• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• Advances in nano research
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• 제13권4호
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• pp.369-378
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• 2022

Dynamic study of concrete plates under impact load is presented in this article. The main objective of this work is presenting a mathematical model for the concrete plates under the impact load. The concrete plate is reinforced by carbon nanoparticles which the effective material proprieties are obtained by mixture's rule. Impacts are assumed to occur normally over the top layer of the plate and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The structure is assumed viscoelastic based on Kelvin-Voigt model. Based on the classical plate theory (CPT), energy method and Hamilton's principle, the motion equations are derived. Applying DQM, the dynamic deflection and contact force of the structure are calculated numerically so that the effects of mass, velocity and height of the impactor, volume percent of nanoparticles, structural damping and geometrical parameters of structure are shown on the dynamic deflection and contact force. Results show that considering structural damping leads to lower dynamic deflection and contact force. In addition, increasing the volume percent of nanoparticles yields to decreases in the deflection.

• Steel and Composite Structures
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• 제44권5호
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• 국제학술발표논문집
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• The 8th International Conference on Construction Engineering and Project Management
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• pp.225-234
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• 2020

Reliability-based structural optimization usually requires designers or engineers model different designs manually, which is considered very time consuming and all possibilities cannot be fully explored. Otherwise, a lot of time are needed for designers or engineers to learn mathematical modeling and programming skills. Therefore, a framework that integrates generative design, structural simulation and reliability theory is proposed. With the proposed framework, various designs are generated based on a set of rules and parameters defined based on visual programming, and their structural performance are simulated by OpenSees. Then, reliability of each design is evaluated based on the simulation results, and an optimal design can be found. The proposed framework and prototype are tested in the optimization of a steel frame structure, and results illustrate that generative design based on visual programming is user friendly and different design possibilities can be explored in an efficient way. It is also reported that structural reliability can be assessed in an automatic way by integrating Dynamo and OpenSees. This research contributes to the body of knowledge by providing a novel framework for automatic reliability evaluation and structural optimization.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Structural Engineering and Mechanics
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• 제91권4호
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• pp.417-426
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• 2024

Nanotechnology has emerged as a promising avenue for enhancing musical structures. In this study, we analyze the static behavior of laser harp (i.e., electronic musical instrument) reinforced with Zinc Oxide (ZnO) nanoparticles. Leveraging the piezoelectric properties of ZnO nanoparticles, the structure is subjected to an electric field for intelligent control. The electronic musical structure is situated in a foundation with vertical springs and shear modulus constants. We employ the exponential Shear Deformation Beam Theory (ESDBT) to mathematically model the structure. A micro-electro-mechanical model is employed to determine the equivalent properties of the system. By utilizing nonlinear stress-strain relations, energy methods, and Hamilton's principle, we derive the motion equations. The buckling load of the electronic musical beam is calculated using the Difference Quadrature Method (DQM). The primary objective of this study is to present a mathematical model for electronic musical beams and determining the buckling load of the structure and to investigate the influence of nanotechnology and electric fields on its buckling behavior. The buckling is the case when the structure becomes deforms and unstable. Our findings reveal that the application of negative external voltage to the electronic musical structure increases both the stiffness and the buckling load of the musical system. Furthermore, reinforcing the electronic musical structure with ZnO nanoparticles results in an increased buckling load. Notably, the maximum enhancement in the 28-day compressive and tensile strengths of samples containing zinc oxide nanoparticles compared to the control sample resulting in increases of 18.70% and 3.77%, respectively.

• Kyungpook Mathematical Journal
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• 제64권3호
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• pp.371-393
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• 2024

Severe Acute Respiratory Syndrome (SARS) is a highly contagious viral disease with high mortality rate. There is no vaccine against SARS, but the spread can be limited by masking or social distancing. In this paper we implement a game-theoretic model of voluntary precautions against SARS. We build on the compartmental ODE model of the 2003 SARS epidemic. We assume that susceptible individuals can mask and/or limit contacts with others in order to decrease their chances of contracting SARS. Since the risk of SARS infection depends on the actions of others, this creates a public goods game. We find the Nash equilibrium, the solution of the game, which is the optimal voluntary level of precautions the individuals should take. We also study the effects of such actions on the spread of SARS and show that the effect significantly depends on the individual cost of the precautions. As soon as the cost rises above a critical threshold, the individuals will have no incentive to use any kind of voluntary precaution.

