• ETRI Journal
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• v.43 no.3
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• pp.483-510
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• 2021

In computational biology, desired patterns are searched in large text databases, and an exact match is preferable. Classical benchmark algorithms obtain competent solutions for pattern matching in O (N) time, whereas quantum algorithm design is based on Grover's method, which completes the search in $O(\sqrt{N})$ time. This paper briefly explains existing quantum algorithms and defines their processing limitations. Our initial work overcomes existing algorithmic constraints by proposing the quantum-based combined exact (QBCE) algorithm for the pattern-matching problem to process exact patterns. Next, quantum random access memory (QRAM) processing is discussed, and based on it, we propose the QRAM processing-based exact (QPBE) pattern-matching algorithm. We show that to find all t occurrences of a pattern, the best case time complexities of the QBCE and QPBE algorithms are $O(\sqrt{t})$ and $O(\sqrt{N})$, and the exceptional worst case is bounded by O (t) and O (N). Thus, the proposed quantum algorithms achieve computational speedup. Our work is proved mathematically and validated with simulation, and complexity analysis demonstrates that our quantum algorithms are better than existing pattern-matching methods.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.513-528
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• 1997

A sort sequence $S_n$ is a sequence of all unordered pairs of indices in $I_n\;=\;{1,\;2,v...,\;n}$. With a sort sequence Sn we assicuate a sorting algorithm ($AS_n$) to sort input set $X\;=\;{x_1,\;x_2,\;...,\;x_n}$ as follows. An execution of the algorithm performs pairwise comparisons of elements in the input set X as defined by the sort sequence $S_n$, except that the comparisons whose outcomes can be inferred from the outcomes of the previous comparisons are not performed. Let $X(S_n)$ denote the acverage number of comparisons required by the algorithm $AS_n$ assuming all input orderings are equally likely. Let $X^{\ast}(n)\;and\;X^{\circ}(n)$ denote the minimum and maximum value respectively of $X(S_n)$ over all sort sequences $S_n$. Exact determination of $X^{\ast}(n),\;X^{\circ}(n)$ and associated extremal sort sequenes seems difficult. Here, we obtain bounds on $X^{\ast}(n)\;and\;X^{\circ}(n)$.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.15-23
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• 2003

In order to compute the Nielsen number N(f) of a self-map $f:X{\rightarrow}X$, some Reidemeister classes in the fundamental group ${\pi}_1(X)$ need to be distinguished. D. Ferrario has some algebraic results which allow distinguishing Reidemeister classes. In this paper we generalize these results to the Reidemeister sets of iterates.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.519-525
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• 1995

By using an exact sequence of extension groups corresponding to an isogeny of a Drinfeld module we investigate which extension classes are coming from Hom(G,C). In the last section of this paper an example was given where the connecting homomorphism can be explictly computed.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.527-539
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• 1995

We consider the Schur groups of some module categories, which are subcategories of category of divisorial modules over a Krull domain. Then we obtain the exact sequence connecting class group, Schur class group and Schur groups of these categories.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.79-84
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• 1999

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.87-96
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• 1998

Using the concept of cellular manufacturing systems(CMS) in job shop manufacturing system is one of the most innovative approaches to improving plant productivity. However. several constraints in machine duplication cost, machining capability, cell space capacity, intercell moves and exceptional elements(EEs) are main problems that prevent achieving the goal of maintaining an ideal CMS environment. Minimizing intercell part traffics and EEs are the main objective of the cell formation problem because it is a critical point that improving production efficiency. Because the intercell moves could be changed according to the sequence of operation, it should be considered in assigning parts and machines to machine ceil. This paper presents a method that eliminates EEs under the constraints of machine duplication cost and ceil space capacity attaining two goals of minimizing machine duplications and minimizing intercell moves simultaneously. Developing an algorithm that calculates the machine duplications by cell-machine incidence matrix and part-machine Incidence matrix, and calculates the exact intercell moves considering the sequence of operation. Based on the number of machine duplications and exact intercell moves, the goal programming model which satisfying minimum machine duplications and minimum intercell moves is developed. A linear programming model is suggested that could calculates more effectively without damaging optimal solution. A numerical example is provided to illustrate these methods.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.263-266
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• 1998

Several constraints in machine duplication cost, machining capability, cell space capacity, intercell moves and exceptional elements(EEs) are main problems that prevent achieving the goal of ideal Cellular Manufacturin System (CMS) environment. Minimizing intercell part traffics and EEs are the main objective of the cell formation problem as it's a critical point that improving production efficiency. Because the intercell moves could be changed according to the sequence of operation, it should be considered in assigning parts and machines to machine cells. This paper presents a method that eliminates EEs under the constraints of machine duplication cost and cell space capacity attaining two goals of minimizing machine duplications and minimizing intercell moves simultaneously. Developing an algorithm that calculates the machine duplications by cell-machine incidence matrix and part-machine incidence matrix, and calculates the exact intercell moves considering the sequence of operation. Based on the number of machine duplications and exact intercell moves, the goal programming model which satisfying minimum machine duplications and minimum intercell moves is developed. A linear programming model is suggested that could calculates more effectively without damaging optimal solution. A numerical example is provided to illustrate these methods.