Comparative Analysis between Triple Cross and Double Cross among Three Parents of Crop

In this paper, the triple cross and double cross were compared by analysing the characteristics of genetic variation in progeny of triple cross hybrid and double cross hybrid among three parents, based on the successful breeding practices of Beijing No.10. The results showed that the selection duration of double cross was one year shorter than that of triple cross. The F1 generations of single cross hybrids of double cross showed higher breeding value, and the multiple cross-ing timing of triple cross was more flexible. More wheat varieties have been bred by triple cross, instead of double cross. Moreover, the double cross has a disad-vantage of heavy workload.

Triple Crossing Numbers of Graphs

We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.

The (e,2e) triple differential cross sections of Cu^+ (3p) in coplanar asymmetric geometry

The three-body distorted=wave Born approximation has been used to calculate the （e, 2e） triple differential cross sections （TDCSs） of Cu＋ （3p） in different kinematical variables in coplanar asymmetric geometry. The angles 4°, 10° and 20° were selected as the scattering electron angles. Under high incident energy （≥500 eV） and high asymmetric detection energy, the binary peaks showed abnormal splits. Such abnormal splits have not been observed in atomic target and outer valence orbitals of ionic target, which indicates that an （e, 2e） process for inner valence orbitals of ionic target would be more complicated than outer valence orbitals. Furthermore, some pronounced peaks appeared at certain ejected angles. We considered that these pronounced peaks are probably related to one kind of double-binary collision.

Triple-differential cross section for single ionization of H_2 by electron impact

The triple-differential cross section （TDCS） for the （e,2e） ionization of a hydrogen molecule is calculated using the molecule distorted-wave Born approximation （MDWBA）. Distorted waves are obtained by solving momentum-space coupled-channel Lippmann-Schwinger equations, including the ground state and the lowest-lying electronic state of b3Σu . TDCSs at the incident energy 100 eV in coplanar asymmetric geometry are reported. The present calculations are compared with the available experimental measurements and the theoretical results.

Triple differential cross sections of magnesium in doubly symmetric geometry

A dynamically screened three-Coulomb-wave （DS3C） method is applied to study the single ionization of magnesium by electron impact. Triple differential cross sections （TDCS） are calculated in doubly symmetric geometry at incident energies of 13.65, 17.65, 22.65, 27.65, 37.65, 47.65, 57.65, and 67.65 eV. Comparisons are made with experimental data and theoretical predictions from a three-Coulomb-wave function （3C） approach and distorted-wave Born approximation （DWBA）. The overall agreement between the predictions of the DS3C model and the DWBA approach with the experimen- tal data is satisfactory.

On the Analysis Method of the Triple Test Cross Design

The analysis method of the triple test cross design has been discussed carefully from the two factor experiment design and the genetic models of additive dominant effect and of epistasis effect.Two points different from the previous reports have been concluded: (1)both the degrees of freedom of the orthogonal terms C2 and C3 are m, (2)the denominator in the F test to C2 and C3 is the error mean of square between plots.

Effect of initial-state target polarization on the single ionization of helium by 1-keV electron impact

We report new results of triple differential cross sections for the single ionization of helium by 1-KeV electron impact at the ejection energy of 10 eV. Investigations have been made for both the perpendicular plane and the plane perpendicular to the momentum transfer geometries. The present calculation is based on the threewCoulomb wave function. Here we have also incorporated the effect of target polarization in the initial state. A comparison is made between the present calculation with the results of other theoretical methods and a recent experiment [Diirr M, Dimopoulou C, Najjari B, Dorn A, Bartschat K, Bray I, Fursa D V, Chen Z, Madison D H and Ullrich J 2008 Phys. Rev. A 77 032717]. At an impact energy of 1 KeV, the target polarization is found to induce a substantial change of the cross section for the ionization process. We observe that the effect of target polarization plays a dominant role in deciding the shape of triple differential cross sections.

The effect of wave function orthogonality on the simultaneous ionization and excitation of helium

Within the framework of the first-order Born approximation, the triple differential cross sections （TDCSs） for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.

Polarization effect in(e,2e) reaction process for Ar(3s) in coplanar asymmetric geometry

The （e, 2e） triple differential cross sections （TDCSs） of Ar （3s） are calculated by using distorted-wave Born approx- imation under coplanar asymmetric geometry. The incident electron energy is 113.5 eV, and the scattering electron angle 01 is -15~. The ejected electron energy is set at 10 eV, 7.5 eV, 5 eV, and 2 eV, respectively. The polarization effects have been discussed and the polarization potential Vpol changing from a second-order to a fourth-order term has been analyzed. Our calculated TDCSs have been compared with reported experimental and theoretical results, and the calculated TDCSs of polarization potential up to the fourth order could give a good fit with experimental results in the binary region, but fail to predict the correct recoil-to-binary ratio in most cases.

Second-order Born calculation of coplanar symmetric(e, 2e) process on Mg

The second-order distorted wave Born aPl6roximation （DWBA） method is employed to investigate the triple differen- tial cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for magnesium at excess energies of 6 eV-20 eV. Comparing with the standard first-order DWBA calculations, the inclusion of the second-order Born term in the scattering amplitude improves the degree of agreement with experiments, especially for backward scattering region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric （e, 2e） problems of two-valence-electron target in low energy range.

Study of(e,2e) process on potassium at 6 e V-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation （DWBA） method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections （TDCS） of coplanar doubly symmetric （e, 2e） collisions for the alkali target potassium at excess energies of 6 eV-60 eV. Compared with the previous first-order DWBA calculations, the present theoretical model improves the degree of agreement with experiments, especially for the backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric （e, 2e） problems in low and intermediate energy ranges.

Electron impact ionization of neon and neonic ions under distorted-wave Born approximation

The （e, 2e） triple differential cross sections of 2s orbitals of neon and neonic ions （Z = 11-14） are calculated using a distorted-wave Born approximation under coplanar asymmetric geometry. The calculated results show that, with the increase in the nuclear charge number Z, the amplitude of triple differential cross sections decreases. The angle difference between the binary peak position and the direction of momentum transfer gradually increases with the increase in the nuclear charge Z, and a new structure appears at an ejected angle 90° 〈 θ2 〈 120°. Three kinds of collision processes are proposed to illustrate the formation mechanism of such collision peaks.