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.

Resistance Evaluation of Capsicum spp. Germplasm to Meloidogyne incognita

[Objective] This study aimed to screen out hot pepper germplasms highly resistant to Meloidogyne incognita, thereby providing resistant resources for hot pep- per breeding. [Method] Comprehensive analysis combining cluster analysis and sub- ordinate function was conducted through determining related resistance indexes of 67 hot pepper germplasms 50 days after inoculated with M. incognita. [Result] The effects of M. incognita on related resistance indexes were significantly different am- ong the hot pepper germplasms. Egg index and gall index had abundant genetic variation with variation coefficients of 143.16% and 118.95%, respectively. Based on the gall indexes, cluster analysis of hot pepper germplasms was performed. The 67 hot pepper germplasms were divided into 4 groups （resistant, moderately resistant, susceptible and high susceptible）. The resistance intensity of the hot pepper germplasms were ranked according to the sum of subordinate function values of various resistance indexes. The total function values of Rela 2 and L506M were the largest （2.00）, indicating that these two germplasms were immune to M. incognita. The total function values of L287-2, L522-1M, L504M, L515-2, 13SM100-1, L512M, L292-1, L319, L316, L317, 13SM87-1 and Rela 5 were larger than 1.95, indicating that these germplasms were highly resistant to M. incognita. [Conclusion] This study could provide certain resistant resources for resistance breeding of hot pepper to M. incognita.

Comprehensive Evaluation on Drought Tolerance of Widely-used Rice Varieties with Subordinate Function Method

Using drought-tolerant cultivar IAPAR 9 （upland rice from Brazil） and drought-sensitive varieties IR64 as the controls, the drought tolerances of total 26 rice varieties widely used in production were evaluated with subordinate function method based on morphological, physiological and yield traits. The results showed that the trait values of grain yield per plant （GYP）, effective panicles per plant （EPP）, seed-setting rate （SSR）, panicle length （PL）, leaf relative water content （RWC） and chlorophyll content （SPAD） in all tested varieties decreased significantly under the conditions of drought stress. The subordinate function values of these traits of all tested rice varieties were thus calculated varieties. Based on the aver- age subordinate function values of all these traits, total 7 （i.e. Y Liangyou 1） and 3 （i.e. Liangyou Peijiu） rice varieties were identified as drought-tolerant and drought- sensitive varieties, respectively.

Comprehensive Evaluation on Drought Resistance of Different Flue-cured Tobacco Cultivars in Bijie Tobacco Growing Area

Based on pot experiments, major agronomic traits, biomass accumulation, leaf water-holding capacity, relative water content, root MDA content, root proline content and other physiological indicators of four different flue-cured tobacco culti-vars under drought stress were investigated, and drought resistance in various flue-cured tobacco cultivars was comprehensively analyzed with subordinate function method, aiming at clarifying the differences in drought resistance among various flue-cured tobacco cultivars. The results indicated that under drought stress, major agronomic traits, fresh and dry mass accumulation, and leaf relative water content of four different flue-cured tobacco cultivars were reduced significantly; the decreas-ing range of Yunyan 87 reached the minimum, fol owed by Bina 1, while Qianxi 1 demonstrated the maximum decreasing range. Leaf water-holding capacity of various flue-cured tobacco cultivars showed a descending order of Yunyan 87 〉 Bina 1 〉Qianxi 1 〉 Jiucaiping 2. MDA content and proline content in roots of various flue-cured tobacco cultivars increased significantly; to be specific, Yunyan 87 and Bina 1 exhibited a slight increase in root MDA content and a significant increase in root proline content, while Jiucaiping 2 and Qianxi 1 showed an opposite trend. Accord-ing to the results of comprehensive analysis with subordinate function method, drought resistance in various flue-cured tobacco cultivars showed a descending or-der of Yunyan 87 〉 Bina 1 〉 Jiucaiping 2 〉 Qianxi 1.

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 New Comprehensive Evaluation System for Thermo-Tolerance in Tomato at Different Growth Stage

With global warming, heat stress is becoming a more frequent event and a major limiting factor for crop production. The evaluation of thermo-tolerance is essential for the cultivators to obtain the heat resistant genotypes and breeders to improve the thermo-tolerance of plants. Therefore, it is very important to perfect the existing evaluation system for thermo-tolerance. In this study, 30 tomato genotypes were treated with heat stress at germination, seedling and flowering stages. Each index was different and diverse in different tomato genotypes by doing variability analysis, difference analysis and Student＇s t test. Before principal component analysis （PCA）, a positive treatment for the negative and moderation indexes was performed. After correlation analysis, the authors performed PCA （including dimensionality reduction （DR）, no dimensionality reduction （NDR） and optimal index （OI））, combining with subordinate function （SF）, weight and cluster analysis. No matter at germination or seedling stage, the members of the groups were basically identical for DR, NDR and OI. Then 10 tomato genotypes were chosen from 30 randomly for verification. Compared all the evaluation systems, OI was the simplest and also could get as credible results as other methods. Therefore, in this study, OI could be adopted and improve the efficiency during the evaluation. At germination stage, germination power （GP） can accurately evaluate the thermo-tolerance, and at seedling stage, it was fresh weight （FW）, internode length （IL） and dry matter percentage of seedling （DMP）. Finally, all the indexes in the three stages were applied correlation analysis. Seedling stage showed significant positive correlation with flowering stage. In conclusion, this work improves the current system and set up a new comprehensive evaluation method named OI, which also improves the efficiency, guarantees reliability in screening thermo-tolerance of tomato for cultivators and expedites the process of breeding for resistance.

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.