• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.971-997
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• 2018

The parity of cyclotomic numbers of order 2, 4 and 6 associated with 4-cyclotomic cosets modulo an odd prime p are obtained. Hence the explicit expressions of primitive idempotents of minimal cyclic codes of length $p^n$, $n{\geq}1$ over the quaternary field $F_4$ are obtained. These codes are observed to be subcodes of Q codes of length $p^n$. Some orthogonal properties of these subcodes are discussed. The minimal cyclic codes of length 17 and 43 are also discussed and it is observed that the minimal cyclic codes of length 17 are two weight codes. Further, it is shown that a Q code of prime length is always cyclotomic like a binary duadic code and it seems that there are infinitely many prime lengths for which cyclotomic Q codes of order 6 exist.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.495-502
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• 2017

Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$, then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1289-1301
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• 2019

In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.229-238
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• 2021

Let R be a ring with characteristic different from 2. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In the present paper, we show that if R is a prime ring satisfying certain identities involving a generalized derivation F associated with a derivation d, then R becomes commutative and in some cases d comes out to be zero (i.e., F becomes a left centralizer). We provide some counter examples to justify that the restrictions imposed in the hypotheses of our theorems are not superfluous.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.595-613
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• 2022

Let R be a commutative ring with identity and let I be a proper ideal of R. In this paper, we study the ideal based extended zero-divisor graph 𝚪'_I (R) and prove that 𝚪'_I (R) is connected with diameter at most two and if 𝚪'_I (R) contains a cycle, then girth is at most four girth at most four. Furthermore, we study affinity the connection between the ideal based extended zero-divisor graph 𝚪'_I (R) and the ideal-based zero-divisor graph 𝚪_I (R) associated with the ideal I of R. Among the other things, for a radical ideal of a ring R, we show that the ideal-based extended zero-divisor graph 𝚪'_I (R) is identical to the ideal-based zero-divisor graph 𝚪_I (R) if and only if R has exactly two minimal prime-ideals which contain I.

• Journal of Industrial Technology
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• v.36
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• pp.65-69
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• 2016

Deflection of the vertical is used in geodetic surveying associated with geoid network construction for geoid modeling and ellipsoid decision and obtained by gravity survey, astronomic survey etc. Technique of astronomic survey and gravity survey is very complex and requires a significant amount of time until gathering data. So this study is to determined a various method which evaluates deflection of the vertical and components about deflection of the vertical using GPS results and orthometric height value decided by leveling. Results of components about deflection of the vertical using GPS/leveling is that ${\xi}$ conponent is distributed $-2.11^{{\prime}{\prime}}{\pm}0.62$, ${\eta}$ component is distributed $1.75^{{\prime}{\prime}}{\pm}0.71$. Decision of component about deflection of the vertical using GPS is less complex than existing astronomic survey. Decision of component about deflection of vertical line using GPS is not complicated than astronomic surveying and can determine in a very short time. So it will be important means to determine the exact orthometric height, topographic study and diastrophism if can periodically calculate.

• Journal of Korean Society on Water Environment
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• v.25 no.5
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• pp.697-703
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• 2009

In this study, changes in the composition of dissolved organic carbon (DOC) were investigated using water samples collected at a downstream site of the Namhan River near the Lake Paldang ($N37^{\circ}24^{\prime}05.33^{{\prime}{\prime}}E127^{\circ}32^{\prime}25.01^{{\prime}{\prime}}$) during a heavy rain event from July 23 to July 28, 2008. The DOC concentrations varied from 1.68 to 3.18 mg/L with the maxium value at a peak of the river water level. Each DOC sample was fractionated into three compositions including hydrophilic (Hi), hydrophobic acid (HoA) and hydrophobic neutral (HoN) fractions. The results showed that HoA was most abundant fractions, constituting 47.2~56.5% of DOC. Refractory dissolved organic carbon (R-DOC) contents were also determined by measuring the DOC concentration after 28-day dark incubation of the samples. R-DOC content was in the range from 83 to 99% of DOC and it was significantly correlated with HoA contents (r = 0.91, p<0.005), while it did not exhibit such a good correlation with the fractions of Hi and HoN (p>0.02). Our results suggest that the HoA, which is associated with humic substances, may be a major composition of refractory organic matters in rivers during storm events.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.187-198
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• 2022

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer n. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic n-roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for n = 16, 18 support the results.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.61-68
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• 1996

We investigate associated prime ideals of the module of generalized fractions defined by poor essential sequences and extend the McAdam and Ratliff's criterion of locally unmixed rings.