• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.997-1000
• /
• 2010

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

• Communications of the Korean Mathematical Society
• /
• v.29 no.4
• /
• pp.569-579
• /
• 2014

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.253-267
• /
• 2021

We study linearly dependent subsets with prescribed cardinality s of a multiprojective space. If the set S is a circuit, there is an upper bound on the number of factors of the minimal multiprojective space containing S. B. Lovitz gave a sharp upper bound for this number. If S has higher dependency, this may be not true without strong assumptions (and we give examples and suitable assumptions). We describe the dependent subsets S with #S = 6.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.643-702
• /
• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• Journal of Pharmacopuncture
• /
• v.18 no.2
• /
• pp.33-41
• /
• 2015

Objectives: The present study evaluated the effects of sa-am acupuncture (SAA) simpo-jeongkyeok (SPJK) treatment on the blood pressure (BP), pulse rate (PR), and body temperature (BT) of patients with hwa byung (HB). Methods: This patient assessor blind, randomized, placebo controlled trial included 50 volunteers, divided randomly into two groups. The treatment group underwent SPJK (PC9, LR1, PC3, KI10) while the control (sham) group received minimal needle insertion at non acupoints. The BP in both arms, PR, and BT at several acupoints were measured before and after treatment at the $1^{st}$, $2^{nd}$, $3^{rd}$, and $4^{th}$ visits and before treatment at the follow-up visit. We analyzed data by using the repeated measured analysis of variance (RM ANOVA), Mann-Whitney U, and wilcoxon signed rank tests; differences at P < 0.05 were considered significant. Results: No significant differences in the systolic blood pressure (SBP), diastolic blood pressure (DBP) and PR between the treatment and control group were observed at each visit. However, the decrease in the SBP for the treatment group before and after each visit was significantly higher than it was in the control group. The SBP in both arms in the treatment group was decreased between visits 1 and 2, 1 and 3, 1 and 4, and 1 and follow-up. The DBP in both arms and in the right arm between visits 1 and 3 in the treatment group showed decreases. A minimal BT increase for treatment at CV06 and CV12 and a minimal BT decrease for treatment at CV17 and (Ex) Yintang were found. Patients in the treatment group who visited more frequently experienced a greater decrease in the PR, but that effect was not maintained. Conclusion: The results suggest that SAA SPJK treatment has instant positive effects on the BP, PR, and BT in patients with HB, but the effects on the BP and PR are not maintained.

• Journal of applied mathematics & informatics
• /
• v.36 no.5_6
• /
• pp.359-368
• /
• 2018

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

• Journal of Communications and Networks
• /
• v.15 no.4
• /
• pp.407-410
• /
• 2013

Secret sharing is that a dealer distributes a piece of information (called a share) about a secret to each participant such that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. In this paper, an access structure can be represented by a label graph G, where a vertex denotes a participant and a complete subgraph of G corresponds to a minimal authorized subset. The vertices of G are labeled into distinct vectors uniquely determined by the maximum prohibited structure. Based on such a label graph, a verifiable secret sharing scheme realizing general access structures is proposed. A major advantage of this scheme is that it applies to any access structure, rather than only structures representable as previous graphs, i.e., the access structures of rank two. Furthermore, verifiability of the proposed scheme can resist possible internal attack performed by malicious participants, who want to obtain additional shares or provide a fake share to other participants.

• Restorative Dentistry and Endodontics
• /
• v.42 no.2
• /
• pp.140-145
• /
• 2017

Objectives: The aim of this randomized, controlled, prospective clinical study was to evaluate patients' intraoperative discomfort during root canal preparations in which either multi-file rotary (Mtwo) or single-file reciprocating (Reciproc) systems were used. Materials and Methods: Fifty-five adult patients, aged between 25 and 69 years old, with irreversible pulpitis or pulp necrosis participated in this study. Either the mesiobuccal or the distobuccal canals for maxillary molars and either the mesiobuccal or the mesiolingual canals for mandibular molars were randomly chosen to be instrumented with Mtwo multi-file rotary or Reciproc single-file reciprocating systems. Immediately after each canal instrumentation under anesthesia, patient discomfort was assessed using a 1 - 10 visual analog scale (VAS), ranging from 'least possible discomfort' (1) to 'greatest possible discomfort' (10). The Wilcoxon signed-rank test was used to determine significant differences at p < 0.05. Results: Little intraoperative discomfort was found in all cases. No statistically significant differences in intraoperative discomfort between the 2 systems were found (p = 0.660). Conclusions: Root canal preparation with multi-file rotary or single-file reciprocating systems had similar and minimal effects on patients' intraoperative discomfort.

• Geomechanics and Engineering
• /
• v.37 no.4
• /
• pp.395-418
• /
• 2024

The epicentral region of earthquakes is typically where liquefaction-related damage takes place. To determine the maximum distance, such as maximum epicentral distance (R_e), maximum fault distance (R_f), or maximum hypocentral distance (R_h), at which an earthquake can inflict damage, given its magnitude, this study, using a recently updated global liquefaction database, multiple ML models are built to predict the limiting distances (R_e, R_f, or R_h) required for an earthquake of a given magnitude to cause damage. Four machine learning models LSTM (Long Short-Term Memory), BiLSTM (Bidirectional Long Short-Term Memory), CNN (Convolutional Neural Network), and XGB (Extreme Gradient Boosting) are developed using the Python programming language. All four proposed ML models performed better than empirical models for limiting distance assessment. Among these models, the XGB model outperformed all the models. In order to determine how well the suggested models can predict limiting distances, a number of statistical parameters have been studied. To compare the accuracy of the proposed models, rank analysis, error matrix, and Taylor diagram have been developed. The ML models proposed in this paper are more robust than other current models and may be used to assess the minimal energy of a liquefaction disaster caused by an earthquake or to estimate the maximum distance of a liquefied site provided an earthquake in rapid disaster mapping.

• Journal of Korean Society of Forest Science
• /
• v.94 no.6
• /
• pp.462-467
• /
• 2005

This study aims to classify the biotope types and evaluate its functions for acquiring the basic information which can support the landscape ecological management of the urban forest in the case of the three parks in Daegu metropolitan city and then to analyze vegetation landscape patterns. The biotope classification was mostly divided into 5 to 6 biotope type groups in the high units and 15 to 20 biotope types belong to them and then could know that the more big the park size, the more diverse and large the biotope types and its average area. The biotope grade over the three parks was dominating low rank grade (1 to 3 grade) 72.7% that forest organism is inadequate as live, and high grade (7 to 9 grade) did not appear entirely. Most in Biotope function estimation were appeared less than the middle rank grade and biotope area is bigger, those grade rises and temperature could know that is fallen. Vegetation landscape patterns was very simple because only two kinds of Robinia pseudo-acacia and Quercus acutissima is appeared as the dominated landscape elements in all of the three parks. And also because average area of those elements is generally 1ha or so, there was much problems in consecutiveness of functional role as forest ecosystem component. Conclusively, Ecological landscape management need to improve Biotope diversity and functionality, and it secures ecological minimal area and space linkage.