• 한국수학교육학회지시리즈A:수학교육
• /
• 제50권1호
• /
• pp.1-12
• /
• 2011

It is the aim of this paper to study the target problem solving process in reference to the base problem. We observed closely how students solve the target problem in reference to the base problem. The students couldn't solve the target problem, although they succeed to find the base problem. This comes from failing to discover the structural similarity between the target problem and the base problem. Especially it is important to cognize the proper corresponding of primary components between the base problem and target problem. And there is sometimes a part component of the target problem equivalent to the base problem and the target problem can't be solved without the insight into this fact. Consequently, finding the base problem fail to reach solving the target problem without the insight into their structural similarity. We have to make efforts to have an insight into the structural similarity between the target problem and the base problem to solve the target problem.

• 대한수학회보
• /
• 제57권3호
• /
• pp.623-647
• /
• 2020

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base b, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base b and omit the proofs for the Thabit numbers of the first kind base b and Cunningham numbers.

• Structural Engineering and Mechanics
• /
• 제2권3호
• /
• pp.295-309
• /
• 1994

The present paper concerns the mathematical study and the numerical treatment of the problem of semirigid connections in bolted steel column base plates by taking into account the possibility of appearance of separation phenomena on the contact surface under certain loading conditions. In order to obtain a convenient discrete form to simulate the structural behaviour of a steel column base plate, the continuous contact problem is first formulated as a variational inequality problem or, equivalently, as a quadratic programming problem. By applying an appropriate finite element scheme, the discrete problem is formulated as a quadratic optimization problem which expresses, from the standpoint of Mechanics, the principle of minimum potential energy of the semirigid connection at the state of equilibrium. For the numerical treatment of this problem, two effective and easy-to-use solution strategies based on quadratic optimization algorithms are proposed. This technique is illustrated by means of a numerical application.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제5권5호
• /
• pp.1069-1084
• /
• 2011

This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited. Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

• 한국정보시스템학회지:정보시스템연구
• /
• 제7권1호
• /
• pp.181-208
• /
• 1998

In many literatures of model management, various schemes for representing model base schema have proposed. Ultimately, the goal is to arrive at a set of mutually supportive and synergistic methodologies and tools for the modeling problem domain and model base design. This paper focus on how best to structure and represent conceptual model of problem domain and schema of model base. Semantic concepts and modeling constructs are valuable conceptual tools for understanding the structural relationships and constraints involved in an model management environment. To this end, we reviewed the model management literature, and analyzed the constructs of modeling tools of data model management graph-based approach. Although they have good tools but most of them are not enough for the representation of structural relationships and constraints. So we wanted more powerful tools which can represent diverse constructs in a decision support modeling and model base schema design. For the design of a model base, we developed object modeling framework which uses Object Modeling Techniques (OMT). In Object Modeling Framework, model base schema are classified into conceptual schema, logical schema, and physical schema. The conceptual schema represents the user's view of problem domain, and the logical schema represents a model formatted by a particular modeling language. The schema design, this paper proposes an extension of Object Model to overcome some of the limitations exhibited by the OMT. The proposed tool, Extended Object Model(EOM) have diverse constructs for the representation of decision support problem domain and conceptual model base schema.

• 정보처리학회논문지C
• /
• 제14C권2호
• /
• pp.179-184
• /
• 2007

이동 통신 시스템의 설계에 있어서 기지국의 위치를 선정하는 문제는 기본적으로 셀 내부 및 외부의 간접전파에 의한 최소 SIR을 만족하면서 최대한의 사용자를 최소의 기지국에 할당하는 문제로서 NP-hard 이다. 기존에 주로 사용된 목적함수는 창고위치문제에서 사용하던 것으로 CDMA 이동통신 시스템으로 직접 이용하는 단계에서 문제점이 발생한다. 그 문제점들을 해결하는 목적함수와 최적해 및 근사해를 구하는 알고리즘을 제안하고, 그에 따른 시뮬레이션을 하여 본 논문의 제안이 타당성이 있는지 평가 및 분석하였다. 본 논문에서는 기지국의 위치문제를 경험적 탐색방법을 사용하지 않고 혼합정수계획법의 완전해를 이용하여 최적해 및 근사해를 구하였다.

