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.

The purpose of this study was to evaluate the environmental risks of Alborz Dam on Bababrood River in Babol city, using multi-criteria decision making methods. Initially, environmental identification of the study area was carried out, Then a list of environmental risks identified in the construction and exploitation phase was prepared and presented to environmental experts familiar with the Alborz dam area in the form of a questionnaire. environmental risks scored by environmental experts based on three indicators, Severity of occurrence, Probability of occurrence, Then environmental risks ranking was performed using TOPSIS and Fuzzy TOPSIS methods. The most important risks of Alborz dam using TOPSIS method in the construction phase, respectively: Was Obtained, Destruction of forest within the dam with a score of 0. 926, Displacement of reservoir residents with a score of 0. 837 And in the phase of operation: Thermal stratification of dam reservoir with a score of 0. 847, Landslide with a score of 0. 751. Also, the most important risks of the Alborz dam using the Fuzzy TOPSIS method in the construction phase, respectively: Was Obtained, Displacement of reservoir residents with a score of 0. 682, Demolition of forest within the dam with a score of 0. 677, And in the phase of operation, respectively: Thermal stratification of dam reservoir with a score of 0. 645, Landslide with a score of 0. 630. Finally, one method of integration (average rating method) was used to resolve the conflict between the results.

We lived in uncertain word and prediction in this uncertain word is a major issue. Prediction in cricket is very complex because there are many factors which are effecting on results. Weather, pitch, Conditions, Home grounds are some of these factors. In this article it is aimed to predict the results of PSL-2020 by using TOPSIS and Fuzzy TOPSIS methods. It will be interesting because first time in PSL history it is going to be held in Pakistan. But we use some serious factor to predict the winner of PSL-2020.

This paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by TOPSIS method. TOPSIS method is technique for order preference by similarity to ideal solution. TOPSIS is one of the renowned methods for classical multi-criteria decision-making (MCDM) problems that defines the positive ideal solution and negative ideal solution to maximize the benefit criteria and minimize the cost criteria. The best solution is a point that has the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. Because of the vagueness of the input data, triangular fuzzy numbers are applied. In addition, Euclidian distance and a new positive and negative ideal solution are used in this paper. This technique is implemented in Marand, Iran to evaluate fifteen important places based on eight criteria of temporal dimensions. Closeness coefficient values verify the ranking order of fifteen important places, which is a vital decision for the urban managers.