• Journal of electromagnetic engineering and science
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• v.3 no.1
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• pp.57-61
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• 2003

The effects of high frequency noises on a perturbational inversion technique for a stratified dispersive medium are investigated in this paper. It is shown that the perturbational solution becomes unstable under high frequency noises. The physical origin of this instability is described. In order to enhance the robustness of the perturbational inverse scattering solution, a parametric inversion technique is introduced. The examples for the 2-pole and the 3-pole reflection coefficients are compared and contrasted, and improvement of the robustness of the solutions is shown.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.161-173
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• 2009

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.89-98
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• 1995

This paper presents the interesting properties of a certain patterned matrix that plays an significant role in the multi-way balanced designs. The necessary and sufficient condition on the existence of the inverse of the patterned matrix and its determinant are described. In special cases of the pattermed matrix, explicit formulas for its inverse, determinant and the characteristic equation are obtained.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.257-261
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• 2000

Northcott and Mckerrow proved that if R is a left noe-therian ring and E is an injective left R-module, then E[x-1] is an injective left R[x]-module. In this paper we generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an in-jective left R-module, then E[x-S] is an injective left R[xS]-module, where S is a submonoid of N (N is the set of all natural numbers).

• Bulletin of the Korean Chemical Society
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• v.32 no.9
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• pp.3355-3360
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• 2011

The nucleophilic substitution reactions of 1,2-phenylene phosphorochloridate (1) with substituted anilines ($XC_6H_4NH_2$) and deuterated anilines ($XC_6H_4ND_2$) are investigated kinetically in acetonitrile at $-15.0^{\circ}C$. The studied substrate of 1,2-phenylene phosphorochloridate is cyclic five-membered ring of phosphorus ester, and the anilinolysis rate of 1 is much faster than its acyclic analogue (4: ethyl phenyl chlorophosphate) because of extremely small magnitude of the entropy of activation of 1 compared to 4. The Hammett and Bronsted plots exhibit biphasic concave upwards for substituent X variations in the nucleophiles with a break point at X = 3-Me. The values of deuterium kinetic isotope effects (DKIEs; $k_H/k_D$) change from secondary inverse ($k_H/k_D$ < 1) with the strongly basic anilines to primary normal ($k_H/k_D$ > 1) with the weakly basic anilines. The secondary inverse with the strongly basic anilines and primary normal DKIEs with the weakly basic anilines are rationalized by the transition state (TS) variation from a predominant backside attack to a predominant frontside attack, in which the reaction mechanism is a concerted $S_N2$ pathway. The primary normal DKIEs are substantiated by a hydrogen bonded, four-center-type TS.

• Communications of the Korean Mathematical Society
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• v.2 no.1
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• pp.129-134
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• 1987

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• Journal of Environmental Science International
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• v.3 no.1
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• pp.49-56
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• 1994

Effect of the liquid circulation velocity on the biofilm development was investigated in an inverse fluidized bed biofilm reactor(IFBBR). To observe the effect of the influent COD concentration on biofilm simultaneously, the influent COD value was adjusted to 1000mg/1 f for 1st reactor, and 2500mg/l for 2nd reactor. The liquid circulation velocity was adjusted by controlling the initial liquid height. As the liquid circulation velocity was decreased, the settling amount of biomass was increased and the amount of effluent biomass was decreased. Since the friction of liquid was decreased by the decrease of liquid circulation velocity, the biofilm thickness was increased and the biofilm dry density was decreased. In the 1st reactor the SCOD removal efficiency was constant regardless of the variation of the liquid circulation velocity, but it was increased by the decrease of the liquid circulation velocity because of more biomass population in 2nd reactor.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.2
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• pp.195-201
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• 2001

An inverse heat conduction problem(IHCP) arises when unknown heat fluxes and whole temperature field are to be found with temperature measurements of a few points. In this paper, observers are proposed as solution algorithm for the IHCP. A 1-dimensional heat transfer problem is modeled with modal analysis and state space equations. Position of the heat source is estimated through test heat inputs and the autocorrelation among a few of temperature data. The modified Bass-Gura method is used to design a state observer to estimate the intensity of heat source and the whole temperature field of a 1-dimensional body. To verify the reliability of this estimator, analytic solutions obtained from the proposed method are compared.