We study the n-dimensional magnetohydrodynamic-α (MHD-α) model in the whole space. Various regularity criteria are established with n ≤ 8, in this paper. As a corollary, the strong solution to this model exists globally, as n ≤ 4. When n = 4, uniqueness of weak solutions is also proved.

The problem of evaluating the goodness of statistical models is investigated from an information-theoretic point of view. Information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models es...

Probability models are estimated by use of penalized log-likelihood criteria related to AIC and MDL. The accuracies of the density estimators are shown to be related to the tradeoff between three terms: the accuracy of approximation, the model dimension, and the descriptive complexity of the model classes. The asymptotic risk is determined under conditions on the penalty term, and is shown to b...

and Applied Analysis 3 for any fixed T > 0. Then v,H can be extended beyond T > 0 if one of the following conditions is satisfied: 1 u ∈ C ( 0, T ;Ln/3 ) , 1.11 2 u ∈ L 0, T ;L with 2 p n q 3, n 3 < q ≤ n, 1.12 3 ∇u ∈ C ( 0, T ;Ln/4 ) , 1.13 4 ∇u ∈ L 0, T ;L with 2 p n q 4 with n 4 < q ≤ n 2 . 1.14 Remark 1.5. If we delete the harmless lower order terms ∂tu − Δu and ∂tB − ΔB in 1.1 and 1.2 , th...

This study used quantifying factors affecting desertification based on the Iranian model of desertification potentialassessment (IMDPA) to assess the current status of desertification in Bordekhun region, Iran. Bordekhun region has anarea of 214.11 km2 and is located near the city of Daiyer in Boushehr province. First, a working unit map of the regionwas selected as the basic map for evaluation...

Desertification refers to land degradation phenomenon in arid, semi-arid and dry sub-humid areas, resulting from various factors including climate variation and human activities. For evaluation and mapping of desertification many research have been conducted leading to regional and local models. In this research, among different existing methods IMDPA‌ was selected and desertification intensity...

Desertification in arid, semi-arid and dry sub-humid regions is a global environmental problem. Considering theincreasing importance of desertification and its complexity, the necessity of giving attention to desertification criteria andindices is essential. Models and methods such as MEDALUS, UNEP-FAO, and others have been proposed on local andnational scales. In this research, IMDPA was selec...

Decision matrix in group decision making problems depends on a lot of criteria. It is essential to know the necessity ofweight or coefficient of each criterion. Accurate and precise selection of weight will help to achieve the intended goal.The aim of this article is to introduce a linear programming model for recognizing the importance of each criterion inmulti criteria group decision making w...