图解法求实长方法的变换推广及“形”“数”关系分析

图解法求实长的方法有三种,即旋转法、直角三角形法和换面法。三种方法既有联系又有区别,虽然作图形式不同,但三种作图方法的原理一致:都是依据正投影原理及直线的投影特性来求得实长,三种求实长方法的实质相同:直线AB的实长等于其三个几何尺度的平方根,即AB=(△X)2+(△Y)2+(△Z)2姨。三种方法互为变式:直角三角形法是换面法的简化形式,换面法是直角三角形法的一般形式,旋转法则可看成是直角三角形法和换面法的最简形式。三种方法中直角三角形法应用最广。三种方法都可以利用直角三角形的性质及代数计算来加以证明。

Comparison of Growth and Development Patterns of Fenneropenaeus chinensis (Osbeck) Huanghai No.1 and the First Generation of Wild Population

[Objective] The aim was to estimate the developmental characteristics of Huanghai No.1 and the first generation of wild population in Fenneropenaeus chinensis for providing a reference for the development, feeding management and breeding. [Method] Four growth models were used to fit the growth patterns of 15 morphological traits. The squared multiple correlation coefficient (R2 ) of the Cubic growth model was higher than the other three models, so it was selected to investigate the growth pattern and age in month at inflexion. [Result] Ages in month at inflexion of body weight in Huanghai No.1 and the G1 population were 2.87 (body weight at inflexion was 14.98 g) and 4.05 (body weight at inflexion was 26.26 g), respectively. In addition, Ages in month at inflexion of morphological characters in Huanghai No.1 were from 0.51 to 3.07. CL had the most rapid growth rate, followed by AW, CH, AH, CW, BL, FL, AL5, AL3, AL4, TL, AL2, AL1, and AL6. Ages in month at inflexion in the G 1 population were from 2.38 to 3.08, except that of AL2, and the order of achieving the most rapid growth rate was AL2, AL1, AL3, AL4, CH, AL5, CW, FL, AH, AW, TL, CL, BL, and AL6, that delayed one month than that of Huanghai No.1 except AL2 and AL1. [Conclusion] The development of Huanghai No.1 cultivar was advanced for about one month compared to that of the G1 population.

Correlations among Important Fruit Quality and Plant Characteristics of Some Fig Genotypes

Experiments were carried to determine correlations of important fruit and plant characteristics using 30 fig genotypes. The correlation coefficients between these traits were calculated using SAS program. Fruit weight, fruit diameter, fruit length, neck length, ostiolium width, abscission of the stalk from the twig, ease of peeling, fruit skin cracks, thickness of the fruit skin, texture of skin, fruit ribs, fruit internal cavity, TSS （total soluble solids）, pH, acidity, TSS/acidity, trunk diameter, shoot length, yield per tree were traits examined in the study. According to five-year data, fruit weight was found to have positive correlation by fruit diameter （r = 0.92; P 〈 0.01）, fruit length （r = 0.81; P 〈 0.01）, neck length （r = 0.35; P 〈 0.01）, ostiolium width （r = 0.23; P 〈 0.01）, trunk diameter （r = 0.26; P 〈 0.01）, fruit skin cracks （r = 0.26; P 〈 0.01） and negative correlation by TSS （r = -0.26; P 〈 0.01） and fruit ribs （r = -0.21; P 〈 0.01）. Relations between some traits such as ostiolium width, abscission of the stalk from the twig, ease of peeling, fruit skin cracks, texture of skin and fruit ribs are deviated based on the years. Some relationships between fig fruit characteristics exist, which may help researchers to solve some problems such as ostiolium width and fruit skin cracking. These studies may contribute to producing fruit with a good quality and help to evaluate new cultivars.

Simplification of Double Folding Model Calculations in Study of Interaction Between Two Deformed Nuclei

The Double Folding （DF） model calculation of the internuclear potential in heavy-ion interactions when the participant nuclei are deformed in their ground states involves a six-dimensional integral. Using the multipole expansion in these calculations, the DF six-dimensional integral reduce to the sum of the products of three single-dimensional integrals. In this paper we have presented a procedure for the calculation of the radius dependent functions in the multipole expansion of the nuclear density and their Fourier transforms. We have also reduced the DF model integrals to the sum of the single dimensional integrals using the obtained relations for the radius dependent functions in the multipole expansion and their Fourier transforms.

An experimental investigation into electromyography, constitutive relationship and morphology of crucian carp for biomechanical “digital fish”

Currently, the integrated biomechanical studies on fish locomotion come into focus, so it is urgent to provide reliable and sys- tematic experimental results, and to establish a biomechanical ＂digital fish＂ database for some typical fish species. Accord- ingly, based on the control framework of ＂Neural Control - Active Contraction of Muscle - Passive Deformation＂, the elec- tromyography （EMG） signals, the mechanical properties and the constitutive relationship of skin, muscle, and body trunk, as well as morphological parameters of crucian carp, are investigated with experiments, from which a simplified database of bio- mechanical ＂digital fish＂ is established. First, the EMG signals from three lateral superficial red muscles of crucian carp, which was evolving in the C-start movement, were acquired with a self-designing amplifier. The modes of muscle activity were also investigated. Secondly, the Young＇s modulus and the reduced relaxation function of crucian carp＇s skin and muscle were de- termined by failure tests and relaxation tests in uniaxial tensile ways, respectively. Viscoelastic models were adopted to deduce the constitutive relationship. The mechanical properties and the angular stiffness of different sites on the crucian carp＇s body trunk were obtained with dynamic bending experiments, where a self-designing dynamic bending test machine was employed. The conclusion was drawn regarding the body trunk of crucian carp under dynamic bending deformation as an approximate elastomer. According to the above experimental results, a possible benefit of body effective stiffness increasing with a little energy dissipation was discussed. Thirdly, the distribution of geometric parameters and weight parameters for a single experi- mental individual and multiple individuals of crucian carp was studied with experiments. Finally, considering all the above re- suits, generic experimental data were obtained by normalization, and a preliminary biomechanical ＂digital fish＂ database for crucian carp was established.

The separable Hamiltonian system and complete biorthogonal expansion method of Mindlin plate bending problems

A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.