• Title/Summary/Keyword: Composite numbers

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Wave dispersion characteristics of porous graphene platelet-reinforced composite shells

  • Ebrahimi, Farzad;Seyfi, Ali;Dabbagh, Ali;Tornabene, Francesco
    • Structural Engineering and Mechanics
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    • v.71 no.1
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    • pp.99-107
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    • 2019
  • Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell's motion are derived according to Hamilton's principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

Public Key Cryptosystem Based on Jordan Form (Jordan 형식을 이용한 공개키 암호체계)

  • Lee, Hee-Jung
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.15 no.4
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    • pp.101-105
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    • 2005
  • Recently a new public key cryptosystem based on a diagonal matrix has been proposed by Zheng. This system uses eigenvalues as a long-term key and random numbers as session key generators. However, there are a couple of flaws in that system. In this paper, we propose a new algorithm in which those flaws are all fixed. Our scheme is based on modular equations over a composite and uses a matrix of Jordan form. We also analyze the security of it.

A Step-by-Step Primality Test (단계적 소수 판별법)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.13 no.3
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    • pp.103-109
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    • 2013
  • Miller-Rabin method is the most prevalently used primality test. However, this method mistakenly reports a Carmichael number or semi-prime number as prime (strong lier) although they are composite numbers. To eradicate this problem, it selects k number of m, whose value satisfies the following : m=[2,n-1], (m,n)=1. The Miller-Rabin method determines that a given number is prime, given that after the computation of $n-1=2^sd$, $0{\leq}r{\leq}s-1$, the outcome satisfies $m^d{\equiv}1$(mod n) or $m^{2^rd}{\equiv}-1$(mod n). This paper proposes a step-by-step primality testing algorithm that restricts m=2, hence achieving 98.8% probability. The proposed method, as a first step, rejects composite numbers that do not satisfy the equation, $n=6k{\pm}1$, $n_1{\neq}5$. Next, it determines prime by computing $2^{2^{s-1}d}{\equiv}{\beta}_{s-1}$(mod n) and $2^d{\equiv}{\beta}_0$(mod n). In the third step, it tests ${\beta}_r{\equiv}-1$ in the range of $1{\leq}r{\leq}s-2$ for ${\beta}_0$ > 1. In the case of ${\beta}_0$ = 1, it retests m=3,5,7,11,13,17 sequentially. When applied to n=[101,1000], the proposed algorithm determined 96.55% of prime in the initial stage. The remaining 3% was performed for ${\beta}_0$ >1 and 0.55% for ${\beta}_0$ = 1.

Exploring fraction knowledge of the stage 3 students in proportion problem solving (단위 조정 3단계 학생의 비례 문제 해결에서 나타나는 분수 지식)

  • Lee, Jin Ah;Lee, Soo Jin
    • The Mathematical Education
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    • v.61 no.1
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    • pp.1-28
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    • 2022
  • The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middle-grade students, each lasting about 30~50 minutes, were carried out from May 2021 to August 2021. The present study focuses on two 7th grade students who exhibited their ability to coordinate three levels of units prior to solving whole number problems. Although the students showed interiorization of three levels of units in solving whole number problems, how they coordinated three levels of units were different in solving proportion problems depending on whether the problems required reasoning with whole numbers or fractions. The students could coordinate three levels of units prior to solving the problems involving whole numbers, they coordinated three levels of units in activity for the problems involving fractions. In particular, the ways the two students employed partitioning operations and how they coordinated quantitative unit structures were different in solving proportion problems involving improper fractions. The study contributes to the field by adding empirical data corroborating the hypotheses that students' ability to transform one three levels of units structure into another one may not only be related to their interiorization of recursive partitioning operations, but it is an important foundation for their construction of splitting operations for composite units.

Analysis of critical fluid velocity and heat transfer in temperature-dependent nanocomposite pipes conveying nanofluid subjected to heat generation, conduction, convection and magnetic field

