Reverse Order Law for the Group Inverse in Semigroups and Rings

In this paper, we provide equivalent conditions for the two-sided reverse order law for the group inverse (ab)^# = b ^# a ^# and (ba)^# = a ^# b ^#, in semigroups and rings. Moreover, we prove that, under finiteness conditions, these conditions are also equivalent with the one-sided reverse order law (ab)^# = b ^# a ^#.     

Batching deteriorating items with applications in computer communication and reverse logistics

We study two deterministic scheduling problems that combine batching and deterioration features. In both problems, there is a certain demand for identical good quality items to be produced in batches. In the first problem, each batch is assigned an individual machine that requires a cost and a time to be activated. All the machines are identical, work in parallel, and always produce good quality items. All the items are available at time zero and they deteriorate while waiting for production. Deterioration results in a linear increase of time and cost of production. In the second problem, there is a single machine that produces good quality as well as defective items in batches. Each batch is preceded by a setup time and requires a setup cost. Defective items have to be reworked on the same machine. They deteriorate while waiting for rework. At a time to be decided, the machine switches from production to rework defective items of the current batch. After rework, every defective item has the required good quality. In both problems, the objective is to find batch partitioning such that a linear combination of the production cost and production completion time is minimized. The two problems are observed at computer service providers and also reverse logistics. In computer service providers, machines and items correspond to communication service channels and information transfer tasks, respectively. We reduce both problems to minimizing a function of one variable representing the number of batches. In an optimal solution of either problem, there are at most two different batch sizes. Linear time algorithms are proposed for both problems.     

The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/∞ system revisited: finiteness,summability, long range dependence,and reverse engineering

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads. AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10     

Radiotracer Investigation of the Copper Ore Concentration Process

One of the most difficult operations for control and identification in copper ore concentration process is grain classification in hydrocyclone batteries. In the paper radiotracer investigations of the classification process immediately give values of hydrocyclones parameters with higher accuracy than obtained from conventional methods. Presented paper includes the results of the investigation which was carried out in “Lubin” Copper Mine in Poland.     

Temporal reflectance from a light pulse irradiated medium embedded with highly scattering cores

This paper presents a new approach to utilize ultrashort pulsed laser for optical diagnostics with numerical simulations. The method is based on the use of ultrafast pulses with a pulsewidth selected according to the probed medium's radiative property and/or size. Our previous work in nonhomogeneous media has shown that the resulting time-resolved reflectance signal will have a unique characteristic: it will show a direct correlation of ballistic photon travel time and interface location, which is in between different layers or nonhomogeneous regions. The premise is based on utilizing the medium's structural information carried by the ballistic and snake photons without being masked by the diffuse photons. In this study, the space-time correlation is further explored in the case of minimally scattered photons from a large scattering coefficient core region embedded within a less-scattering medium. Time-resolved reflectance signals of the single scattering core and multiple scattering cores within a three-dimensional medium demonstrate the concept and illustrate the additional effect due to the scattered photons from the core region. A unique temporal signal profile's correlation at various detector positions with respect to the scattering core is explained in detail. The result has important implications. This approach will lead to a much simpler and more precise determination of the probed medium's composition or structure. Due to the large computational requirement to obtain the physical details of the light pulse propagation inside highly scattering multi-dimensional media, the reverse Monte-Carlo method is used. The potential applications of the method include non-destructive diagnostics, optical imaging, and remote sensing of underwater objects.     

The Effect of Oleic Acid Emulsification using SPE on Fluorite and Dolomite Flotation**

Collector OA, oleic acid, is widely used industrially for fluorite flotation. Low selectivity, dispersibility and collecting capability of the OA collector are always observed. In this study, compared with flotation of dolomite, a collector mixture of OA and SPE (styrylphenol polyoxyethylene ether) demonstrated significantly better performances for the fluorite. An optimal mass ratio 4 : 1 OA : SPE was found, and the recovery of fluorite was increased from over 85 % to more than 94 % compared with pure OA. Furthermore, the dosage of the collector agent was reduced from 50 mg mL⁻¹ to 20 mg mL⁻¹, which did not negatively impact the recovery of dolomite. The results from the contact angle tests indicated that SPE selectively increased the surface hydrophobicity of fluorite but had little effect on dolomite. Besides, zeta potential measurements and IR analyses revealed that the addition of SPE led to strong chemical adsorption on the surface of fluorite, resulting in a significant difference in the flotation performances of the two minerals. Therefore, SPE-emulsified OA is corroborated to prompt more selectivity and collecting capability on flotation of fluorite over dolomite.     

Reverse permeation of sodium ions driven by pH difference across a liquid membrane: time dependencies of membrane resistance and membrane potential in a reverse permeation system

The diffusional flux of sodium ions across a liquid membrane was observed as a reverse permeation phenomenon: sodium ions were transported across the membrane against their own concentration difference. A supported liquid membrane having stearic acid as an ionic carrier was used. The internal aqueous phase contained NaCl and HCl and the external aqueous phase contained NaOH of the same initial concentration as NaCl in the internal aqueous phase. The reverse permeation occurred with a long time delay. During the delay, sodium ions flowed from the acidic to alkaline solution. The diffusion coefficient of sodium ion estimated from the flux equation taking into account the Donnan equilibrium at the interface was found to be much greater than that in the membrane solvent, 1-octanol. In the same membrane system as for the flux measurement, the membrane conductance and the membrane potential were measured as a function of time. The time dependence of the membrane potential in the presteady state showed a biphasic behavior. The initial rapid phase could be attributed to the change in the phase boundary potential and the subsequent slow step to the change in the diffusion potential within the membrane. Before the steady membrane potential had been reached, the reverse permeation of sodium ions against their own concentration difference was not observed. During the slow relaxation process of the membrane potential, the membrane resistance decreased to approach the steady state. Moreover, the oscillation of membrane potential abruptly started at a time in the slow step of the potential change and continued during the steady state. It was suggested that, at the presteady state, the increase in the amount of water in the membrane would drive a drastic change in the state of the liquid membrane in the filter pore, e.g. an inverted micellar structure making.     

反相流动注射-化学发光法测定苯胺

在酸性介质中,苯胺与过量亚硝酸盐重氮化,剩余亚硝酸盐快速氧化亚铁氰化钾,生成的铁氰化钾与鲁米诺发生化学发光反应。据此,建立了反相流动注射 化学发光法测定苯胺的新方法。方法的线性范围为0 070～10.0mg L,检出限为0 03mg L,相对标准偏差(n=11,ρ=1.0mg L)为2 0%。方法已用于环境水样中苯胺的测定。