• Korean Journal of Mathematics
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• v.24 no.2
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.121-126
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• 2001

In this paper, for n = 2m and odd prime p, new generalized bent functions from the finite field F$\_$p$^n$/ to the prime field F$\_$p/ are constructed from the partial spreads for F$\_$p$^n$/. Closed form expressions for the proposed generalized bent functions and their trace transform are derived in the form of the trace functions. The trace expressions for the bent functions and their trace transforms defined on F(equation omitted) constructed by using PS- are also derived.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.6
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• pp.1273-1278
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• 1997

Pseudonoise sequences of period 2$^{m}$ -1 with idel autocorrelation have been researched such as m-sequences, GMW sequences, Legendre sequences, and extended sequences. The m-sequences, the GMW sequences, the Legendre sequences, and the extended sequences are best described in terms of the trace function by previous works. Besides, there are Hall's sextic residue sequences and miscellaneous sequences with ideal autocorrelation, whose general constructions are not known so far. However, are are no explicit descripton of the Hall's sextic residue sequences and the miscellaneous sequences in terms of the trace function. In this paper, the Hall's sextic residue sequences and the miscellaneous sequences of period 2$^{m}$ -1 are expressed as a sum of trace functions. The miscellaneous sequences with ideal autocorrelation, which are newly found by computer search, are also expressed as a sum of trace functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.763-769
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• 2004

It is known that a bent function corresponds to a perfect nonlinear function, which makes it difficult to do the differential cryptanalysis in DES and in many other block ciphers. In this paper, for an odd prime p, quadratic p-ary bent functions defined on finite fields are given from the families of p-ary sequences with optimal correlation properly. And quadratic p-ary bent functions, that is, perfect nonlinear functions from the finite field F $_{p^{m}}$ to its prime field $F_{p}$ are constructed by using the trace functions. trace functions.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.17-25
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• 2006

In this paper, we study the right regular representation $R_\Gamma$ of a finite group G on the vector space consisting of vector valued functions on ${\Gamma}/G$ with a subgroup r of G and give a trace formula using the work of M. -F. Vigneras.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.6
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• pp.1095-1100
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• 2008

In a process of insect foot recognition, footprint segments as basic areas for recognition need to be extracted from scanned insect footprints and appropriate features should be found from the footprint segments in order to discriminate kinds of insects, because the characteristics of the features are important to classify insects. In this paper, we propose methods for automatic footprint segmentation and feature extraction. We use a Trace transform method in order to find out appropriate features from the extracted segments by the above methods. The Trace transform method builds a new type of data structure from the segmented images by functions using parallel trace lines and the new type of data structure has characteristics invariant to translation, rotation and reflection of images. This data structure is converted to Triple features by Diametric and Circus functions, and the Triple features are used for discriminating patterns of insect footprints. In this paper, we show that the Triple features found by the proposed methods are enough distinguishable and appropriate for classifying kinds of insects.

• Structural Engineering and Mechanics
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• v.54 no.5
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• pp.937-953
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• 2015

This paper investigates the load model for single footfall trace of human walking. A large amount of single person walking load tests were conducted using the three-dimensional gait analysis system. Based on the experimental data, Fourier series functions were adopted to model single footfall trace in three directions, i.e. along walking direction, direction perpendicular to the walking path and vertical direction. Function parameters such as trace duration time, number of Fourier series orders, dynamic load factors (DLFs) and phase angles were determined from the experimental records. Stochastic models were then suggested by treating walking rates, duration time and DLFs as independent random variables, whose probability density functions were obtained from experimental data. Simulation procedures using the stochastic models are presented with examples. The simulated single footfall traces are similar to the experimental records.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2006.07a
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• pp.573-573
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• 2006

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.11 no.sup1
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• pp.117-126
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• 2008

Trace elements compose a very small portion of the body, however they have a variety of essential functions. Various diseases are caused by trace element deficiencies, and sometimes they can be fatal. Long-term TPN is a risk factor of trace element deficiency, and trace elements need to be checked regularly while receiving TPN. It is important to provide sufficient requirements of trace elements regarding the clinical features and the problems of trace element excess or deficiency. Moreover extensive studies to establish the efficiency of examining human hair and nails, recent method to determine the trace elements, are required.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.