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The induced path number $$\rho (G)$$ of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a path. A product Nordhaus-Gaddum-type result is a bound on the product of a parameter of a graph and its complement. Hattingh et al. (Util Math 94:275-285, ) showed that if G is a graph of order n, then $$\lceil \frac{n}{4} \rceil \le \rho (G) \rho (\overline{G}) \le n \lceil \frac{n}{2} \rceil $$ , where these bounds are best possible. It was also noted that the upper bound is achieved when either G or $$\overline{G}$$ is a graph consisting of n isolated vertices. In this paper, we determine best possible upper and lower bounds for $$\rho (G) \rho (\overline{G})$$ when either both G and $$\overline{G}$$ are connected or neither G nor $$\overline{G}$$ has isolated vertices. [ABSTRACT FROM AUTHOR]

The method introduced in this paper extends the trim-loss problem or also known as 2D rectangular SLOPP to the multiple sheet situation where N same size two-dimensional sheets have to be cut optimally producing demand items that partially or totally satisfy the requirements of a given order. The cutting methodology is constrained to be of the guillotine type and rotation of pieces is allowed. Sets of patterns are generated in a sequential way. For each set found, an integer program is solved to produce a feasible or sometimes optimal solution to the N-sheet problem if possible. If a feasible solution cannot be identified, the waste acceptance tolerance is relaxed somewhat until solutions are obtained. Sets of cutting patterns consisting of N cutting patterns, one for each of the N sheets, is then analysed for optimality using criteria developed here. This process continues until an optimal solution is identified. Finally, it is indicated how a given order of demand items can be totally satisfied in an optimal way by identifying the smallest N and associated cutting patterns to minimize wastage. Empirical results are reported on a set of 120 problem instances based on well known problems from the literature. The results reported for this data set of problems suggest the feasibility of this approach to optimize the cutting stock problem over more than one same size stock sheet. The main contribution of this research shows the details of an extension of the Wang methodology to obtain and prove exact solutions for the multiple same size stock sheet case. [ABSTRACT FROM AUTHOR]

This paper is concerned with wastage reduction in constrained two-dimensional guillotine-cut cutting stock problems, often called trim loss problems. A number of researchers report in the literature on algorithmic approaches to find exact solutions for the trim loss problem. Alternative heuristic functions are investigated and applied to the modified Wang method. This involves the sharpening of underestimates used in the methods heuristic function. Two aspects of these solution approaches are considered and some empirical results are given. The first part considers the feasibility to construct more informed heuristic functions. The second part investigates the role of more informedness on the computational cost of these search processes. [ABSTRACT FROM AUTHOR]

There are many practical decision problems that fall in the category of network flow problems and numerous examples of applications can be found in areas such as telecommunication, logistics, engineering and computer science. In this paper, the feasibility of representing a network flow model as a tree network model and subsequently solving it using an extended tree knapsack approach is investigated. To compare and validate the proposed technique, a specific case study (an oil pipeline design problem) was chosen from the literature that can be used as a basis for the paper. Following on an overview of the pipeline design problem, the extended tree knapsack model is developed. The application of this approach to the oil pipeline design problem is then presented. Results indicate that it is feasible to apply an extended tree knapsack approach to solve certain network flow problems. [ABSTRACT FROM AUTHOR]

Parts of the Local Access Telecommunication Network planning problem may be modelled as an Extended Tree Knapsack Problem. The Local Access Telecommunication Network can contribute up to 60% of the total network costs. This paper presents partitioning algorithms that use standard off-the-shelf software coupled with enhanced modelling. Enhancements to the algorithms and empirical results for both the Tree Knapsack Problem and Extended Tree Knapsack Problem are presented. [ABSTRACT FROM AUTHOR]

Let G = ( V, E) be a graph. A set $${S \subseteq V}$$ is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted by γ tr( G), is the smallest cardinality of a total restrained dominating set of G. We show that if δ ≥ 3, then γ tr( G) ≤ n − δ − 2 provided G is not one of several forbidden graphs. Furthermore, we show that if G is r − regular, where 4 ≤ r ≤ n − 3, then γ tr( G) ≤ n − diam( G) − r + 1. [ABSTRACT FROM AUTHOR]

Most people tend to focus on the visible part of water. Therefore, water quality has been undervalued in water management, with people often not having the necessary understanding and knowledge to manage water quality effectively. Policies and strategies also tend to give more attention to managing quantity. This paper highlights the legislative principles of equity, efficiency and sustainability in the context of water resource management in South Africa. It provides two examples of practical implementation of these principles from a water quality perspective and highlights the challenges relating to the realization of these principles in practice. [ABSTRACT FROM AUTHOR]

