Marinari-Parisi and Supersymmetric Collective Field Theory

A field theoretic formulation of the Marinari-Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari-Parisi models a continuum limit similar to that of the d=1 bosonic string.Comment: 45 page

A Continuum Description of Super-Calogero Models

An investigation is made of the super-Calogero model with particular emphasis on its continuum formulation and possible application in the context of supersymmetrizing the bosonic collective d=1 string field theory.Comment: 80 page

Estimation of recharge using a revised CRD method

The cumulative rainfall departure (CRD) method, based on the water-balance principle, is often used for mimicking of water level fluctuations. Because of its simplicity and minimal requirement of spatial data, the CRD method has been applied widely for estimating either effective recharge or aquifer storativity, and consequently gained a focus in South Africa. This paper critically reviews this method and proposes expanded algorithm. Validation of the method under typical South African conditions is discussed based on model-generated and known cases. The study is aided with a user-friendly Excel program called Recharge Estimation Model in Excel (REME).Web of Scienc

Capture zone simulation for boreholes located in fractured dykes using the linesink concept

Delineation of capture zones for groundwater source protection is normally performed by using numerical codes which are based on the porous medium flow equation. However, boreholes are often sited in or along permeable dykes or single fracture zones through which aquifers are drained. It is very important to take into account dyke-influenced aquifers. This paper makes use of Linesink to simulate permeable dyke or fractured zones and utilises the pathline distribution to delineate the capture zones. Conditions when the influence of a fractured dyke can be considered negligible are also discussed through comparison with stagnation point in a uniform flow field. The approach may be sufficient to illustrate protection zoning requirements when dyke aquifers are considered.Web of Scienc

Advantages and disadvantages of partial codification of directors’ duties in the South African Companies Act 71 of 2008

This article offers a critical examination of partial codification and its effect on the interpretation of the directors’ standard of conduct provision. Previously, the fiduciary duties and the duty of care and skill were regulated by the common law and case law. In May 2004, the Department of Trade and Industry released a policy document entitled South African company law for the 21st century: Guidelines for corporate law reform. The policy document acknowledged that South Africa had no extensive statutory dispensation that covered the duties of directors. The policy document recognised the need to bring South African company law in line with international trends and to reflect and accommodate the changing environment for businesses locally and internationally. For the first time in South Africa’s corporate law history, the Companies Act 71 of 2008 partially codifies the fiduciary duties of directors, the duty of care and skill, and introduces the business judgement rule (also referred to as the ‘safe-harbour provisions’) into South African company law. The Companies Act 71 of 2008 prescribes   certain duties and its  extent, but the content of those duties, such as bona fides, is still determined by the common law

Supersymmetry and integrability for a class of XY central spin models

Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we report that a class of central spin models with XY interactions is also supersymmetric and integrable. The associated Bethe Ansatz solution is presented for the case where all particles are spin-1/2.Comment: 9 pages, no figure

Racemic tricarbonyl[(4a,5,6,7,8,8a-η)-2-phenyl-3,4-dihydro-2H-1-benzopyran]chromium(0)

The title compound, [Cr(C15H14O)(CO)3], displays a distorted envelope configuration of the dihydro­pyrane ring. The dihedral angle between the phenyl and phenyl­ene rings is 50.63 (4)°. The Cr0 atom is coordinated by three CO groups and the phenyl­ene ring of the flavan ligand in an η6 mode, with a common arene-to-metal distanc

Racemic tricarbon­yl(η6-7-meth­oxy­flavan)chromium(0)

In the title compound [systematic name: tricarbonyl(η6-7-methoxy-2-phenyl-3,4-dihydro-2H-1-benzopyran)chromium(0)], [Cr(C16H16O2)(CO)3], the Cr(CO)3 unit is coordinated by the phenyl­ene ring of the flavan ligand, exhibiting a three-legged piano-stool conformation, with a point to plane distance of 1.750 (1) Å. The phenyl ring is twisted away from the fused ring system by 36.49 (5)° (r.m.s. deviation = 0.027 Å; fitted atoms are the C6 ring and the attached fused-ring C and O atoms). The dihydro­pyran ring displays a distorted envelope configuration by displacement of the phenyl-bearing and the adjacent ring C atoms from the fused-ring system plane by 0.356 (2) and 0.402 (2) Å, respectively