Let F be an (α, β)-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group G. We consider the automorphism and Isometry groups of the Finsler manifold (G, F) and their intersection. We prove that for an arbitrary left invariant vector field X and any compact subgroup K of automorphisms which X is invariant under them, there exists an (α, β)-metric such that K is a subgroup of its Isometry group.

In this paper, we classify up to Isometry the connected and simply connected Riemannian nilmanifolds on six-dimensional filiform Lie groups and we compute the corresponding Isometry groups.

We construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite p-group G. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup H of G. When G is a semidirect product of two finite p-groups H and K, both H and K admit Gray maps and the corresponding homomorphism  y: H®Aut (K) is compatible with the Gray map of K in a sense which we will explain, we construct type-II Gray maps for G. Finally, we consider group codes over the dihedral group D8 of order 8 given by the set of their generators, and derive a representation and an encoding procedure for such codes.

When the density current smashes into the lower dense fluid mass a plunge region will occur. Since the plunge depth bounds between density current and ambient fluid, determining of this point is important. In this research, the hydraulic parameters of density current and bed slope of stagnant fluid were investigated. To achieve the purpose of this research a physical model was built in the hydraulic laboratory of Shahid Chamran University (SCU) and various experiments were performed. In the experiments, the plunge depth at the different discharge of density current and density difference 6, 9, 13 and 16 kg/m3 at three slopes 8, 12 and 16% was measured. Then using Flow-3D under RNG turbulence model, plunge depth was simulated for the same experimental condition. The comparison of results obtained showed that the predicted plunge depth with Flow-3D under RNG turbulence model had a high and satisfactory accuracy. Finding showed that for the 8% bed slope, the results of RNG turbulence model 14% was more than experimental data. While, for the entire slope, the results of RNG turbulence model was predicted 10.5% in average more than measured data. Generally, the statistical investigations showed that the RNG turbulence model with satisfactory precision estimated the plunge point depth.

Context and purpose. Obtaining the private GAP standard for healthy product certification due to costs is out of reach in many small and mediumsized farms among smallholder farmers. groupGAP has provided a much-anticipated alternative where operators and farmers' cooperatives can pay the cost of certification on a cost-sharing basis. Therefore, the purpose of this research was to explain the development strategies of GAP standard with emphasis on groupGAP in the rice production system of Mazandaran province. Methodology/approach. Current research is qualitative and data analysis was conducted in the grounded theory method, during a three-stage process of open coding, central coding, and selective coding. The data collection tool included an in-depth and semi-structured interview with a qualitative content analysis technique, which was analyzed through Maxquda software. The statistical population of the research was 18 experts and specialists of the Agricultural Jihad Organization and managers of the Rice Farmers Cooperative Company of Mazandaran Province, who were selected by the purposeful sampling method. Findings and conclusions. After extracting the concepts of the content analysis of the interviews, 9 conceptual codes out of 30 initial codes were identified in the first stage of coding. After refining and merging, the codes were classified into 3 subcategories. These components include the group certification system, the development of publicGAP programs and the development of private GAP. In the group certificates, the two dimensions of contract system development and guaranteed purchase, the development of the cooperative company for the production of healthy products have been taken into consideration. It is recommended to strengthen the organizations and cooperatives of farmers and exporters, especially to strengthen young farmers and women organizations. Originality. Originality/innovation: Due to the importance of the GAP standard issue and farmers' problems in providing the audit fees and establishment of GAP certificate, so far, no comprehensive study has been carried out in Iran on the development of operational strategies for the establishment of GAP and groupGAP. Therefore, the current research is an attempt to provide a useful framework in explaining GAP standard development strategies with the participation of farmers in adopting the government, private, group and cooperative certification system.

The effects of two isolates of Pasteuria penetrans were evaluated on root knot nematodes, Meloidogyne javanica and M. incognita-R2 on two month seedlings of Badamiriz pistachio cultivar. Two experiments were carried out with two concentrations of endospores of PA and PNG isolates (104 & 6.4×105 endospores/g soil) and cadusafos (50 Mg/1500 g soil) in a Randomized Complete Block Design in green house condition were planted in pot and treatments were applied at seedling stage (4-6 leaf). 80 days after planting the seedlings were removed from soil and all stages of nematodes were extracted and counted in roots and soils. The results showed that the PA isolate with 104 endospores/g soil was the best treatment in decreasing 88.8٪ of the final population of M. incognita-R2 in comparison with control, also PNG isolate with 6.4×105 endospores/g soil was the best treatment after nematicide in decreasing 71.2% of the final population of M. javanica when compared with control.

We chracterize orbit spaces and orbits of cohomogeneity two isometric actions on hyperbolic spaces.