The optimal allocation of internal auditing time among competing projects is a multi-criteria problem that includes both qualitative and quantitative factors. This paper discusses an integrated approach where the analytic hierarchy process (AHP) is used to deal with qualitative risk assessments and a goal programming (GP) model to distribute available hours in such a way that risk is minimised. Additional considerations, such as maximum and minimum allowable project hours, risk reducing factors and risk levels, are also taken into account. Following a description of the models and framework, a brief case study is presented in which the framework was empirically evaluated. [ABSTRACT FROM AUTHOR]

The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth [13] included cardinality constraints to derive tight upper bounds for the 0-1 Knapsack Problem. Encouraged by their results, we partition the search space by using equality cardinality constraints. Instead of solving the original problem, an equivalent problem, which consists of one or more 0-1 Knapsack Problem with an exact cardinality bound, is solved. By explicitly including a bound on the cardinality, one is able to reduce the size of each subproblem and compute tight upper bounds. Good feasible solutions found along the way are employed to reduce the computational effort by reducing the number of trees searched and the size of the subsequent search trees. We give a brief description of two Lagrangian-based Branch-and-Bound algorithms proposed in Kruger [9] for solving the exact cardinality bounded subproblems and report on results of numerical experiments with a sequential implementation. Implications for and strategies towards parallel implementation are also given. [ABSTRACT FROM AUTHOR]

Most of the time, the criticism is not aimed at one's person, but at our actions and once one realises that, it is easier to accept that there are different ways to reach the same goal and that positive criticism can actually help us to do so more effectively. Copyright of South African Pharmaceutical Journal is the property of Medpharm Publications (Pty) Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. I do not think so, but we certainly need to keep a close watch on our thought pattern to ensure we maintain a positive, "can-do" attitude at all times. [Extracted from the article]

Reports on the differences in physiological response to the drug succinyldicholine of the African elephant and buffalo. Route of administration of the drug; Observations of drug effect in the neuromuscular junction; Selection of drugs that act as neuromuscular blockers.

Investigates arterial blood pressure in anaesthetized South African elephants. Development of a pink frothy discharge from external nares; Death of some elephants caused by severe lung edema; Recommendation to add azaperone to immobilization mixtures when elephants are subjected to herding prior to darting.

Investigates arterial blood pressure and blood gas composition in white rhinoceroses immobilized with either etorphine/fentanyl or etorphine/azaperone anaesthesia. Higher arterial pressure observed in the etorphine/phentanyl group; Hypoxemia and hypercapnia associated with anaesthesia.

Abstract: The paper analyses and discusses the concept of integrated water resources management (IWRM) and its application in South Africa. The central characteristics of IWRM are discussed and another feature, good governance, is highlighted as being crucial for effective IWRM. The paper focuses on those features that distinguish water management challenges in developing countries from those experienced in developed countries (where most of the current definitions of IWRM originated). The case study discussed in this paper, the Mhlatuze Catchment in South Africa, was selected as being representative of a catchment situated in one of the country’s 19 water management areas (WMAs) where attempts are being made to implement IWRM. The available evidence indicates that three sets of reasons are responsible for the failure to achieve full implementation of IWRM in the Mhlatuze Catchment. First, the national custodian of water resources – DWAF – continues to experience severe internal (technical capacity) problems that hinder its efforts to successfully manage the Usutu to Mhlatuze WMA (of which the Mhlatuze Catchment forms a part) as a unit. Secondly, while IWRM is, on paper, a key part of national policy, the concept has not been fully accepted and practiced by local water managers. Thirdly, a range of institutional challenges persist because there is insufficient alignment and cooperation between the policies of different government departments and the practices of different water use sectors that impact on water. [Copyright &y& Elsevier]

Prosthetic care is a vital aspect of healthcare and rehabilitation for veterans and servicemembers with major traumatic limb loss. Our survey queried 581 veterans and servicemembers with limb loss from the Vietnam and Operation Iraqi Freedom (OIF)/Operation Enduring Freedom (OEF) conflicts. Among survey participants, 78.2% from the Vietnam conflict and 90.5% from the OIF/OEF conflict currently use prosthetic devices. In Vietnam respondents, 78% received prosthetic care from private sources, 16% from Department of Veterans Affairs (VA) prosthetic laboratories, 0.9% from Department of Defense (DOD), and 5% from multiple sources. In OIF/OEF respondents, 42% received prosthetic care from private sources, 9% percent from VA, 39% from DOD, and 10% from multiple sources. Participants identified their satisfaction with current prosthetic devices and prosthetic services. Reports of pain, sweating, skin irritation, and problems with socket fit continue to be significant issues for participants from both conflicts regardless of level of amputation or site of service. In those with upper-limb loss who used myoelectric prostheses, minimal effect on prosthesis use and satisfaction was noted. Among lower-limb loss participants from both conflicts, notable differences existed in prosthesis satisfaction by source of care. [ABSTRACT FROM AUTHOR]