• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• The Journal of the Acoustical Society of Korea
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• v.39 no.3
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• pp.200-206
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• 2020

In this paper, we propose a broadband beamforming method using the Spatial Response Variation (SRV) which is defined to measure the fluctuation of the array spatial response within the desired frequency band. By applying the SRV to regularization term, we achieve a good quality main beam width variation less than 1 degree within the desired frequency band. In design experiments, we show that the proposed method is better than the existing method.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.339-351
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• 1998

Designs for discriminating between two linear regression models are studied under $\Lambda$-type optimalities maximizing the measure for the lack of fit for the designs with fixed model inadequacy. The problem of selecting an appropriate $\Lambda$-type optimalities is shown to be closely related to the estimation method. $\Lambda$-type optimalities for the least squares and minimum bias estimation methods are considered. The minimum bias designs are suggested for the designs invariant with respect to the two estimation methods. First order minimum bias designs optimal under $\Lambda$-type optimalities are then derived. Finally for the case where the lack of fit test is significant, an approach to the construction of a second order design accommodating the optimal first order minimum bias design is illustrated.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.285-287
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• 1992

This paper considers the design of robust stabilizing controller of a linear time-invariant digital system subject to variations of parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability Margin of the closed-loop system. Based on this calculation a design procedure is proposed to robustify a given stabilizing controller. This algorithm iteratively enlarges the stability hypersphere in parameter space and can be used to design a controller to stabilize a plant subject to given ranges of parameter perturbations. These results are illustrated by an example.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.41-47
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• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.224-241
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• 2015

Multiview plus depth (MVD) videos are widely used in free-viewpoint TV systems. The best-known technique to determine depth information is based on stereo vision. In this paper, we propose a novel local stereo matching algorithm which is radiometric invariant. The key idea is to use a combined matching cost of intensity and gradient based similarity measure. In addition, we realize an adaptive cost aggregation scheme by constructing an adaptive support window for each pixel, which can solve the boundary and low texture problems. In the disparity refinement process, we propose a four-step post-processing technique to handle outliers and occlusions. Moreover, we conduct stereo reconstruction tests to verify the performance of the algorithm more intuitively. Experimental results show that the proposed method is effective and robust against local radiometric distortion. It has an average error of 5.93% on the Middlebury benchmark and is compatible to the state-of-art local methods.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1087-1099
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• 2004

We study the metrical and topological pressure for flows without fixed points on a compact metric space, and get the results as follows: (1) The metrical pressure with respect to an ergodic measure can be defined by (t, $\varepsilon$)-spanning sets. (2) The topological pressure is the supremum of metrical pressures with respect to all ergodic measures. (3) The properties that the topological pressure is zero, nonzero, finite or infinite respectively are invariant under weak equivalence.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1143-1158
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• 2006

We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space using an analytic continuation argument. In this paper we show this method can be further generalized to find the volume of a domain with smooth boundary with suitable regularity in dimension 2 and 3. We also discuss that this volume is invariant under the group of hyperbolic isometries and that this regularity condition is sharp.

• Journal of Information Processing Systems
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• v.12 no.3
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• pp.502-510
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• 2016

Considering video copy transform diversity, a multi-feature video copy detection algorithm based on a Speeded-Up Robust Features (SURF) local descriptor is proposed in this paper. Video copy coarse detection is done by an ordinal measure (OM) algorithm after the video is preprocessed. If the matching result is greater than the specified threshold, the video copy fine detection is done based on a SURF descriptor and a box filter is used to extract integral video. In order to improve video copy detection speed, the Hessian matrix trace of the SURF descriptor is used to pre-match, and dimension reduction is done to the traditional SURF feature vector for video matching. Our experimental results indicate that video copy detection precision and recall are greatly improved compared with traditional algorithms, and that our proposed multiple features algorithm has good robustness and discrimination accuracy, as it demonstrated that video detection speed was also improved.

• Journal of KSNVE
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• v.9 no.5
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• pp.943-948
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• 1999

This paper proposes a feasible and effective method for measuring the mechanical-acoustic transfer function by the application of equivalent area and velocity transfer function, a manifestation of the vibro-acoustical reciprocity principle. On the contrary to the volume velocity used in traditional method, the equivalent area is a peculiar raidation characteristics of sound sources and not influenced by any input signal for driving sound source. This invariant property of equivalent area can get rid of boresome works to measure the volume velocity of a sound source every time the driving signal is changed. Moreover, this method has a remarkable advantage to use a general loudspeaker as an accoustic exciter without the assumption of point source and can be applied to all kinds of sound sources even if they are not omni-directional sources.