• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.419-429
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• 2022

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)R_P = PR_P for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.223-228
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• 1997

In this paper, we present a closed-form expression of binary sequences of longer period with ideal autocorrelation property in a trace representation, if a given binary sequence with ideal autocorrelation property is described using the trace function. We also enumerate the number of cyclically distinct binary sequences of a longer period with ideal autocorrelation property, which are extended from a given binary sequence with ideal autocorrelation property.

• 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.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.373-411
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• 2023

Gompf proposed a conjecture on Cappell-Shaneson matrices whose affirmative answer implies that all Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We study Gompf conjecture on Cappell-Shaneson matrices using various algebraic number theoretic techniques. We find a hidden symmetry between trace n Cappell-Shaneson matrices and trace 5 - n Cappell-Shaneson matrices which was suggested by Gompf experimentally. Using this symmetry, we prove that Gompf conjecture for the trace n case is equivalent to the trace 5 - n case. We confirm Gompf conjecture for the special cases that -64 ≤ trace ≤ 69 and corresponding Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We also give a new infinite family of Cappell-Shaneson spheres which are diffeomorphic to the standard 4-sphere.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.5
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• pp.1165-1172
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• 1998

In this paper, we present a construction for binary pseudorandom sequences of period $2^{m}-1$ with ideal autocorraltion property using the polynomial $z^{d}+(z+1)^{d}$. We show that the sequence obtained from the polynomial becomes an m-sequence for certain values of d. We also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is $3k{\pm}1$, where k is a positive integer. These new sequences are represented using trace function and the results are tabulated.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.789-794
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• 2007

Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• Journal of the Korean Chemical Society
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• v.61 no.4
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• pp.139-142
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• 2017

Ethene ($C_2H_4$), which is produced in plants as they mature, was used to study its photoacoustic properties using photoacoustic spectroscopy. Detection of trace amounts, with $N_2$ gas, of $C_2H_4$ gas was also applied. The gas was tested in various conditions-temperature, concentration of the gas, gas cell length, and power of the laser- to determine their effect on the photoacoustic signal, the ideal conditions to detect trace gas amounts, and concentration of $C_2H_4$ produced by an avocado and a banana. A detection limit of 10 ppm was determined for pure $C_2H_4$. A detection of 5% and 13% (by volume) concentration of $C_2H_4$ was produced for a ripening avocado and banana, respectively, in closed space.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.819-826
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• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• Korean Institute of Interior Design Journal
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• no.11
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• pp.57-63
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• 1997

In the early 20'c, scientific thoughts make a change the absolute and separate concept of space-time into relative concept of continual entity; a kind of ideal world. It suggests that the meaning of geometry as absolute truth with which has endowed human beings would changed to a relative meaning of accumulation in intellectual work on 'nature'. This cognitive changes appeared into absolute arts in 20'c like Cubism, Superematism or Constructivism. De Stijl movement which had recepted the relative concepts like Einstein's 'theory of relativity' as a developed thought from Newton-Cartesian cognition on the world. Abstration would be adequate method for expressing the dynamics and interrelationship between forms and for giving values to indivisual elements in a compositiov. This method had appeared Modern architectural form, as a common framework. The expression characteristics of geometrical design in Deconstructive and Experimental architecture were summerized in four features through the results of the analysis. First, the relation of architectural element and intertextuality is expressed in discontinuation of context and refusal of functional building. Second, the concept of trace expresses as connection of place, decomposing of excavation of trace, trace of axis, trace of fragments. Third, anti-gravity expression is there to express of open cubic, to outgrow of rectangular system, to outgrow of volume, to separate of ground connectiov. Fourth, the complex composition of abstracted geometric form is these to abstracted geometry about indefinite shape, to layer through the overlap and collage, to de-meaning and amusement of form through the pursuit of uncertainty, to indeterminate of formal meaning through operation and composition of similar form cause to the diverse of meaning.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1113-1121
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• 2018

Let R be a prime ring (or semiprime ring) with center Z(R), I a nonzero ideal of R, T an automorphism of $R,S:R^n{\rightarrow}R$ be a symmetric skew n-derivation associated with the automorphism T and ${\Delta}$ is the trace of S. In this paper, we shall prove that S($x_1,{\ldots},x_n$) = 0 for all $x_1,{\ldots},x_n{\in}R$ if any one of the following holds: i) ${\Delta}(x)=0$, ii) [${\Delta}(x),T(x)]=0$ for all $x{\in}I$. Moreover, we prove that if $[{\Delta}(x),T(x)]{\in}Z(R)$ for all $x{\in}I$, then R is a commutative ring.