the spectral domain. Applying a residue theorem to the Fourier transformed equation and Fourier inverse transformed equation which is necessary for interchanging the space domain and the spectral domain, the electromagnetic fields are expressed as algebraic equations whichare relatively easier to handle. the distributions of the electromagnetic field are shown at the range of -5w/2.leq.x.leq.5w/2, 0.lep.y.leq.4h for z=0. It agrees well with the results of the Quasi-TEM mode analysis.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1017-1031
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• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.387-397
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• 2018

In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy's residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.

• Journal of Korean Society of Disaster and Security
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• v.6 no.3
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• pp.1-8
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• 2013

Based on random vibration theory, a procedure for calculating the dynamic response of the tall building to time-dependent random excitation is developed. In this paper, the fluctuating along- wind load is assumed as time-dependent random process described by the time-independent random process with deterministic function during a short duration of time. By deterministic function A(t)=1-exp($-{\beta}t$), the absolute value square of oscillatory function is represented from author's studies. The time-dependent random response spectral density is represented by using the absolute value square of oscillatory function and equivalent wind load spectrum of Solari. Especially, dynamic mean square response of the tall building subjected to fluctuating wind loads was derived as analysis function by the Cauchy's Integral Formula and Residue Theorem. As analysis examples, there were compared the numerical integral analytic results with the analysis fun. results by dynamic properties of the tall uilding.

• ETRI Journal
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• v.38 no.2
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• pp.326-336
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• 2016

We propose and describe new error control algorithms for redundant residue number systems (RRNSs) and residue number system product codes. These algorithms employ search techniques for obtaining error values from within a set of values (that contains all possible error values). For a given RRNS, the error control algorithms have a computational complexity of $t{\cdot}O(log_2\;n+log_2\;{\bar{m}})$ comparison operations, where t denotes the error correcting capability, n denotes the number of moduli, and ${\bar{m}}$ denotes the geometric average of moduli. These algorithms avoid most modular operations. We describe a refinement to the proposed algorithms that further avoids the modular operation required in their respective first steps, with an increase of ${\lceil}log_2\;n{\rceil}$ to their computational complexity. The new algorithms provide significant computational advantages over existing methods.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.67-77
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• 2011

We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.81-85
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• 1983

It is the purpose of this paper to give some remarks on finite fields. We shall show that the little theorem of Fermat, Euler's criterion for quadratic residue mod p, and other few theorems in the number theory can be derived from the theorems in theory of finite field K=GF(p), where p is a prime. The forms of some irreducible ploynomials over K-GF(p) will be given explicitly.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.11
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• pp.22-27
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• 2011

In spectrum sensing, an energy detector compares the energy of a received signal with a predetermined detection threshold and decides whether a primary user is active or not in a licensed frequency band. Here the detection threshold is related to the noise power level in the band. Most previous works on energy detection have assumed that the noise power is exactly known a priori. However, this assumption does not hold in practice since there may be some uncertainty about the noise power. So it is necessary to investigate its effects on the performance of energy detection for spectrum sensing. In this paper, we analyze the effects using the residue theorem for contour integral and present the associated numerical results.