SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

The tachyon potential in the sliver frame

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Closed Time-like Curves and Inertial Frame Dragging: How to Time Travel via Spacetime Rotation

As the number of solutions to the Einstein equations with realistic matter sources that admit closed time-like curves (CTC's) has grown drastically, it has provoked some authors [10] to call for a physical interpretation of these seemingly exotic curves that could possibly allow for causality violations. A first step in drafting a physical interpretation would be to understand how CTC's are created because the recent work of [16] has suggested that, to follow a CTC, observers must counter-rotate with the rotating matter, contrary to the currently accepted explanation that it is due to inertial frame dragging that CTC's are created. The exact link between inertialframe dragging and CTC's is investigated by simulating particle geodesics and the precession of gyroscopes along CTC's and backward in time oriented circular orbits in the van Stockum metric, known to have CTC's that could be traversal, so the van Stockum cylinder could be exploited as a time machine. This study of gyroscopeprecession, in the van Stockum metric, supports the theory that CTC's are produced by inertial frame dragging due to rotating spacetime metrics.

Territorial Cohesion through Spatial Policies: An Analysis with Cultural Theory and Clumsy Solutions

The European Territorial Cohesion Policy has been the subject of numerous debates in recent years. Most contributions focus on understanding the term itself and figuring out what is behind it, or arguing for or against a stronger formal competence of the European Union in this field. This article will leave out these aspects and pay attention to (undefined and legally non-binding) conceptual elements of territorial cohesion, focusing on the challenge of linking it within spatial policies and organising the relations. Therefore, the theoretical approach of Cultural Theory and its concept of clumsy solution are applied to overcome the dilemma of typical dichotomies by adding a third and a fourth (but not a fifth) perspective. In doing so, normative contradictions between different rational approaches can be revealed, explained and approached with the concept of ‘clumsy solutions’. This contribution aims at discussing how this theoretical approach helps us explain and frame a coalition between the Territorial Cohesion Policy and spatial policies. This approach contributes to finding the best way of linking and organising policies, although the solution might be clumsy according to the different rationalities involved.

Technical Challenges in the Construction of Gothic Vaults: The Gothic Theory of Structural Design

The construction of a Gothic vault implied the solution of several technical challenges. The literature on Gothic vault construction is quite large and its growth continues steadily. The main challenge of any structure is that, during and after construction, it must be "safe", that is, it must not collapse. Indeed, it must be amply safe, able to support different loads for long periods of time. Masonry architecture has shown its structural safety for centuries or millennia. The Pantheon of Rome stands today after almost 2,000 years without having needed any structural reinforcement (of course, the survival of any building implies continuous maintenance) . Hagia Sophia in Istanbul, finished in the 6th century AD, has withstood not only the dead loads but also many severe earthquakes . Finally, the Gothic cathedrals, with their appearance of weakness, are• more than a half millennium old. The question arises of what the source of this amazing strength is and how the illiterate master masons were able to design such daring and safe structures . This question is usually evaded in manuals of Gothic architecture. This is quite surprising, the structure being a fundamental part of Gothic buildings. The present article aims to give such an explanation, which has been studied in detail elsewhere. In the first part, the Gothic design methods "V ill be discussed. In the second part, the validity of these methods wi11 be verified within the frame of the modern theory of masonry structures . References have been reduced to a minimum to make the text simpler and more direct.

Adaptive control system based on lineal control theory for the path-following problem of a car-like mobile robot

The objective of this paper is to design a path following control system for a car-like mobile robot using classical linear control techniques, so that it adapts on-line to varying conditions during the trajectory following task. The main advantages of the proposed control structure is that well known linear control theory can be applied in calculating the PID controllers to full control requirements, while at the same time it is exible to be applied in non-linear changing conditions of the path following task. For this purpose the Frenet frame kinematic model of the robot is linearised at a varying working point that is calculated as a function of the actual velocity, the path curvature and kinematic parameters of the robot, yielding a transfer function that varies during the trajectory. The proposed controller is formed by a combination of an adaptive PID and a feed-forward controller, which varies accordingly with the working conditions and compensates the non-linearity of the system. The good features and exibility of the proposed control structure have been demonstrated through realistic simulations that include both kinematics and dynamics of the car-like robot.

