At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

Technical efficiency,managerial efficiency and objective-setting in the educational system: an international comparison

This study uses data envelopment analysis to analyse the efficiency of educational systems in 31 countries. This type of evaluation is of interest both when formulating a model for analysis and when applying such a model empirically. The efficiency of an educational system must take into account the students' economic and social background, as this is an environmental factor that decisively influences their performance. This is a highly important aspect and so we propose a specific evaluative process for it. Secondly, we evaluate the efficiency of educational systems in different countries, an analysis that has few forerunners since the majority of previous research has focused on analysing a single country. The results suggest that, in general, the most efficient management of educational systems can be found in those countries with a Communist past. They also suggest that there is a series of developed countries, which, judging by the results obtained, could increase their students' performance with even fewer resources than those currently allocated to their educational systems.     

Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

In a financial market with one riskless asset and n risky assets whose prices are lognormal, we solve in a closed form the problem of a pension fund maximizing the expected CRRA utility of its surplus till the (stochastic) death time of a representative agent. We consider a unique asset allocation problem for both accumulation and decumulation phases. The optimal investment in the risky assets must decrease during the first phase and increase during the second one. We accordingly suggest it is not optimal to manage the two phases separately, and outsourcing of allocation decisions should be avoided in both phases. JEL: G23, G11 MSC 2000: 62P05, 91B28, 91B30, 91B70, 93E20     

A rule-based risk decision-making approach and its application in China's customs inspection decision

This paper addresses a kind of risk decision-making problem existing widely in public administration and business management, which is characterized by (1) occurrence probabilities of states of nature can be estimated by analysing historical observations, but historical observations of different objects are unhomogeneous, (2) the relation between observations and occurrence probabilities of states of nature are affected by some qualitative and quantitative indicators, (3) it is a real-time decision-making problem, that is, there are many decisions for different objects to be made in a limited time, (4) considering decision's execution, impact of resource constrains is an important issue in decision-making process. In this paper, we develop a rule-based approach to address the problem. In the proposed approach, a two-step clustering method is employed to classify objects into categories, and observations in each category can be approximately viewed as homogeneous. For objects in each category, occurrence probabilities of states of nature are estimated by logistic regression, and the decision rule is obtained through solving an optimization model, which is to minimize the total decision risks while satisfying resource constrains. Effect and efficacy of our approach are illustrated through its application to China's customs inspection decision.     

Synergistic effect between 4-(2-pyridylazo) resorcin and chloride ion on the corrosion of cold rolled steel in 0.5 M sulfuric acid

The corrosion inhibition of 1-(2-pyridylazo)-2-naphthol (PAR) on the corrosion of cold rolled steel in 0.5 M sulfuric acid (H₂SO₄) was studied using weight loss method and potentiodynamic polarization method. Results obtained revealed that together with chloride ion, PAR is an effective corrosion inhibitor for steel corrosion in sulfuric acid. It was found that for steel corrosion inhibition in the presence of single PAR in sulfuric acid the Temkin adsorption isotherm may be used to explain the adsorption phenomenon. For the mixture of PAR and NaCl used as corrosion inhibitor, however, the Langmuir adsorption isotherm can be used to satisfactorily elucidate the adsorption of mixture of PAR and NaCl. Potentiodynamic polarization studies showed that single PAR mainly acts as a cathodic inhibitor for the corrosion of steel in 0.5 M sulfuric acid. The mixture of PAR and chloride ion, however, acts as a mixed type inhibitor that mainly inhibits cathodic reaction of the steel corrosion in sulfuric acid. By means of electrochemical polarization tests, a desorption potential at ca. −370 mV was observed for the adsorption of mixture of PAR and chloride ion, when potential reaches this value, adsorbed inhibitor molecule heavily departs from the steel surface. For the mixture of PAR and chloride ion, thermodynamic parameters such as adsorption heat, adsorption entropy and adsorption free energy were obtained from experimental data of the temperature studies of the inhibition process at four temperatures ranging from 30 to 45 °C, the kinetic data such as apparent activation energies and pre-exponential factors at different concentrations of the inhibitor were calculated, and the effect of the apparent activation energies and pre-exponential factors on the corrosion rates of cold rolled steel was discussed. The most suitable range of inhibitor concentration was discussed. The inhibitive action was satisfactorily explained by using both thermodynamic and kinetic models. Synergism between chloride ion and PAR was proposed. The results obtained from weight loss and potentiodynamic polarization were in good agreement.     

An Enhancement of the Drezner—Wesolowsky Algorithm for Single-Facility Location with Maximin of Rectilinear Distance

In this note, we examine the algorithm of Drezner and Wesolowsky for locating a facility with maximin rectilinear distance to a given set of demand points. The concept of the closest-point constraint is introduced as a technique for increasing the efficiency of the algorithm. This potential increase in efficiency is demonstrated by an example.     

Modelling treatment effects in the HIV/AIDS epidemic

Advances in recent treatments for HIV/AIDS patients have shown dramatic outcomes in extending the incubation period and AIDS survival time, while also providing significant improvements in the quality of patients' lives. A compartmental model is proposed to analyse the effects of the various treatment regimens which have been introduced. The results produced are in good agreement with routinely collected data relating to levels of HIV/AIDS incidence and prevalence in the UK homosexual population. Some parameter values within the model are obtained from surveys, census results, etc, but others are derived using a maximum likelihood estimation procedure. Finally, the model is used to project levels of incidence and prevalence over the next few years, and to investigate several possible scenarios.     

The energy exchange and the optimum length of the sample tube of opfirl

The energy exchange between the pumping laser and FIR signal in the optically pumped FIR laser (OPFIRL) system was studied. The iteration method has been used to calculate the power density of the pumping and FIR signals at any point along the optical axis of the sample tube. It was found that the power density of the FIR signal did not always increase along the length of the laser tube. There was a maximum FIR power density at the appropriate point in the sample tube. If the distance of maximum power point from the entrance of the OPFIRL tube was taken as the length of sample tube Z_opt, the maximum FIR laser output should be obtained. This was the optimum length of OPFIRL tube. The value of Z_opt was closely related to the parameter of OPFIRL such as the pumping power density, the pumping detuning and the frequency of the FIR laser. The energy-exchange and the maximum output of the fir laser were calculated under the ideal condition.