In order to study the genotype x environment interaction, replicated yield trials were performed using 19 barley genotypes in a randomized complete block design with four replications, at eight agricultural research stations of temperate regions for three years. Mean grain yield and two environmental variables, mean air temperature and mean soil pH were used for Redundancy Analysts. In this method, two variables RA1 and RA2 were constructed. Each one was the linear combination of environmental variables mentioned above. The genotypes 3 and 15 in relation to RA1 and the genotypes 1, 11, 12, 13, 14 and 19 in relation to RA2 had large percentage sum of squares per genotype (R2) These values for genotypes 3 and 15 were 87 and 81, and for next six cultivates mentioned above were 22, 20, 38, 29, 18 and 36, respectively. Thus in comparison with other genotypes, the interactions among these cultivars and the locations under study were determined mainly by air temperature and soil pH, and these genotypes were more sensitive to the temperature and pH. The R2 for RA1 and RA2 models were small for the genotypes 2, 4, 5, 7 and 16. Therefore, these cultivars were considered to be adapted and insensitive to the environmental factors. The genotypes 5 and 7 had the high grain yield, too. The replacement of residuals obtained from the regressions of local indices and the environmental variables in Redundancy analysis model, and doing Partial Redundancy analysis, showed that in addition to the air temperature and soil pH, the other environmental variables were more or less effective in forming the genotype by location interactions. Cultivars 5, 17 and 18 showed smaller interactions as compared to others. To construct the LISREL model, the means of air temperature, soil pH, date of maturity, date of heading and plant height as the environment and phonologic variables, and the mean grain yield and 1000 grain weight as the variables related to the genotype × environment interaction, were entered in the model. Results indicated the further importance of air temperature and grain yield variables. Also combination of LISREL and Redundancy analysis models indicated that because of large coefficients of grain yield and air temperature in the LISREL model, study of genotype× environment interaction using these variables by Redundancy analysis model was worthwhile.      

In this paper kinematics model of a nonholonomic mobile manipulator is formulated. The kinematics equations for a mechanical mobile manipulator are developed in such a way that the kinematics interaction between the mobile platform and mechanical manipulator explicitly appears in the equations. In both conditions the motion constraints and kinematics Redundancy are considered and analyzed. These concepts are expanded in general cases by using special subjects, on linear algebra and functional analysis. A useful and unique kinematics model for Redundancy resolution of mobile manipulators is introduced by defining specified variables. Finally, the application of the model is verified by simulation results in order to find the maximum allowable load of a mobile manipulator.

In this note, our aim is to present the relation between msets and L-fuzzy sets. We prove that an mset can be viewed as an L-fuzzy set. An mset topology can be viewed as an L-topology. Therefore, it follows that mset topologies are redundant in theoretical sense.

This paper proposes an efficient algorithm based on memetic algorithm (MA) for a Redundancy allocation problem without component mixing (RAPCM) in a series-parallel system when the Redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general RAPCM assume that the type of a Redundancy strategy for each subsystem is pre-determined and known a priori. In general, active Redundancy has traditionally received greater attention; however, in practice both active and cold-standby redundancies may be used within a particular system design. The choice of the Redundancy strategy then becomes an additional decision variable. Thus, the problem is to select the best Redundancy strategy, component and Redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. Due to its complexity and NP-hardness, it is so difficult to optimally solve such a problem by using traditional optimization tools. To validate the performance of the proposed MA in terms of solution quality, a number of test problems are examined and the robustness of this algorithm is then discussed. Finally, the related results are reported and it is shown that the proposed MA performs well.

To increase the reliability of a specific system, using redundant components is a common method which is called Redundancy allocation problem (RAP). Some of the RAP studies have focused on k -out-of- n systems. However, all of these studies assumed predetermined active or standby strategies for each subsystem. In this paper, for the first time, we propose a k -out-of-n system with a choice of Redundancy strategies. Therefore, a k-out-of- n series–parallel system is considered when the Redundancy strategy can be chosen for each subsystem. In other words, in the proposed model, the Redundancy strategy is considered as an additional decision variable and an exact method based on integer programming is used to obtain the optimal solution of the problem. As the optimization of RAP belongs to the NP-hard class of problems, a modified version of genetic algorithm (GA) is also developed. The exact method and the proposed GA are implemented on a well-known test problem and the results demonstrate the efficiency of the new approach compared with the previous studies.