A theory for optimal monitoring of marine reserves

Monitoring of marine reserves has traditionally focused on the task of rejecting the null hypothesis that marine reserves have no impact on the population and community structure of harvested populations. We consider the role of monitoring of marine reserves to gain information needed for management decisions. In particular we use a decision theoretic framework to answer the question: how long should we monitor the recovery of an over-fished stock to determine the fraction of that stock to reserve? This exposes a natural tension between the cost (in terms of time and money) of additional monitoring, and the benefit of more accurately parameterizing a population model for the stock, that in turn leads to a better decision about the optimal size for the reserve with respect to harvesting. We found that the optimal monitoring time frame is rarely more than 5 years. A higher economic discount rate decreased the optimal monitoring time frame, making the expected benefit of more certainty about parameters in the system negligible compared with the expected gain from earlier exploitation.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

A temporary connection for an aluminium space frame

This thesis examines theoretically and experimentally the behaviour of a temporary end plate connection for an aluminium space frame structure, subjected to static loading conditions. Theoretical weld failure criterions are derived from basic fundamentals for both tensile and shear fillet welds. Direct account of weld penetration is taken by incorporating it into a more exact poposed weld model. Theoretical relationships between weld penetration and weld failure loads, failure planes and failure lengths are derived. Also, the variation in strength between tensile and shear fillet welds is shown to be dependent upon the extent of weld penetration achieved/ The proposed tensile weld failure theory is extended to predict the theoretical failure of the welds in the end plate space frame connection. A finite element analysis is conducted to verify the assumptions made for this theory. Experimental hardness and tensile tests are conducted to substantiate the extent and severity of the heat affected zone in aluminium alloy 6082-T6. Simple transverse and longitudinal fillet welded specimens of the same alloy, are tested to failure. These results together with those of other authors are compared to the theoretical predictions made by the proposed weld failure theories and by those made using Kamtekar's and Kato and Morita's failure equations, the -formula and BS 8118. Experimental tests are also conducted on the temporary space frame connection. The maximum stresses and displacements recorded are checked against results obtained from a finite element analysis of the connection. Failure predictions made by the proposed extended weld failure theory, are compared against the experimental results.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Theory, the uncanny and the sacred

This paper examines the related but different concepts of the uncanny and the sacred. Drawing on two cases – one fictional and one real – and using Žižek’s Symbolic-Real-Imaginary as an organising frame, the paper analyses how the uncanny and the sacred are connected. It then proceeds to examine the role of theorising in sacralising the uncanny and profaning the sacred. Finally, it briefly discusses how theory might be re-enchanted.

Theory games

This paper examines the remarkable and unexplored correspondence between games (and board games in particular) and what is commonly understood as theory in the social sciences. It argues that games exhibit many if not most of the attributes of theory, but that theory is missing some of the features of games. As such, game provide a way of rethinking what we mean by theory and theorizing. Specifically, games and their relationship with the ‘real’ world, provide a way of thinking about theory and theorizing that is consistent with recent calls to frame social inquiry around the concept of phrónēsis.

Relocating the Frame: Object-Oriented (1.) and Locative Art (2.) Environments

The locative project is in a condition of emergence, an embryonic state in which everything is still up for grabs, a zone of consistency yet to emerge. As an emergent practice locative art, like locative media generally, it is simultaneously opening up new ways of engaging in the world and mapping its own domain. (Drew Hemment, 2004) Artists and scientists have always used whatever emerging technologies existed at their particular time throughout history to push the boundaries of their fields of practice. The use of new technologies or the notion of ‘new’ media is neither particularly new nor novel. Humans are adaptive, evolving and will continue to invent and explore technological innovation. This paper asks the following questions: what role does adaptive and/or intelligent art play in the future of public spaces, and how does this intervention alter the relationship between theory and practice? Does locative or installation-based art reach more people, and does ‘intelligent’ or ‘smart’ art have a larger role to play in the beginning of this century? The speakers will discuss their current collaborative prototype and within the presentation demonstrate how software art has the potential to activate public spaces, and therefore contribute to a change in spatial or locative awareness. It is argued that the role and perhaps even the representation of the audience/viewer is left altered through this intervention. 1. A form of electronic imagery created by a collection of mathematically defined lines and/or curves. 2. An experiential form of art which engages the viewer both from within a specific location and in response to their intentional or unintentional input.

Evaluating consumer price perception: a mental accounting and frame dependent perspective

In this thesis, we evaluate consumer purchase behaviour from the perspective of heuristic decision making. Heuristic decision processes are quick and easy mental shortcuts, adopted by individuals to reduce the amount of time spent in decision making. In particular, we examine those heuristics which are caused by framing – prospect theory and mental accounting, and examine these within price related decision scenarios. The impact of price framing on consumer behaviour has been studied under the broad umbrella of reference price, which suggests that decision makers use reference points as standards of comparison when making a purchase decision. We investigate four reference points - a retailer's past prices, a competitor's current prices, a competitor's past prices, and consumers' expectation of immediate future price changes, to further our understanding of the impact of price framing on mental accounting, and in turn, contribute to the growing body of reference price literature in Marketing research. We carry out experiments in which levels of price frame and monetary outcomes are manipulated in repeated measures analysis of variance (ANOVA). Our results show that where these reference points are clearly specified in decision problems, price framing significantly affects consumers' perceptions of monetary gains derived through discounts, and leads to reversals in consumer preferences. We also found that monetary losses were not sensitive to price frame manipulations.