The aim of this study was to develop the mixed-effects model and compare it with nonlinear models for estimating beech (Fagus Orientalis Lipsky) and hornbeam (Carpinus betulus L. ) heights in the Shast-kalateh forests (district 1 and 2) of Gorgan. We applied a systematic sampling method to collect the field data within a 150×200 m network (308 circular plots) and in each plot, tree species were identified and height and diameter at breast height (DBH) of all trees were measured. model fitting was done in two stages: Fixed-effect approach was used in the first stage wherein candidate models where height (dependent variable) and DBH (independent variable). These were refitted in the second stage using a mixed-effect approach. The adjusted coefficient of determination and root mean square error, were used to assess the models. The results of fitting nonlinear models showed that for the beech, Curtis and Naslund models had the highest coefficient of determination of 0. 76 and the lowest root mean square error of 3. 35 and 3. 40, respectively. For hornbeam, Naslund and Michailoff models with the coefficient of determination of 0. 40 and the root mean square error of 2. 95 and 2. 90 were selected as the best models. The results of nonlinear mixed effects model showed that the R2 for beech and hornbeam species increased by 10% and 30% respectively, and the RMSE improved about 0. 65 for beech and 0. 6 for hornbeam.

A multiple marker analysis approach in the framework of the mixed-effects model was developed, allowing all markers of the entire genome to be included simultaneously in the analysis. The approach was extended to multitrait situations. The proposed method is a one-stage process, which simultaneously models the residuals and genetic effects. In addition, it can easily accommodate co-variates, extra sources of variation, fixed or random including polygenic effects and it can easily be generalized to experimental and crossing designs commonly used. The developed approach considered an unstructured co-variance model for the traits residuals and fitted a multiplicative model for the trait by marker effects. The particular multiplicative model considered herein was the factor analytic model. This provided a parsimonious model specification to limit the numberof parameters to be estimated. It was shown through the simulation study that modelling multiple phenotypes in a single linkage analysis simultaneously could markedly increase the power, compared with modelling of each phenotype separately. Correlations among phenotypes can arise from several different causal processes, which may have different implications for the power and performance of the multivariate linkage analysis. Obviously, further studies using the approach suggested herein for multitrait quantitative trait loci (QTL) mapping that specifically consider different situations, should be undertaken. Furthermore, the efficiency of the model to distinguish between a pleiotropic QTL and closely linked QTL affecting different traits is another area that needs more investigation.

I In this paper, we propose an algorithm base on decomposition technique for solving the mixed integer linear multiplicative-linear bilevel problems. In fact, this algorithm is an application of the algorithm given by G. K. Saharidis et al for the case in which the first level objective function is linear multiplicative. We use properties of quasi-concave of bilevel programming problems and decompose the initial problem into two subproblems named RMP and SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is less than an arbitrary tolerance. In conclusion, some numerical examples are presented in order to show the efficiency of algorithm.

Walnut has a high economic value because of the good quality of wood and fruits. So this species has been harvested since many years ago till today and has been introduced as a protected species. The performance of Juglans regia increases in wet years, but reduces in dry years, hence paying attention to physiological and morphological parameters in order to identify the genomic regions related to drought resistant is important for breeding programs in walnut. In this study, genetic diversity by SSR markers has been evaluated. Also, the association of used primers with physiological and morphological traits were analyzed before and after drought stress. 10 SSR primer pairs generated 53 alleles in 62 walnut seedlings. All locies showed significant difference (p£0.01) from the Hardy-Weinberg. Dendrogram of the Neighbour-Joining method showed that 62 walnut seedlings divided to four main groups. Analyses of population structure by Structure 2.3.1 software identified two sub populations (k=2). Based on association mapping analysis, by using MLM (mixed liner model) method, transpiration, conductance and photosynthesis have been controlled by WGA9 and WGA69 locies in normal condition. In stress condition WGA1 loci showed relationship with CO2 concentration that was covered %75 of variations of this trait. The results of this study can be used in breeding programs of Juglans regia to identify drought resistant varieties.

Our main purpose of this paper is to study the relationship between multiplicative maps and almost multiplicative maps between probabilistic normed algebras. We first derive some properties of invertible elements and their relation with multiplicative maps. Then we show that every complex homomorphism on elements whose probabilistic norm is equal to 1, is bounded. In the following, we give an open problem about the functionally continuous of unital commutative probabilistic Banach algebra. Finally, we prove that every almost multiplicative map that is not a multiplicative map is continuous.

Invertible members of some of the most famous multiplicative quasilinear spaces are exactly equal to invertible elements of the linear subspace of such spaces. But with the old definition of invertible elements, we do not get anything extra. So, in the present paper, we develop the introductory algebra and introduce an extended model of invertible elements. This new concept plays a fundamental role in the definition of the generalized spectrum model. These new objects are constructed in such a way that can provide acceptable results. For example, we will be able to generalize the well-known theorem ``Spectral mapping property for polynomials'' with these new notions.

In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated.