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A general notarial bond registered over movable property grants the bondholder a real security right enforceable against third parties only if the bond has been perfected by transferring possession of the property to the bondholder. Based on the facts and judgment in Absa Bank Limited v Go On Supermarket (Pty) Limited, this analysis revisits the basic principles of and requirements for the perfection of a general bond. We ultimately criticise the judgment on three scores. Firstly, the court regarded the form of delivery (transfer of possession) applicable in this matter as symbolic delivery, but we point out that it amounted to constitutum possessorium – meaning that the attempted perfection of the bond was ineffective. Secondly, the parties conceded and the court accepted that the general bond could not be perfected over property subject to the special notarial bond of another creditor. We reason that this is incorrect. It is indeed possible to attach property subject to the security right of another creditor, although the first creditor's rights will be preferred over those of the creditor who subsequently attached the property. Thirdly, the court rejected the argument that the general bond could not be perfected over property owned by another creditor in terms of a reservation-of-ownership clause in a sale agreement. However, the court should not have rejected this argument, since it was correct. A general bond indeed cannot cover property belonging to someone other than the debtor, unless the person agreed, and thus it was not possible in this case to attach the property belonging to someone other than the debtor. [ABSTRACT FROM AUTHOR]

If $A$ is a commutative $C^{\star }$ -algebra and if $\unicode[STIX]{x1D719}:A\rightarrow \mathbb{C}$ is a continuous multiplicative functional such that $\unicode[STIX]{x1D719}(x)$ belongs to the spectrum of $x$ for each $x\in A$ , then $\unicode[STIX]{x1D719}$ is linear and hence a character of $A$. This establishes a multiplicative Gleason–Kahane–Żelazko theorem for $C(X)$. [ABSTRACT FROM AUTHOR]

In stark contrast to the case of finite rank operators on a Banach space, the socle of a general, complex, semisimple and unital Banach algebra A may exhibit the ‘pathological’ property that not all traceless elements of the socle of A can be expressed as the commutator of two elements belonging to the socle. The aim of this paper is to show how one may develop an extension of A which removes the aforementioned problem. A naive way of achieving this is to simply embed A in the algebra of bounded linear operators on A, i.e. the natural embedding of A into . But this extension is so large that it may not preserve the socle of A in the extended algebra . Our proposed extension, which we shall call the Shoda-completion of A, is natural in the sense that it is small enough for the socle of A to retain the status of socle elements in the extension. [ABSTRACT FROM AUTHOR]

The National Credit Act 34 of 2005 prohibits the granting of reckless credit and also provides for certain remedies that courts can grant to consumers who have fallen victim to reckless lending practices. Depending on the circumstances, these remedies are the partial or full setting aside of the consumer's rights and obligations under the agreement; the temporary suspension of the effect of the agreement; and the restructuring of the consumer's obligations. This article investigates these remedies with a focus on the effect that they would have on a credit provider under a mortgage agreement. The argument is made that the contractual and security rights of credit providers amount to "property" for the purposes of section 25(1) of the Constitution of the Republic of |South Africa, 1996 (the property clause) and that, to some degree or another, each of these remedies involves a "deprivation" (limitation or modification) of the creditor provider's rights (property). The consequence is that, when one of these remedies is granted to a consumer, the court must tailor the remedy in such a way that the effect on the credit provider is not "arbitrary" as meant in the property clause. Therefore, the proposal is that there must be a sufficient relationship between the purpose of the remedy (to discourage reckless lending and to rectify the damage caused) and the effects thereof on the credit provider. In general, the remedy should not go further than is necessary to rectify the prejudice suffered by the consumer due to the credit provider's conduct. The formulation of the remedy should accommodate considerations such as whether and to what extent either or both parties have already performed under the agreement, and it should accordingly ensure that the consumer will not be unjustifiably enriched. The remedy should also account for the effect that it would have if the consumer is permitted to keep the property that was subject to the reckless credit agreement. The article furthermore raises doubts regarding the recent high court judgment in ABSA v De Beer 2016 3 SA 432 (GP), where all the consumer's rights and obligations under a mortgage agreement were set aside due to the credit provider's reckless conduct. Remedies like this have serious consequences and therefore it is imperative that courts carefully investigate all the effects that the order would have, so that a just and reasonable outcome is achieved. This article accordingly aims to provide some guidance with reference to the principles of constitutional property law. [ABSTRACT FROM AUTHOR]

The ability of a coal-fired power station to meet its generation targets is influenced by periods of coal shortage. In this article, we propose a multi-objective inventory model to assist with the management of coal stockpiles. The model is applicable to power utilities with a network of two or more coal-fired power stations. The aim is to determine the near-optimal amount of coal inventory to stockpile at each station in the network. A Monte Carlo coal stockpile simulator is used to incorporate stochastic uncertainty into the stockpile levels, while a metaheuristic uses the simulator as an estimator of two objective functions. The metaheuristic finds good values for the coal stockpile level at each power station in the network. The algorithm for multi-objective optimisation using the cross-entropy method is proposed as a suitable metaheuristic. A hypothetical case study is used to validate the inventory model and to showcase the optimisation results. [ABSTRACT FROM AUTHOR]

The article reviews the volume 16, number 4 of the "Arbitrary Deprivation of an Unregistered Credit Provider's Right to Claim Restitution of Performance Rendered."

LetAbe a complex semisimple Banach algebra with identity. We explore the situation whereby a portion of the elements ofAhave the same spectrum under multiplication bya ∈ A, as under multiplication byb ∈ A; and when this situation implies thataandbare the same. In particular we show that if the spectrum ofaxequals the spectrum ofbxfor allxwith a spectral radius away from the identity less than 1, thenaandbcoincide. By way of examples we show that this is the best situation possible in general. In another result we show that in the case where these spectra are finite, the assumption need only hold for an arbitrarily small open set inA, with the same conclusion. Additive versions of these results are also discussed. [ABSTRACT FROM AUTHOR]

For a complex Banach algebra A with unit 1, we give several characterizations of the scalars, that is, multiples of the identity. To a large extent, this work is a continuation and generalization of the work done on characterizations of the radical in Banach algebras. In particular it is shown that if a ∈ A has the property that the number of elements in the spectrum of ax is less than or equal to the number of elements in the spectrum of x for all x in an arbitrary neighbourhood of 1, then a is a scalar. Moreover, as a consequence of some of the results, new spectral characterizations of commutative Banach algebras are obtained. In particular, A is commutative if and only if it has the property that the number of elements in the spectrum remains invariant under all permutations of three elements in some neighbourhood of the identity. [ABSTRACT FROM PUBLISHER]

For a unital Banach algebra A over ℂ, we give improvements on the well-known multiplicative spectral characterization of the Jacobson radical, (1), in terms of several spectral parameters. In particular, we show that every non-invertible element a ϵ A for which the number of elements in the spectrum of ax is less or equal to the number of elements in the spectrum of x, for all x in an arbitrary small neighborhood of the unit, must belong to the Jacobson radical. [ABSTRACT FROM AUTHOR]