• 대한수학교육학회지:수학교육학연구
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• 제17권3호
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• pp.309-331
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• 2007

수 지도에 관한 문제는 수학교육의 역사에서 가장 활발하게 논의된 주제로서, 수학적, 철학적, 심리학적, 수학교육학적 측면에서 다양한 관점과 주장이 제기 되었다. 수 개념은 하나의 관점에서 규정될 수 없는 복합적인 개념이며, 그 지도 역시 결코 간단한 문제가 아니다. 그럼에도 불구하고 수 개념 및 그 지도에 관한 대부분의 논의는 수 개념의 한정된 측면을 중심으로 한 것이었다. 본 연구에서는 자연수 개념을 어떻게 지도하는 것이 좋은가 하는 자연수 개념 지도 문제에 대해, 자연수 개념의 제 측면에 대해서 현대 수학교육의 근본적인 이념이 되고 있는 활동주의적 접근을 시도하고자 하였다. 이를 위해 본 연구에서는 자연수 개념의 역사적, 수리철학적 논의와 수 개념의 제측면에 관해 고찰하고, 지식의 활동적 구성과 활동을 통한 자연수 개념의 구성 및 자연수 개념 지도의 활동주의적 접근을 논의한 제 학자들의 입장을 비판적으로 분석하는 가운데 자연수 개념의 제 측면을 의미 있게 지도하기 위한 활동주의적 접근 방안을 연구 제시하였다.

• 한국도서관정보학회지
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• 제8권
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• pp.127-154
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• 1981

Today's complicated society with a rapid change needs more objective and accurate data for the better managerical decisions and the prospect for the future other than the intuition or subjective experience by men themselves. These data can't be extracted without the analysis of actual data by a n.0, pplying any of mathematical techniques. One of these mathematical techniques, called bibliometrics has been newly developed in the field of library and information science to extract the objective data for the better services through the library operations. The Beadford's Law, one important law in bibliometrics has provided rather scientific and objective basis on the more valid building of library collection within the constraints of budget. The purpose of the study is to investigate the theory of the Bradford's Law, to clarify the possible areas of its a n.0, pplication, and to discern some problems in doing so. The results of the study can be summarized as follows; (1) There is certain difference between the graphical formulation and verbal formulation of Bradford's Law. But this law is very useful for the field of library and information science, owing to the flexibility of the a n.0, pplication of the law in the field. (2) The minimal nucleus can consist of a single periodical only if j, the number of relevant papers in the most productive journals is greater than Z/2. On the other hand, if j is less than or equal to Z/2, then the minimal nucleus will consist of 2 or more periodicals. (3) It is possible to design the most compact selection of scientific periodicals covering any specified percentage P among the total periodicals by using the formulation, log n=Plog N+(1-P)logs, or Nlog N/s=P center dot N log N/s. (4) If there is need to provide all the articles needed by users the given budget, the library can purchase the proper number of journals, by using the formulation, f center dot AN=An+PN (log N/s-logn/s). (5) In the building of the library collection based on the decreasing ratio of use, the library can subscribe to the proper number of journals according to the satisfactory degree of the need, by using the formulation, f=Nu+uNlogN/S-uNlogn/s / nNlogN/s = 1+logN/m /logN/s (6) If the order of valuable journals is decided according to the frequency of being cited, the order can't always represent the value. (7) The evaluation criteria for the journals with high value, but less cited should be made a further study.

• 한국언론정보학보
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• 제37권
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• pp.377-417
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• 2007

본 연구에서는 이제까지 매스미디어 효과론 연구에서 등한시 되어온 매스미디어의 긍정적 효과를 학생들의 지능발달과 학업성적과 매스미디어 이용과의 상관관계를 통해 그 가능성을 점검해보고자 하였다. 매스미디어의 이러한 효과를 총체적으로 매스미디어의 '인지개발 효과'라는 한다면, 이제까지의 인지개발효과 연구들에는 텔레비전에 관한 연구가 대부분이라고 할 수 있다. 뿐만 아니라, 아이큐(IQ)를 종속변인으로 사용해 왔지만 아이큐검사의 타당성에 한계가 많기 때문에 새로운 지능이론을 원용하여 인지개발효과를 검증해볼 필요도 있다고 하겠다. 본 연구의 의의를 요약하면, 첫째는 텔레비전과 신문, 그리고 인터넷 전체를 대상으로 기존 연구에서 산발적으로 사용된 매체들의 이용 동기, 이용량, 그리고 이용형태 모두를 독립변인으로 설정하여 그 영향력을 비교 검토하였고, 둘째는 종속변인으로서의 지능개념에 새로운 다중지능이론을 원용했다는 점을 들 수 있다. 연구결과를 보면, 지능과 학업성적의 경우 모두에서 매체 이용형태가 가장 많은 영향을 미치는 것으로 나타났는데, 이는 학생들의 지능 발달이나 학업성적에 있어서 어떤 내용을 접하느냐가 중요하며, 접촉하는 내용에 따라서는 인지개발에 긍정적인 영향을 미칠 수 있는 것으로 나타났다. 인간의 지능을 여러 가지로 나누어 보았을 때에 매체관련변인들이 지능의 종류에 따라 각각 상반된 영향을 미치고 있다는 것도 본 연구의 중요한 발견의 하나라고 할 수 있다. 따라서 매체관련변인들이 8개의 다중지능들과 학업성적에 미치는 영향이 각각 다르다는 점에서 설정된 종속변인에 따라 그에 대한 설명틀도 각각 달라져야 할 것으로 생각된다.