We are concerned with the study of the following nonlocal diffusion problem, ut = J * u − u + f(u) in  W× (0, T), u = 0 in (RN-W ) × (0, T), u(x, 0) = u0(x)³ 0 in , W where W is a bounded domain in RN with smooth boundary ¶W, J*u(x, t) = ¦RN J(x - y)u(y, t)dy, J: RN ® R is a kernel which is nonnegative, symmetric (J(z) = J(-z)), bounded and = 1 and f : (-¥, b) ® (0, ¥) is a C1 convex, increasing function, lims a®b ¦ (s) = ¥, ¦b0 d/¦(a)< ¥ with b a positive constant. The initial datum u0Î = C1 o/(W) is nonnegative in W, with ‖u0‖¥ =supzÎW ïU0(x)ïnder some assumptions, we show that if ku0k1 is large enough, then the solution of the above problem quenches in a finite time, and its quenching time goes to that of the solution of the differential equation, a’ (t) = ¦ (a (t)), t > 0, a (0) = ‖u0‖¥, as ‖u0‖¥ tends to b. Finally, we give some numerical results to illustrate our analysis.

(Process) tolerancing based on the (Process) capability studies is the optimistic and pragmatic approach of determining the manufacturing (Process) tolerances. On adopting the define-measure-analyze-improve-control approach, the (Process) potential capability index (Cp) and the (Process) performance capability index (Cpk) values of identified (Process) characteristics of connecting rod machining (Process) are achieved to be greater than the industry benchmark of 1.33, i.e., four sigma level. The tolerance chain diagram methodology is applied to the connecting rod in order to verify the manufacturing (Process) tolerances at various operations of the connecting rod manufacturing (Process). This paper bridges the gap between the existing dimensional tolerances obtained via tolerance charting and (Process) capability studies of the connecting rod component. Finally, the (Process) tolerancing comparison has been done by adopting a tolerance capability expert software.

Ten polycyclic aromatic hydrocarbons associated with suspended particulate matter in the ambient air were collected at two sampling sites: urban and suburban residential areas of Yokohama, Japan from 1999 to 2005. The concentrations of target compounds were determined using gas chromatography-mass spectrometry. The total concentrations were higher in urban residential area than suburban residential area. They ranged from 0.31 to 6.16 ng/m3 with a mean of 2.07 ng/m3 and 0.33 to 2.87 ng/m3 with a mean of 1.02 ng/m3 in the urban and suburban residential areas, respectively. The predominant compounds determined both in the urban and suburban residential areas were benzo [b] fluoranthene, benzo [ghi] perylene, indeno [1, 2, 3-cd] pyrene and benzo [e] pyrene. The concentrations of 5- and 6-ring polycyclic aromatic hydrocarbons were higher in the urban than the suburban residential area, accounting for 77.3 % and 72.1% of total polycyclic aromatic hydrocarbons, respectively. Source identification was performed by principal component analysis. Two principal components were identified for each study area and these accounted for 95.9% and 83.3% of total variance, respectively. The results revealed that stationary source and vehicle emissions were the major pollution sources in the studied areas. The impact of emission regulations for automobiles in large Japanese cities, which were enacted during 2002 and 2003, was also studied. Based on the average total concentration, emission reduction was 47.8% and 18.6% in urban residential and suburban residential areas, respectively.

Statistical (Process) control is an excellent quality assurance tool to improve the quality of manufacture and ultimately scores on end-customer satisfaction. SPC uses (Process) monitoring charts to record the key quality characteristics (KQCs) of the component in manufacture. This paper elaborates on one such KQC of the manufacturing of a connecting rod of an internal combustion engine. Here the journey to attain the (Process) potential capability index (Cp) and the (Process) performance capability index (Cpk) values greater than 1.33 is elaborated by identifying the root cause through quality control tools like the cause-and-effect diagram and examining each cause one after another. In this paper, the define-measure-analyze-improve-control (DMAIC) approach is employed. The definition phase starts with (Process) mapping and identifying the KQC. The next phase is the measurement phase comprising the cause-and-effect diagram and data collection of KQC measurements. Then follows the analysis phase where the (Process) potential and performance capability indices are calculated, followed by the analysis of variance (ANOVA) of the mean values. Finally, the (Process) monitoring charts are used to control the (Process) and prevent any deviations. By using this DMAIC approach, standard deviation is reduced from 0.48 to 0.048, the Cp values from 0.12 to 1.72, and the Cpk values from 0.12 to 1.37, respectively.

A procedure is presented that synthesizes fractional crystallization separation (Process)es to obtain pure solids from multi-component solutions. The method includes a procedure to generate a network flow model to identify alternative (Process) designs for fractional crystallization. The main advantage of this systematic procedure with respect to other reported procedures is using non-equilibrium solubility values for crystallizers and mixing tanks as (Process) points. By employing an approach factor to show the distance from equilibrium, a non-linear programming model is obtained. Solving the non-linear programming model, optimal (Process) flowsheet and the corresponding non-equilibrium solubility values for (Process) points are presented. The proposed procedure is used to design an optimal flowsheet for production of sodium carbonate and sodium sulfate from Burkeite. The results show that when the approach factor goes to unity, the maximum efficiency of separation (Process) is attained which corresponds to the minimum total flow rates and total cost of the (Process).