  • Fakhar, Mohammad Hosein;Fakhar, Ahmad;Tabatabaei, Hamidreza
    • Steel and Composite Structures
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    • v.30 no.3
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    • pp.281-292
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    • 2019
  • In this paper, analysis of critical fluid velocity and heat transfer in the nanocomposite pipes conveying nanofluid is presented. The pipe is reinforced by carbon nanotubes (CNTs) and the fluid is mixed by $AL_2O_3$ nanoparticles. The material properties of the nanocomposite pipe and nanofluid are considered temperature-dependent and the structure is subjected to magnetic field. The forces of fluid viscosity and turbulent pressure are obtained using momentum equations of fluid. Based on energy balance, the convection of inner and outer fluids, conduction of pipe and heat generation are considered. For mathematical modeling of the nanocomposite pipes, the first order shear deformation theory (FSDT) and energy method are used. Utilizing the Lagrange method, the coupled pipe-nanofluid motion equations are derived. Applying a semi-analytical method, the motion equations are solved for obtaining the critical fluid velocity and critical Reynolds and Nusselt numbers. The effects of CNTs volume percent, $AL_2O_3$ nanoparticles volume percent, length to radius ratio of the pipe and shell surface roughness were shown on the critical fluid velocity, critical Reynolds and Nusselt numbers. The results are validated with other published work which shows the accuracy of obtained results of this work. Numerical results indicate that for heat generation of $Q=10MW/m^3$, adding 6% $AL_2O_3$ nanoparticles to the fluid increases 20% the critical fluid velocity and 15% the Nusselt number which can be useful for heat exchangers.

Experimental investigation on flexural behaviour of HSS stud connected steel-concrete composite girders

  • Prakash, Amar;Anandavalli, N.;Madheswaran, C.K.;Lakshmanan, N.
    • Steel and Composite Structures
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    • v.13 no.3
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    • pp.239-258
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    • 2012
  • In this paper, experimental investigations on high strength steel (HSS) stud connected steel-concrete composite (SCC) girders to understand the effect of shear connector density on their flexural behaviour is presented. SCC girder specimens were designed for three different shear capacities (100%, 85%, and 70%), by varying the number of stud connectors in the shear span. Three SCC girder specimens were tested under monotonic/quasi-static loading, while three similar girder specimens were subjected to non-reversal cyclic loading under simply supported end conditions. Details of casting the specimens, experimental set-up, and method of testing, instrumentation for the measurement of deflection, interface-slip and strain are discussed. It is found that SCC girder specimen designed for full shear capacity exhibits interface slip for loads beyond 25% of the ultimate load capacity. Specimens with lesser degree of shear connection show lower values of load at initiation of slip. Very good ductility is exhibited by all the HSS stud connected SCC girder specimens. It is observed that the ultimate moment of resistance as well as ductility gets reduced for HSS stud connected SCC girder with reduction in stud shear connector density. Efficiency factor indicating the effectiveness of high strength stud connectors in resisting interface forces is estimated to be 0.8 from the analysis. Failure mode is primarily flexure with fracturing of stud connectors and characterised by flexural cracking and crushing of concrete at top in the pure bending region. Local buckling in the top flange of steel beam was also observed at the loads near to failure, which is influenced by spacing of studs and top flange thickness of rolled steel section. One of the recommendations is that the ultimate load capacity can be limited to 1.5 times the plastic moment capacity of the section such that the post peak load reduction is kept within limits. Load-deflection behaviour for monotonic tests compared well with the envelope of load-deflection curves for cyclic tests. It is concluded from the experimental investigations that use of HSS studs will reduce their numbers for given loading, which is advantageous in case of long spans. Buckling of top flange of rolled section is observed at failure stage. Provision of lips in the top flange is suggested to avoid this buckling. This is possible in case of longer spans, where normally built-up sections are used.

Activity-Theoretical Analysis on the Relation of Small Group Activity on Gifted Elementary Student's Concept Formation of Prime and Composite Numbers (소집단 활동체계와 초등영재의 소수와 합성수 개념 형성 사이의 관계 분석)

  • Kang, Young Ran;Kim, Jin Hwan
    • School Mathematics
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    • v.16 no.3
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    • pp.613-631
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    • 2014
  • The aim of this study was to investigate how the small group activity system influences individual to form concepts of prime number and composite number through activity theory on learning process of mathematically gifted 5th-grade students. Student's worksheets, recorded video, and interview were gathered and transcribed for analyzing data. Process of concept formation and using symbol behavior were used to derive the stage of mathematical concept from students, and the activity system and stage of concept formation process were schematized through analysis of whole class activity system and small group activity system based on activity theory. According to the results of this study, two students who were in different activity groups separated into the state of semi-concept and the stage of complex thinking respectively, and therefore, social context and the activity system had effects on process of concept formation among the students.

