• Journal of the Korean Mathematical Society
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• v.7 no.2
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• pp.49-53
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• 1970

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.127-135
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• 2015

We determine two-interval normalized tight frame wavelet sets for real dilation $d{\in}(1,{\infty})$, and characterize all symmetric normalized tight frame wavelet sets. We also construct a normalized tight frame wavelet set which has an infinite number of components accumulating at the origin. These normalized tight frame wavelet sets and their closures possess the same measure. Finally an example of a normalized tight frame wavelet set is provided whose measure is strictly less than the measure of its closure.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.279-287
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• 1995

Let $F$ be a set of distributions on R with the topology of weak convergence, and let $A$ be the $\sigma$-field generated by the open sets. We denote by $F_1^\infty$ the space consisting of all infinite sequence $(F_1, F_2, \cdots), F_n \in F and R_1^\infty$ the space consisting of all infinite sequences $(x_1, x_2, \cdots)$ of real numbers. Take the $\sigma$-field $F_1^\infty$ to be the smallest $\sigma$-field of subsets of $F_1^\infty$ containing all finite-dimensional rectangles and take $B_1^\infty$ to be the Borel $\sigma$-field $R_1^\infty$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.66-75
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• 1999

This paper is concerned with a analysis of noise by inverse problem available for analyzing the two and three-dimensional acoustic field problems. The noise of analysis considered in this study can be reduced to an optimum problem to find the optimal set of parameters defining the vibrating state of noise source surfaces. The optimal set of parameters are searched by the standard optimization procedure minimizing the square sum of the residuals between the measured and computed quantities of sound pressure at some points in the acoustic field. Computation is carried out for typical examples in which the noise sources are located on the infinite plane. It is demonstrated that the noise of analysis can be effectively made by using the sensitive reference data.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1263-1275
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• 2010

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.4
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• pp.22-30
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• 2001

In this paper, active control of vibrational intensity at a reference point in an infinite, elastic plate was discussed. The plate is excised harmonically by a vibrating source, which has a vertical point force. The optimal condition of controller was investigated to minimize the vibrational intensity being transmitted from the vibrating source to a reference point. Hence the method of feedforward control was employed for the control strategy and then the cost function was evaluated to find the optimal control force. Three types of control force (Vertical force, Moment, and Coupling force (a set of vertical force and moment) ) and controller's positions were examined to define the optimal condition of the controller. The vibrational intensity at a reference point was found to be reduced down to a zero level, compared with the uncontrolled case. Especially maximum reduction of vibrational intensity was achieved when the controller was collinearly positioned between a vibrating source and a reference point.

• Bulletin of the Korean Chemical Society
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• v.28 no.9
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• pp.1477-1484
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• 2007

Artificial neural networks (ANNs), for a first time, were successfully developed for the prediction partial molar heat capacity of aqueous solutions at infinite dilution for various polar aromatic compounds over wide range of temperatures (303.55-623.20 K) and pressures (0.1-30.2 MPa). Two three-layered feed forward ANNs with back-propagation of error were generated using three (the heat capacity in T = 303.55 K and P = 0.1 MPa, temperature and pressure) and six parameters (four theoretical descriptors, temperature and pressure) as inputs and its output is partial molar heat capacity at infinite dilution. It was found that properly selected and trained neural networks could fairly represent dependence of the heat capacity on the molecular descriptors, temperature and pressure. Mean percentage deviations (MPD) for prediction set by the models are 4.755 and 4.642, respectively.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.31-52
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• 2008

The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.