• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1057-1073
• /
• 2020

In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids M that are hereditarily atomic (i.e., every submonoid of M is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.83-116
• /
• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.

• Communications of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.279-302
• /
• 2024

In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.869-915
• /
• 2019

Let H be a Krull monoid with class group G such that every class contains a prime divisor. Then every nonunit $a{\in}H$ can be written as a finite product of irreducible elements. If $a=u_1{\cdot}\;{\ldots}\;{\cdot}u_k$ with irreducibles $u_1,{\ldots},u_k{\in}H$, then k is called the length of the factorization and the set L(a) of all possible k is the set of lengths of a. It is well-known that the system ${\mathcal{L}}(H)=\{{\mathcal{L}}(a){\mid}a{\in}H\}$ depends only on the class group G. We study the inverse question asking whether the system ${\mathcal{L}}(H)$ is characteristic for the class group. Let H' be a further Krull monoid with class group G' such that every class contains a prime divisor and suppose that ${\mathcal{L}}(H)={\mathcal{L}}(H^{\prime})$. We show that, if one of the groups G and G' is finite and has rank at most two, then G and G' are isomorphic (apart from two well-known exceptions).

• Journal of Radiation Protection and Research
• /
• v.47 no.1
• /
• pp.50-57
• /
• 2022

Background: There are several proton therapy facilities in operation or planned in Taiwan, and these facilities are anticipated to not only treat cancer but also provide beam services to the industry or academia. The simplified approach based on the Monte Carlo-based data sets (source terms and attenuation lengths) with the point-source line-of-sight approximation is friendly in the design stage of the proton therapy facilities because it is intuitive and easy to use. The purpose of this study is to expand the Monte Carlo-based data sets to allow the simplified approach to cover the application of proton beams more widely. Materials and Methods: In this work, the MCNP6 Monte Carlo code was used in three simulations to achieve the purpose, including the neutron yield calculation, Monte Carlo-based data sets generation, and dose assessment in simple cases to demonstrate the effectiveness of the generated data sets. Results and Discussion: The consistent comparison of the simplified approach and Monte Carlo simulation results show the effectiveness and advantage of applying the data set to a quick shielding design and conservative dose assessment for proton therapy facilities. Conclusion: This study has expanded the existing Monte Carlo-based data set to allow the simplified approach method to be used for dose assessment or shielding design for beam services in proton therapy facilities. It should be noted that the default model of the MCNP6 is no longer the Bertini model but the CEM (cascade-exciton model), therefore, the results of the simplified approach will be more conservative when it was used to do the double confirmation of the final shielding design.

• Journal of Communications and Networks
• /
• v.14 no.3
• /
• pp.230-236
• /
• 2012

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with themethod proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

• Journal of Microbiology and Biotechnology
• /
• v.16 no.5
• /
• pp.683-688
• /
• 2006

We have developed a program for generating shotgun data sets from known genome sequences. Generation of synthetic data sets by computer program is a useful alternative to real data to which students and researchers have limited access. Uniformly-distributed-sampling clones that were adopted by previous programs cannot account for the real situation where sampled reads tend to come from particular regions of the target genome. To reflect such situation, a probabilistic model for biased sampling distribution was developed by using an experimental data set derived from a microbial genome project. Among the experimental parameters tested (varied fragment or read lengths, chimerism, and sequencing error), the extent of sequencing error was the most critical factor that hampered sequence assembly. We propose that an optimum sequencing strategy employing different insert lengths and redundancy can be established by performing a variety of simulations.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.421-426
• /
• 2007

A parametric study to investigate the effects of composition variables on the glass transition and mechanical properties of CNT-based nanocomposites was performed using molecular dynamics simulations. In this study, matrix chain length and CNT length were chosen as the candidate characteristic parameters. In order to understand the effect of both parameters in detail, three sample sets having different chain lengths with the same CNT configuration and two sample sets having different CNT lengths with same chain length were prepared. Other parameters such as volume fraction and density were fixed to enable rigorous comparisons. Amorphous polyethylene is used as matrix polymer and (10,0) zigzag CNT is embedded into the matrix to reinforce polymer matrix. As a result, longer polymer chain length of matrix solely increased glass transition temperature but no reinforcing enhancement was observed. CNT length showed similar increase with little enhancement of elastic modulus. In addition to this, nanocomposites showed temperature-dependent elastic modulus jump passing thorough the glass transition region agrees well with experimental results.

• Journal of the Korean Chemical Society
• /
• v.42 no.1
• /
• pp.9-15
• /
• 1998

The geometrical parameters, vibrational frequencies, and IR intensities of dimethyldioxirane had been investigated using high level ab initio quantum mechanical methods with various basis sets. The polarization function decreases C-O and C-C bond distances significantly and the electron correlation effect increases those bond lengths slightly, while other bond lengths and bond angles are relatively stable for basis set size and correlation effect. The experimental and other theoretical vibrational frequencies and IR intensities of dimethyldioxirane will be compared and discussed with our high level theoretical predictions.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.25 no.3
• /
• pp.164-170
• /
• 2016

A proposed pneumatic cylinder-driven roll feeder and an air press were designed to be operated automatically by a PLC. The accuracy of the intermittent feed pitch of the roll feeder was evaluated by measuring lengths of cut-offs of a strip stock by a digimatic vernier caliper. At each predetermined feed pitch, the proposed roll feeder was tested 100 times by varying the feed/cut intervals as 2.0/1.5, 3.0/2.0, and 3.5/2.5 s as test sets. The lengths of the cutoffs of the strip stock ranged from 9.89-10.34, 12.1-12.65, and 15.21-15.67 mm at the predetermined 10, 12, and 15 mm feed pitch, respectively, among the total of 300 samples in each feed pitch, regardless of the feed/shear interval. Therefore, the feed/cut interval at each selected feed pitch was found to have no effect on the accuracy of the intermittent advancing of the strip stock.