Reciprocal constructions using Ponclelet duality and conic section

The fundamental theorem of linear algebra establishes a duality between the statics of a pin-jointed truss structure and its kinematics. Graphic statics visualizes the forces in a truss as a reciprocal diagram that is dual to the truss geometry. In this article, we combine these two dualities to provide insights not available from a graphical or algebraic approach alone. We begin by observing that the force diagram of a statically indeterminate truss, although itself typically a kinematically loose structure, must support a self-stress state of its own. Such an “extra” self-stress state is described by the fundamental theorem of linear algebra. We show that the self-stress states of a truss are in a one-to-one correspondence with linkage-mechanism displacements of its reciprocal, and the relative centers of rotation of these mechanism displacements correspond to centers of perspective of a projection of a plane-faced three-dimensional polyhedral mesh. We prove that this polyhedral mesh is exactly the continuum Airy stress function, restricted to describe equilibrium of a truss structure. We use the Airy function to prove James Clerk Maxwell’s conjecture that a two-dimensional truss structure of arbitrary topology has a self-stress state if and only if its geometry is given by the projection of a three-dimensional plane-faced polyhedron. Although a very limited number of engineers have been aware of the relationship between trusses and a polyhedral Airy function, the authors believe that this is the first truly rigorous elucidation. We summarize the properties of this “dual duality,” which has the Airy function at its core, and conclude by showing applications to design of tensegrities, planar panelization of architectural surfaces, and optimization of trusses.

Self-Similar Expansion (SSE) fitting models the leading edge of the Coronal Mass Ejection (CME) as a self-similar expansion sphere with a fixed propagation direction and a fixed angular width. Cone angle of the heliocentric cone which is tangent to the sphere usually refers to the angular width of the CME, ranging from 0 to 90 degrees. Angular widths of Fixed-Φ (FΦ) and Harmonic-mean (HM) fitting are defined, corresponding to 0 and 90 degrees of SSE model, respectively. Modified SSE (MSSE) fitting discussed in this paper models the leading edge of the CME as a self-similar expansion semi-sphere. It is able to extract CME parameters using MSSE fitting, including propagation direction, velocity and cone angle of the heliocentric cone, whose conic section is across the center of the semi-sphere, ranging from 0 to 90 degrees. Cone angles of FΦ and HM fitting are defined, corresponding to 0 and 45 degrees of MSSE model, respectively. Leading edge of the CME can be assumed as a heliocentric semi-sphere when cone angle is assumed to be 90 degrees. MSSE fitting expands the morphology of leading edge of the CME and considers cone model as a reference to determine whether and when the CME will reach a satellite. 23 CMEs were analyzed based on the observations by Heliospheric Imager (HI) from one spacecraft of STEREO, combined with in-situ observations of solar wind on STEREO and ACE. We found that the error of the CME propagation direction, arrival speed and theoretical arrival time analyzed by MSSE fitting decreased, compared to FΦ, HM and SSE fitting.

In the optical fiber communication system of high-speed and large capacity, the dispersion is one of the main technical indicators. The dispersion causes the light pulse broadening, so it leads to the distortion of signal transmission and BER (bit error rate). The main research is the single-mode optical fiber dispersion compensation. The design and performance of system structure on the dispersion compensation fiber communication system is accomplished by using of the optic system optical fiber communication system simulation. Through the analysis of system structure and the research of the performance of the key components of the system, the output signal waveform is simulated and the influence of the output signal waveform by the system structure and key components performance of the receiving end is compared. The design can reduce the system dispersion.

An important part of classical geometry is the wide area of projective geometry. Here a brief and elementary introduction is given to this field based upon plane sections of pyramids in three‐dimensional Euclidean space (see section 1). In section 2 conic sections are constructed as the perspective images of a circle. In the last section we construct conic sections given by five elements (points or tangents). Systematically we solve all of the six possible problems. This part is very much different from what can be found in the standard references on projective geometry but it gives good insight into the methods of this powerful tool.

