• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.2
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• pp.9-14
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• 2022

This paper presents a subset sum problem (SSP) algorithm which takes the time complexity of O(nlogn). The SSP can be classified into either super-increasing sequence or random sequence depending on the element of Set S. Additive algorithm that runs in O(nlogn) has already been proposed to and utilized for the super-increasing sequence SSP, but exhaustive Brute-Force method with time complexity of O(n2ⁿ) remains as the only viable algorithm for the random sequence SSP, which is thus considered NP-complete. The proposed subtractive algorithm basically selects a subset S comprised of values lower than target value t, then sets the subset sum less the target value as the Residual r, only to remove from S the maximum value among those lower than t. When tested on various super-increasing and random sequence SSPs, the algorithm has obtained optimal solutions running less than the cardinality of S. It can therefore be used as a general algorithm for the SSP.

• Journal of Broadcast Engineering
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• v.20 no.1
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• pp.92-109
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• 2015

Broadcast encryption is a cryptographic primitive that allows a sender to securely broadcast a message to a set of receivers. The most influential broadcast encryption system was proposed in 2001 by Naor, Naor, Lotspiech, based on a pseudo-random generator and the Subset Difference (SD) method. In this paper, we suggest a new broadcast encryption system that is based on secret sharing and SD methods. On an efficiency aspect, our system achieves O(r) transmission cost, O($log^2n$) storage cost, and O(1) computational cost for the number n of users and the number r of revoked users. Compared to O(log n) computational cost in the previous SD method, our system has the advantage that it needs only constant-sized computational cost for decryption, regardless of the number n or r. On a security aspect, our system can achieve tighter security reduction than the previous SD method and the gap of security loss is about O(n log n). Moreover, our result shows that it is possible to give the effect of the SD method while using an information-theoretically secure key distribution technique as in the Complete Subtree method.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.23-30
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• 2003

In this note, we introduce the concept of the modulus of a curve family in $R^n$ and examine some basic properties. And we study the boundary behavior of quasiconformal mappings on a domain $D{\subset}\bar{R}^n$ and present some geometric applications.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.567-572
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• 2001

Wurful gave a characterization of those rings R which satisfy that for every ring extension $R{\subset}S$. Ho $m_{R}$(S, -) preserves injective envelopes. In this note, we consider an analogous problem concerning injective covers.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.97-112
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• 2023

In this paper, we introduce and study the u-S-weak global dimension u-S-w.gl.dim(R) of a commutative ring R for some multiplicative subset S of R. Moreover, the u-S-weak global dimensions of factor rings and polynomial rings are investigated.

• Bulletin of the Korean Chemical Society
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• v.29 no.8
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• pp.1499-1504
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• 2008

Pyrazine derivatives bind to b-RAF receptor which is important in cancer therapy. The ligand-receptor interactions have been studied by comparative molecular field analysis (CoMFA) and molecular docking methods. Applying conventional ligand-based alignment schemes for the whole set was not successful. However, QM and DFT results suggested that some ligands have electrostatic interaction while others have steric interactions. On the basis of these results, we divided the dataset into two subsets. Electrostatic effect was found to be important in one set while steric effect for the other. Best docking modes were obtained for each subset based on the available crystal structure. These receptor-guided CoMFA models propose an interesting possibility which is difficult to obtain otherwise. i.e., in one binding mode the electrostatic interaction plays a key role for one subset ($q^2$ = 0.46, $r^2$ = 0.98), while in another binding mode steric effect is important with another subset ($q^2$ = 0.43, $r^2$ = 0.74).

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.977-986
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• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.19-26
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• 2000

In this paper, it is shown that if R is a commutative ring with identity and there exists a multiplicatively closed subset S of R such that $S{\cap}Z(R/(I_1I_2{{\cdots}I_n))={\emptyset}$ and $I_1R_s,I_2R_s{\cdots},I_nR_s$ are pairwise comaximal, then $I_1I_2{\cdots}I_n=I_1{\cap}I_2{\cap}{\cdots}{\cap}I_n={\cap}^n_{i=1}(I_i\;:_R\;I_1{\cdots}I_{i-1}I_{i+1}{\cdots}I_n)$.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-345
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• 2022

Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B²) ⊆ (I : B³) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1523-1537
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.