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INFLUENCES OF CAMPHOROQUINONE ON THE PROPERTIES OF COMPOSITES (Camphoroquinone이 복합레진의 특성에 미치는 영향)

  • 탁흥수;박상진
    • Restorative Dentistry and Endodontics
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    • v.26 no.1
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    • pp.41-50
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    • 2001
  • The purpose of this study was to examine the influences of camphoroquinone on the properties of five experimental composites. The contents of camphoroquinone were varied as 0.2%, 0.3%, 0.4%, 0.5%, and 0.6%, with silanized filler 75% and tertiary amine 0.2%. Five kinds of experimental composites were prepared, and diametral tensile strength, shear bond strength, depth of cure and yellowish discoloration were tested as a measurement. Specimen numbers of 10 were applied to all test items and experimental groups. Specimens for testing the diametral tensile strengths with internal diameter of 6mm in diameter and 3mm in height were filled with 5 experimental composites which were crushed with 1mm/min cross-head speed on Instron universal testing machine (Model No. 4467). Shear bond strength was measured on specimens attached to bovine teeth enamel etched with 37% phosphoric acid. Depth of cure was measured by the measurement of height of specimens which were removed the un-polymerized portion with acetone. Yellowness measurements were made by chromometer(Minolta Co. Japan) using L$^*$a$^*$b$^*$ values. ANOVA and Multiple range tests were used analyzed data with confidence level at 95%. The mean value of the shear bond strengths ranged from 31.03MPa to 39.49MPa. Following results were obtained ; 1. Diametral tensile strength was highest in experimental group 3, then was not affected by the contents of camphoroquinone ($r^2$=0.0422). 2. Composite resins containing 0.4% camphoroquinone showed the highest shear bond strength, but there was no statistical significance (p=0.3718). 3. Camphoroquinone reduces the depth of cure in the composite resins (p=0.0004, $r^2$=0.9483). 4. Camphoroquinone made the composites yellowish ($r^2$=0.9815). These results mean that increased content of camphoroquinone reduces the depth of cure, and that camphoroquinone make composites yellowish.

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Reliability Analysis on Stability of Armor Units for Foundation Mound of Composite Breakwaters (혼성제 기초 마운드의 피복재 안정성에 대한 신뢰성 해석)

  • Cheol-Eung Lee
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.35 no.2
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    • pp.23-32
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    • 2023
  • Probabilistic and deterministic analyses are implemented for the armor units of rubble foundation mound of composite breakwaters which is needed to protect the upright section against the scour of foundation mounds. By a little modification and incorporation of the previous empirical formulas that has commonly been applied to design the armor units of foundation mound, a new type formula of stability number has been suggested which is capable of taking into account slopes of foundation mounds, damage ratios of armor units, and incident wave numbers. The new proposed formula becomes mathematically identical with the previous empirical formula under the same conditions used in the developing process. Deterministic design have first been carried out to evaluate the minimum weights of armor units for several conditions associated with a typical section of composite breakwater. When the slopes of foundation mound become steepening and the incident wave numbers are increasing, the bigger armor units more than those from the previous empirical formula should be required. The opposite trends however are shown if the damage ratios is much more allowed. Meanwhile, the reliability analysis, which is one of probabilistic models, has been performed in order to quantitatively verify how the armor unit resulted from the deterministic design is stable. It has been confirmed that 1.2% of annual encounter probability of failure has been evaluated under the condition of 1% damage ratio of armor units for the design wave of 50 years return period. By additionally calculating the influence factors of the related random variables on the failure probability due to those uncertainties, it has been found that Hudson's stability coefficient, significant wave height, and water depth above foundation mound have sequentially been given the impacts on failure regardless of the incident wave angles. Finally, sensitivity analysis has been interpreted with respect to the variations of random variables which are implicitly involved in the formula of stability number for armor units of foundation mound. Then, the probability of failure have been rapidly decreased as the water depth above foundation mound are deepening. However, it has been shown that the probability of failure have been increased according as the berm width of foundation mound are widening and wave periods become shortening.

Experimental Study on Concrete Steel Circular Tubes Confined by Carbon Fiber Sheet under Axial Compression Loads (탄소섬유쉬트로 구속된 콘크리트충전 원형강관기둥의 단조압축실험)

  • Park, Jai-Woo;Hong, Young-Kyun;Hong, Gi-Soup;Choi, Sung-Mo
    • Journal of the Earthquake Engineering Society of Korea
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    • v.13 no.5
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    • pp.61-71
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    • 2009
  • This paper presents the results of an experiment comparing the current circular CFT columns and circular CFT columns that were additionally confined by carbon fiber sheets (CFS) under axial loading. The main experimental parameters are the numbers of CFS layers and the diameter-to-thickness ratio. 10 specimens were prepared according to the experimental parameter plans, and axial compression tests were conducted. From the tests, the failure procedure, load-axial deformation curve, maximum axial strength, and deformation capacity of the CFT columns and confined CFT columns were compared. The test results showed that the maximum axial strengths of CFT columns additionally confined by CFS are increased higher than those of the current CFT columns, and that local buckling can be delayed due to the confinement effect of CFS.