Stochastic model updating using distance discrimination analysis

SAP2000 is well-known commercial software for analysis and design of structural systems that is equipped with an open application programming interface (OAPI). In this work, a code written in C# able to solve three-dimensional topology optimization problems is presented, where a topology optimization framework was integrated into SAP2000 taking advantage of its OAPI feature. The code is partially based on the 99 and 88 line codes written by Sigmund (Struct Multidiscip Optim 21(2):120–127, 2001) and Andreassen et al. (Struct Multidiscip Optim 43(1):1–16, 2011). The code solves the problem of minimum compliance while through OAPI it takes advantage of all modelling capabilities of SAP2000. The paper covers the theoretical aspects of topology optimization incorporated in the code and provides detailed description of their numerical implementations. Special effort was made to the latter one, describing in detail all numerical aspects of the code, in order to facilitate the reader to understand the code, and therefore being able to further enhance its capabilities. The complete code can be downloaded from GitHub ( https://github.com/nikoslagaros/TOCP ).

Conics on a Sphere

Objective To determine the safety and efficacy of laser in situ keratomileusis (LASIK) in standard sphere/cylindrical or ellipsoidal ablation model to treat moderate and high compound myopic astigmatism. Methods The LaserSight SLX laser (5.3 software) was used in LASIK. In standard sphere/cylindrical ablation model group (23 eyes), the preoperative mean uncorrected visual acuity (UCVA) was 0.155: 0.09,sphere -4.40± 2.07D, cylinder -2.42± 0.47D, the final follow-up 6.04± 3.74 months. In ellipsoidal ablation model group (33 eyes), the UCVA was 0.13± 0.05, sphere -5.43±2.26D, cylinder-2.71± 0.76D, the final follow-up 6.91± 5.10 months. Results In two groups, the UCVA was 1.11± 0.17 and 1.05± 0.10, sphere -0.17± 0.77D and-0.18± 0.89, cylinder-0.62± 0.39D and-0.64± 0.68, respectively. No statistical different was found (P > 0.05 ). However, the postoperatively mean corneal asphericity (Q-value) was 0.60± 0.35 in sphere/cylindrical group and 0.29± 0.5928.1% (9/32) in ellipsoidai group with statistical difference. Conclusions LASIK using the LaserSight SLX excimer laser (5.3 software) in standard sphere/cylindrical or custom ellipsoidal ablation model is effective and stable for moderate and high compound myopic astigmatism. The postoperative Q-value in ellipsoidal ablation model is easier to maintain preoperatively negative characteristic. Key words: Compound myopic astigmatism; Laser in Situ Keratomileusis (LASIK); Q-value

This chapter examines how a system developed using the Structured Systems Analysis and Design Methodology (SSADM) evolves to fit the UML and XML. As a vehicle, the chapter will consider the addition of a new user story to an existing SSADM system. SSADM developed in the early 1980’s. It is still popular. It is similar to other Structured Analysis and Design methods. Evolving SSADM to use the UML and XML is important. This chapter argues that XML is an opportunity, not a problem. It also shows that the earlier UMLs did not support SSADM but the new UML 2.0 does.

The case study described in this chapter concerns the introduction of a new computer based integrated Clinical Information System (CIS) into a British National Health Services Trust-the Sunrise Trust. At the time of the study most of the system modules had been developed and were being tested largely for technical aspects. The system was being introduced during a period when the organization was experiencing significant changes. It was an environment where new structures were being created and the existing ones changed. Indeed, the case study was selected primarily because of these factors. The analysis of these structures, formal and informal, provides insight into the management of information systems. Various stakeholders in the Hospital Trust felt that a computer based information system would facilitate the change process. However the analysis and design of the system posed its own problems. The system turned out to be inflexible with respect to the core health care delivery process. It was also nonresponsive to the needs of the key stakeholders. Analysis of the case shows that clearly the formal methods adopted by the system analysts fell short of determining the rapid changes required for care. In particular this was an important issue, since the context of the British National Health Services posed pressures on individual trusts to be cost effective. This resulted in long term patients being moved out into the community. However, this richness in the context was overlooked by the analysts. They developed “logical” models of the system, which ended up in being “tidy pictures of reality” and were prescriptive and utterly inflexible. Structured Systems Analysis and Design Method (SSADM) was used as a modelling tool, which amplified the rational view of decision making and information technology (IT) applications (for more details on SSADM see Downs et al., 1988). The interpretations identified in the case show a clear mis-match between the formal models and perceptions of the system users who inevitably reflect a more informal and pragmatic approach to their own organizational realities. The analysis of the case poses a number of interesting issues. It questions the relationship between the complexity of the social relations and systems design. Furthermore it brings to the fore the paradoxical viewpoints of different stakeholders and the emergent concerns for a system analyst. The chapter also identifies the impact of an “overformalized” information system on the integrity of an organization. In doing so it evaluates the nature and significance of social power structures in systems analysis, design and implementation.

