Caveats - Limited extensions effectively unlimited

The decision of Young J in McCosker v Lovitt (1995) 12 BCL 146 paces an interpretation upon s 74J of the Real Property Act 1900 (NSW) likely to surprise the unwary respondent to proceedings in New South Wales involving an application for an order to extend a caveat. Further, the similarity in critical respects between s74J and the legislation relating to lapse and extension of caveats in some jurisdictions when contrasted with other lapse provisions suggests that a court order extending a caveat for a specified period only may have very different consequences in different jurisdictions.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

Asymmetric price range effects on vertical extensions

Vertical line extensions, both step-up and step-down, are common occurrence in consumer products. For example, Timex recently launched its luxury high-end Valentino line. On the other hand, many companies use downscale extensions to increase the overall sales volume. For instance, a number of luxury watch brands recently introduced watch collections with lower price points, like TAG Heur’s affordable watch the Aquaracer Calibre 5. Previous literature on vertical extensions has investigated how number of products in the line (Dacin and Smith 1994), the direction of the extension, brand concept (Kim, Lavack, and Smith 2001), and perceived risk (Lei, de Ruyter, and Wetzels 2008) affect extensions’ evaluation. Common to this literature is the use of models based on adaptation-level theory, which states that all relevant price information is integrated into a single prototype value and used in consumer judgments of price (Helson 1947; Mazumdar, Raj, and Sinha 2005). In the current research we argue that, while adaptation-level theory can be viewed as a useful simplification to understanding consumers’ evaluations, it misses out important contextual influences caused by a brand’s price range. Drawing on research on range-frequency theory (Mellers and Cooke 1994; Parducci 1965) we investigate the effects of price point distance and parent brand’s price range on evaluations of vertical extensions. Our reasoning leads to two important predictions that we test in a series of three experiments...

Diminishing effects of perceived fit on vertical extensions

A common finding in brand extension literature is that extension’s favorability is a function of the perceived fit between the parent brand and its extension (Aaker and Keller 1990; Park, Milberg, and Lawson 1991; Volckner and Sattler 2006) that is partially mediated by perceptions of risk (Milberg, Sinn, and Goodstein 2010; Smith and Andrews 1995). In other words, as fit between the parent brand and its extension increases, parent brand beliefs become more readily available, thus increasing consumer certainty and confidence about the new extension, which results in more positive evaluations. On the other hand, as perceived fit decreases, consumer certainty about the parent brand’s ability to introduce the extension is reduced, leading to more negative evaluations. Building on the notion that perceived fit of vertical line extensions is a function of the price/quality distance between parent brand and its extension (Lei, de Ruyter, and Wetzels 2008), traditional brand extension knowledge predicts a directionally consistent impact of perceived fit on evaluations of vertical extensions. Hence, vertical (upscale or downscale) extensions that are placed closer to the parent brand in the price/quality spectrum should lead to higher favorability ratings compared to more distant ones.

Path algebra for mobile robots

In this paper, we introduce a path algebra well suited for navigation in environments that can be abstracted as topological graphs. From this path algebra, we derive algorithms to reduce routes in such environments. The routes are reduced in the sense that they are shorter (contain fewer edges), but still connect the endpoints of the initial routes. Contrary to planning methods descended from Disjktra’s Shortest Path Algorithm like D , the navigation methods derived from our path algebra do not require any graph representation. We prove that the reduced routes are optimal when the graphs are without cycles. In the case of graphs with cycles, we prove that whatever the length of the initial route, the length of the reduced route is bounded by a constant that only depends on the structure of the environment.

Real-World Extensions To Scheduling Algorithms Based On Lagrangian Relaxation

Recently, efficient scheduling algorithms based on Lagrangian relaxation have been proposed for scheduling parallel machine systems and job shops. In this article, we develop real-world extensions to these scheduling methods. In the first part of the paper, we consider the problem of scheduling single operation jobs on parallel identical machines and extend the methodology to handle multiple classes of jobs, taking into account setup times and setup costs, The proposed methodology uses Lagrangian relaxation and simulated annealing in a hybrid framework, In the second part of the paper, we consider a Lagrangian relaxation based method for scheduling job shops and extend it to obtain a scheduling methodology for a real-world flexible manufacturing system with centralized material handling.

Improving decisions for invasive species management: Reformulation and extensions of the Panetta-Lawes eradication graph

Aim: Effective decisions for managing invasive species depend on feedback about the progress of eradication efforts. Panetta & Lawes. developed the eradograph, an intuitive graphical tool that summarizes the temporal trajectories of delimitation and extirpation to support decision-making. We correct and extend the tool, which was affected by incompatibilities in the units used to measure these features that made the axes impossible to interpret biologically. Location: Victoria, New South Wales and Queensland, Australia. Methods: Panetta and Lawes' approach represented delimitation with estimates of the changes in the area known to be infested and extirpation with changes in the mean time since the last detection. We retain the original structure but propose different metrics that improve biological interpretability. We illustrate the methods with a hypothetical example and real examples of invasion and treatment of branched broomrape (Orobanche ramosa L.) and the guava rust complex (Puccinia psidii (Winter 1884)) in Australia. Results: These examples illustrate the potential of the tool to guide decisions about the effectiveness of search and control activities. Main conclusions: The eradograph is a graphical data summary tool that provides insight into the progress of eradication. Our correction and extension of the tool make it easier to interpret and provide managers with better decision support. © 2013 John Wiley & Sons Ltd.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Max-Coloring Paths: Tight Bounds and Extensions

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V, E) with a non-negative weight function w on V such that Sigma(k)(i=1) max(v epsilon Ci) w(v(i)) is minimized, where C-1, ... , C-k are the various color classes. Max-coloring general graphs is as hard as the classical vertex coloring problem, a special case where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring abroad class of trees and show it can be solved in time O(vertical bar V vertical bar+time for sorting the vertex weights). When vertex weights belong to R, we show a matching lower bound of Omega(vertical bar V vertical bar log vertical bar V vertical bar) in the algebraic computation tree model.

A denotational semantics for the generalized ER model and a simple ER algebra

The recent spurt of research activities in Entity-Relationship Approach to databases calls for a close scrutiny of the semantics of the underlying Entity-Relationship models, data manipulation languages, data definition languages, etc. For reasons well known, it is very desirable and sometimes imperative to give formal description of the semantics. In this paper, we consider a specific ER model, the generalized Entity-Relationship model (without attributes on relationships) and give denotational semantics for the model as well as a simple ER algebra based on the model. Our formalism is based on the Vienna Development Method—the meta language (VDM). We also discuss the salient features of the given semantics in detail and suggest directions for further work.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.