• 대한수학회보
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• 제56권5호
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• 한국정보과학회논문지:시스템및이론
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• 제27권8호
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• pp.730-740
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• 2000

고가용성 다중계 시스템의 소프트웨어 재활 기법은 시스템의 결함 발생 이후에 수동적으로 대처하기보다는 결함이 발생하기 전에 이를 미연에 방지하는 능동적 차원의 결함 허용 방법이다. 특히 멀티미디어 이동 컴퓨팅에서 사용되는 소프트웨어는 통신 단절, 데이터 유실 등으로 인한 노화 진행이 일반 소프트웨어보다 상당히 빠르게 진행되기 때문에 소프트웨어 재활에 의한 결함 예방 방법은 대규모 멀티미디어 이동 컴퓨팅 시스템에 사용될 가능성이 높다고 볼 수 있다. 본 연구에서는 서버에서 수행되는 소프트웨어의 재활 주기, 재활 소요시간, 서버의 고장률, 수리률, 동시에 가동되는 서버의 수, 서버의 가동 기간 및 가동 방식 등의 시스템 운영 파라미터에 기초하여, 소프트웨어 재활 정책에 대한 평가를 위한 평형 상태에서의 확률, downtime, 가용도, 손실 비용 등을 계산하였다 수학적 분석을 통해 구한 재활 모델의 closed-form 해는 다양한 시스템 운영 상태에 대한 실험을 통해 검증하였으며, 소프트웨어 재활을 통한 예방적 결함허용 기법의 적용 가능성이 높다는 것을 확인하였다. 또한 서버의 고장률 및 불안정률이 소프트웨어 재활 정책 결정에 중요한 요소임을 파악하였다.

• 한국정보통신학회논문지
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• 제23권2호
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• pp.201-206
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• 2019

소프트웨어 노화에 따른 시스템의 예기치 않은 장애 발생은 재활 기능을 주기적으로 수행함으로써 줄일 수 있다. 이 시스템 재활 기능은 주로 시스템이 가장 한가한 시간에 수행하는 것이 효과적이다. 이를 통해 시스템 가용도를 높일 수 있다. 재활 기법은 크게 시간 기반과 조건 기반의 두 가지 종류로 나눌 수 있다. 시간 기반 재활은 정해진 시간 간격마다 수행되고, 조건 기반 재활은 시스템 상태가 특정 조건을 만족할 때 수행된다. 조건 기반 방식은 시스템 감시와 정보의 수집 및 통계적 분석을 통해 재활 시점을 추정해야하기 때문에 추가적인 비용이 발생한다. 본 논문은 시간 기반 소프트웨어 재활 기법을 분석할 수 있는 확률 모형을 제시한다. 제시한 모형은 재활을 주기적으로 수행하는 시간 간격을 일정하게 유지할 수 있는 현실적인 상황을 반영한다. 해당 확률 모형을 수학적으로 분석하여, 정상 상태에서의 시스템 가용도와 사용자 인지 가용도 및 이에 따른 비용을 분석한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.1904-1909
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• 1991

Software linear and exponential acceleration/deceleration algorithms for control of machine axes of motion in industrial robots and CNC machine tools are proposed. Typical hardware systems used to accelerate and decelerate axes of motion are mathematically analyzed. Discrete-time state equations are derived from the mathematical analyses for the development of software acceleration/deceleration algorithms. Synchronous control method of multiple axes of motion in industrial robots and CNC machine tools is shown to be easily obtained on the basis of the proposed acceleration/deceleration algorithms. The path error analyses are carried out for the case where the software linear and exponential acceleration/deceleration algorithms are applied to a circular interpolator. A motion control system based on a floating point digital signal processor (DSP) TMS 320C30 is developed in order to implement the proposed algorithms. Experimental results demonstrate that the developed algorithms and the motion control system are available for control of multiple axes and nonlinear motion composed of a combination of lines and circles which industrial robots and CNC machine tools require.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권10호
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• pp.4703-4723
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• 2018

In recent years, dense small cell network has been deployed to address the challenge that has resulted from the unprecendented growth of mobile data traffic and users. It has proven to be a cost efficeient solution to offload traffic from macro-cells. Software defined heterogeneous wireless network can decouple the control plane from the data plane. The control signal goes through the macro-cell while the data traffic can be offloaded by small cells. In this paper, we propose a framework for cell virtualization and user association in order to satisfy versatile requirements of multiple tenants. In the proposed framework, we propose an interference graph partioning based virtual-cell association and customized physical-cell association for multi-homed users in a software defined small cell network. The proposed user association scheme includes 3 steps: initialization, virtual-cell association and physical-cell association. Simulation results show that the proposed virtual-cell association outperforms the other schemes. For physical-cell association, the results on resource utilization and user fairness are examined for mobile users and infrastructure providers.