Results of survey of use of SSADM in commercial and government sectors in United Kingdom

This research work focused on development of a model of web based virtual University Administration for Nigerian universities. This is necessary as there is still a noticeable administrative constraint in our Universities, the establishment of many University Web portals notwithstanding. More efforts are therefore needed to enhance or improve on the software that drives these portals to make them more efficient and render real time services. The model enables members of academic community to set up curriculum, register students and staff, enter exam scores, post news, view results, pay school fees, request for transcripts, obtain vital information from the university and update information on daily basis. The model has a watch-dog monitor called Web Patrol that monitors and keeps a log of the transactions by students and staff. The methodologies adopted for this work are top-down, prototyping and Structured Systems Analysis and Design Methodology (SSADM). This research work helps in bringing university administrative products and services to the door steps of people, thereby reducing administrative bottleneck witnessed in our universities today. It generates results and transcripts, thereby solving the current problems of delay in result and transcript processing and transfer in our universities.

The present internet version which was established and consolidated over internet protocol version 4 (IPV4) in 1981, and whose amount of public addresses available is insufficient to meet the demands explosion and current internet multimedia devices, services and application intensive environment has posed serious problems of incomplete web transactions. Stakeholders and communication industry in Nigeria are unwilling and feel reluctant to migrate to IPV6 because of inhibiting factors. This needs urgent redress to overcome the tractions that are responsible for apathy to migration from IPV4 to IPV6 launched in 1994 by the Internet Engineering Task Force (IETF). If nothing is done, sometime, internet may run out of space, ARIN [1]. Users may suffer disillusionment and frustration. The objective of this study therefore is to design a model for predicting migration from IPV4 to IPV6 in Nigeria by 2027 based on growth trend developed from statistical indices. The essence is to explore and analyze the factors that can encourage migration to IPV6 in the next 10 years and use those factors to forecast growth, so that IPV6 will receive boost in terms of growth and patronage. The study also aims at designing a predictive model that simulates the behaviour of the restrictive policies on migration to 1PV6 so as to ascertain the current impact on non-motivation and unwillingness to migrate to IPV6 in Nigeria. The motivation behind this study is to identify the inhibiting factors responsible for lack of motivation to migrate from IPV4 to IPV6 in Nigeria. The methodologies that were deployed in packaging the model include the statistical methodology, Structured Systems Analysis and Design Methodology (SSADM) and prototyping. The result is indeed functional software, programmed through Visual Basic. Net. (VB.Net) that can be used to simulate the behavioural impact of any government policy formulation for Telecommunication industry and stakeholders.

I worked for a British computer company in the 1990s, and it was company policy to use SSADM (Structured Systems Analysis and Design Method) for any new projects. At the time, we were working on a part of the London Underground (also called the Tube) automation. I went to my manager with the time estimate for a new module that I was designing. The estimate was high, and he asked, “What are all these tasks for gathering requirement specifications and technical system options?” I said those were SSADM-based tasks. He replied: “We can do the documentation later. Right now, get on with the database design and front-end development.” A lot of years later, that attitude has not gone away.

This paper presents a prototype for a structural analysis and design system by using the STEP for the representation and exchange of information on steel structures, by integrating the product model of steel framed structures of AP 230, the geometric and topological information of Part 42, and the detailed Finite Element Analysis information of Part 104 into an unified system. Thus, the STEP-based system makes engineering information more clearable and exchangeable between computer applications than any other conventional methods. This system may be further extended to incorporate such computer applications as detailed engineering and manufacturing information on steel structures.