• Structural Engineering and Mechanics
• /
• 제6권1호
• /
• pp.63-76
• /
• 1998

This paper presents dynamic responses of structures with sliding base which limits the translation of external loads from ground excitation. A discrete element model based on the discontinuous deformation analysis method is proposed to study this sliding boundary problem. The sliding base is simulated using sets of fictitious contact springs along the sliding interface. The set of contact spring is to translate friction force from ground to superstructure. Validity of the proposed model is examined by the closed-form solutions of an idealized mass-spring structural model subjected to harmonic ground excitation. This model is also applied to a problem of a three-story structural model subjected to the ground excitation of 1940 El Centro earthquake. Analyses of both sliding-base and fixed-base conditions are performed as comparisons. This study shows that using this model can simulate the dynamic response of a sliding structure with frictional cut-off quite accurately. Results reveal that lowering the frictional coefficient of the sliding joint will reduce the peak responses. The structure responses in little deformation, but it displaces at the end of excitation.

• 대한수학교육학회지:수학교육학연구
• /
• 제27권1호
• /
• pp.51-67
• /
• 2017

유추는 학생들의 문제 해결력, 귀납적 추론, 수학적 발견술, 창의성 신장에 도움을 줄 수 있는 수학 교육적으로 유용한 사고 방법이다. 학생들은 서로 다른 수학적 대상에 대해 유사성을 바탕으로 연결함으로써 두 대상 사이의 관계를 인식할 수 있다. 본 연구에서는 예비수학교사들이 이심률의 정의에 따른 이차곡선의 작도 과정에서 드러난 사고의 특징을 유추의 관점에서 분석하였다. 그 결과, 바탕 문제에 관한 수학적 지식의 부재와 바탕 문제의 수학적 지식에 대응하는 목표 문제의 수학적 지식의 부재는 목표 문제의 해결에 도움되지 못하였다. 바탕 문제의 다양한 해결 방법은 목표 문제의 해결에 도움을 주었으며, 일부는 작도 문제의 해결에 있어 적절한 바탕 문제를 설정하고 대수적 방법을 통해 문제를 해결하였다. 마지막으로 잠재적 유사성에 근거한 유추는 새로운 풀이 방법을 발견하는데 도움을 주었다.

• 한국정보통신학회논문지
• /
• 제13권1호
• /
• pp.81-86
• /
• 2009

사용자 고유번호와 패스워드 기반의 사용자 인증 매커니즘을 수행하는 네트워크 시스템 환경에서는 스니퍼 프로그램 등을 이용하여 불법 도청함으로써 쉽게 사용자의 패스워드를 알아낼 수 있다. 이러한 불법적인 도청에 의한 패스워드 노출 문제를 해결하는 방법으로 일회용 패스워드, Challenge-Response 인증 방식이 유용하게 사용되며, 클라이언트/서버 환경에서는 별도 동기가 필요 없는 시간을 이용한 일회용 패스워드 방식이 특히 유용하게 사용될 수 있다. 본 논문에서는 안전성은 Square root problem에 기초를 두고 있고, 프리플레이 공격, 오프라인 사전적 공격 그리고 서버 등을 포함하여 지금까지 잘 알려진 공격(해킹)들에 대해서 안전성을 높이기 위한 암호기반 시스템을 제안한다. 암호기반 시스템 확인은 패스워드를 생성하는데 특별한 키를 생성할 필요가 없다는 것이다. 암호기반 시스템은 검증자를 확인하는데 걸리는 시간이 적게 소요되면서 특출하다.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제17권5호
• /
• pp.1503-1515
• /
• 2023

This paper considers the jointly active and passive beamforming design in the IRS-aided MISO downlink vehicle communication system where both V2I and V2V communication paradigms coexist. We formulate the problem as an optimization problem aiming to minimize the total transmit power of the base station subject to SINR requirements of both V2I and V2V users, total transmit power of base station and IRS's phase shift constraints. To deal with this non-convex problem, we propose a method which can alternately optimize the active beamforming at the base station and the passive beamforming at the IRS. By using first-order Taylor expansion, matrix analysis theory and penalized convex-concave process method, the non-convex optimization problem with coupled variables is converted into two decoupled convex sub-problems. The simulation results show that the proposed alternate optimization algorithm can significantly decrease the total transmit power of the vehicle base station.