• 한국컴퓨터산업학회논문지
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• 제3권2호
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• pp.227-234
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• 2002

클러스터 웹서버 시스템에서는 다수 서버의 장애로 인해 발생하는 가용도 저하 문제와 소프트웨어의 노화로 인하여 높은 성능과 가용도를 제공하기 쉽지 않다. 본 연구에서는 n대의 주 서버와 k대의 여분서버로 구성되는 클러스터 웹 서버 시스템에 성능과 작업전이 시간을 고려한 소프트웨어 재활 모델을 제시하였고 다양한 시스템 운영 파라미터에 기초하여 소프트웨어의 재활정책에 대한 평가를 위해 평형 상태에서의 확률, 가용도, 손실비용 등을 계산하였다. 수학적 분석을 통해 다양한 시스템 운영 상태에 대한 실험을 통해 검증하였으며, 소프트웨어의 재활 정책에 의한 예방적 결함허용 기법이 시스템의 안정성에 중요한 요소임을 확인하였다.

• 대한수학교육학회지:수학교육학연구
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• 제9권1호
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권9호
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• pp.3885-3906
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• 2020

Hybrid fuzzing which combines fuzzing and concolic execution, has proved its ability to achieve higher code coverage and therefore find more bugs. However, current hybrid fuzzers usually suffer from inefficiency and poor scalability when applied to complex, real-world program testing. We observed that the performance bottleneck is the inefficient cooperation between the fuzzer and concolic executor and the slow symbolic emulation. In this paper, we propose a novel solution named EPfuzzer to improve hybrid fuzzing. EPfuzzer implements two key ideas: 1) only the hardest-to-reach branch will be prioritized for concolic execution to avoid generating uninteresting inputs; and 2) only input bytes relevant to the target branch to be flipped will be symbolized to reduce the overhead of the symbolic emulation. With these optimizations, EPfuzzer can be efficiently targeted to the hardest-to-reach branch. We evaluated EPfuzzer with three sets of programs: five real-world applications and two popular benchmarks (LAVA-M and the Google Fuzzer Test Suite). The evaluation results showed that EPfuzzer was much more efficient and scalable than the state-of-the-art concolic execution engine (QSYM). EPfuzzer was able to find more bugs and achieve better code coverage. In addition, we discovered seven previously unknown security bugs in five real-world programs and reported them to the vendors.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권9호
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• pp.4529-4548
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• 2016

DDoS attacks have had a devastating effect on the Internet, which can cause millions of dollars of damage within hours or even minutes. In this paper we propose a practical dynamic defense approach that overcomes the shortage of static defense mechanisms. Our approach employs a group of SDN-based proxy switches to relay data flow between users and servers. By substituting backup proxy switches for attacked ones and reassigning suspect users onto the new proxy switches, innocent users are isolated and saved from malicious attackers through a sequence of remapping process. In order to improve the speed of attacker segregation, we have designed and implemented an efficient greedy algorithm which has been demonstrated to have little influence on legitimate traffic. Simulations, which were then performed with the open source controller Ryu, show that our approach is effective in alleviating DDoS attacks and quarantining the attackers by numerable remapping process. The simulations also demonstrate that our dynamic defense imposes little effect on legitimate users, and the overhead introduced by remapping procedure is acceptable.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권1호
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• pp.65-81
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• 2015

The purpose of this study is to investigate the international trends of how the core competencies are reflected in mathematics curriculum, and to find the implications for the revision of Korean mathematics curriculum. For this purpose, the curriculum of the 9 countries including the U.S., Canada(Ontario), England, Australia, Poland, Singapore, China, Taiwan, and Hong Kong were thoroughly reviewed. It was found that a variety of core competencies were reflected in mathematics curricula in the 9 countries such as problem solving, reasoning, communication, mathematical knowledge and skills, selection and use of tools, critical thinking, connection, modelling, application of strategies, mathematical thinking, representation, creativity, utilization of information, and reflection etc. Especially the four most common core competencies (problem solving, reasoning, communication, and creativity) were further analyzed to identify their sub components. Consequently, it was recommended that new mathematics curriculum should consider reflecting various core competencies beyond problem solving, reasoning, and communication, and these core competencies are supposed to combine with mathematics contents to increase their feasibility. Finally considering the fact that software education is getting greater attention in the new curriculum, it is necessary to incorporate computational thinking into mathematics curriculum.