THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.

Identification and Evaluation of Resistance to Meloidogyne incognita in Bitter Gourd Germplasms

[ Objective] This study aimed to identify and evaluate the resistance of bitter gourd germplasms to Meloidogyne incognita. [ Method] A total of 71 bit-ter gourd germplasms were artificially inoculated with M. incognita at seedling stage to investigate the effects of M. incognita on resistance indexes of bitter gourd seedlings. Cluster analysis and subordinate function analysis were performed to identify and evaluate the resistance of experimental materials. [ Result] The infec-tion of M. incognita increased the variation coefficients of resistance indexes. The resistance to M. incognita varied significantly among different bitter gourd germ- plasms. Based on gall index, 71 bitter gourd germplasms were divided into five types by cluster analysis, including resistant materials, moderately resistant materi-als ,moderately susceptible materials, susceptible materials and highly susceptible materials. The subordinate function analysis showed that total subordinate func-tion values of Y107, Y109, Y108, Y51, Y105, Y81, Y89, Y140 and Y94 exceeded 1.95 , indicating high resistance to M. incognita. [ Conclusion] This study could provide resistant materials for breeding root-knot nematode resistant varieties of bitter gourd.

Comprehensive Evaluation of Aluminum Tolerance in Sugarcane Varieties at the Seedling Stage and Screening of Identification Indexes

[Objectives]Aluminum toxicity is one of the important stress factors affecting sugarcane quality and yield in south China,breeding aluminum tolerant varieties is a cost-effective and practical way.In order to explore the characteristics of aluminum toxicity tolerance in different sugarcane varieties and establish the comprehensive evaluation system for screening and breeding new varieties with aluminum toxicity tolerance,this study was conducted to perform comprehensive evaluation of aluminum tolerance in different sugarcane varieties and screening of identification indexes.[Methods]With 26 sugarcane varieties bred in different ecological areas as materials,through a pot experiment,nine indexes which include sugarcane plant height,root length,shoot dry weight,root dry weight,root-shoot ratio,relative chlorophyll content,leaf proline content,and shoot and root aluminum contents at the seedling stage under acid-aluminum stress and control conditions were measured,and the aluminum toxicity tolerance coefficients of various indexes of each variety were calculated.On this basis,the aluminum tolerance of all varieties was comprehensively evaluated by principal component analysis,subordinate function,cluster analysis and stepwise regression analysis.[Results]Compared with the control,the nine indexes showed more abundant variation among the 26 varieties under acid-aluminum stress.The correlation analysis confirmed that the contributions of the nine measured indexes to aluminum tolerance were significantly overlapped,and the subsequent principal component analysis summarized and combined the ones with strong correlation among the nine indexes,converting them into two new independent comprehensive indexes.The cumulative contribution rate showed that the two new indexes covered 82.448%of the information of the original nine indexes.Then,the comprehensive evaluation D values of the acid-aluminum tolerance of the 26 varieties were calculated based on the subordinate function values combined with the weights of the contribution rates of the two new comprehensive indexes.By clustering analysis on the D values,the 26 varieties were divided into 3 groups.Three varieties with the highest D values among the 26 varieties,Yunzhe 11-1074,Zhongtang 2 and Haizhe 28,were classified as varieties with strong aluminum tolerance,and 11 varieties including Yuegan 56 and Guitang 58,were moderately aluminum tolerant,while 12 varieties including Haizhe 32 and Yunrui 10-187 were sensitive to aluminum stress.Finally,the optimal regression equation analysis was carried out with the comprehensive evaluation D value of aluminum tolerance as the dependent variable and the aluminum toxicity tolerance coefficients of various indexes as independent variables,and the evaluation model of aluminum tolerance in sugarcane was established.Root length,root dry weight,relative chlorophyll content,leaf proline content,shoot aluminum content and root aluminum content,which had significant effects on aluminum tolerance of sugarcane seedlings,were selected as the evaluation indexes of acid-aluminum tolerance of sugarcane seedlings.[Conclusions]This study not only obtained a number of aluminum-tolerant varieties,but also provides a theoretical basis and reference for future genetic breeding of aluminum-tolerant sugarcane.

A Study on the Xenia Effect in Castanea henryi

The xenia effect results in pollen affecting the setting rate and the appearance and quality of fruits. To further understand this phenomenon,we investigated the xenia effect in Castanea henryi using the cultivars ‘Huali 1', ‘Huali 2', ‘Huali 3', and ‘Huangzhen' as materials. Twenty combinations of self-, cross-, and natural pollination were undertaken in a chestnut orchard in Chenzhou City, Hunan Province, China. Significant differences were observed among the pollination combinations in terms of the time of fruit ripening, rate of fruit setting, size of the barbed shell and nut, and content of soluble sugars, fats, proteins, amylose, and vitamin C. No significant differences were observed with regard to nut rate,content of total starch, and moisture content. The fruit quality of the 20 pollination combinations was evaluated using a subordinate function method,and showed that Huali 2 × Huali 3 was the best combination, and Huangzhen × Huangzhen was the most ineffective combination. Therefore, we recommend the combination of Huali 2 × Huali 3 for the future production of C. henryi.