Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Boundary value estimates for harmonic forms

We prove a bound for the -norm of harmonic forms in terms of certain -norms of their normal and tangential components. In turn, this is used to show the -norm equivalence of the normal and tangential components of harmonic forms on manifolds.

     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Efficiency of connected binary block designs when a single observation is unavailable

In this paper the problem of finding the design efficiency is considered when a single observation is unavailable in a connected binary block design. The explicit expression of efficiency is found for the resulting design when the original design is a balanced incomplete block design or a group divisible, singular or semiregular or regular with ₁>0, design. The efficiency does not depend on the position of the unavailable observation. For a regular group divisible design with ₁>0, the efficiency depends on the position of the unavailable observation. The bounds, both lower and upper, on the efficiency are given in this situation. The efficiencies of designs resulting from a balanced incomplete block design and a group divisible design are in fact high when a single observation is unavailable.The work of the first author is sponsored by the Air Force Office of Scientific Research under Grant AFOSR-90-0092.On leave from Indian Statistical Institute, Calcutta, India. The work of the third author was supported by a grant from the CMDS, Indian Institute of Management, Calcutta.     

A Note on Casoratian Solutions to Two-Dimensional Toda Lattice

In this short paper we generalize the conditions that Casoratian entries satisfy for the two-dlmenslonal Toda lattice. Although we finally conclude that our generalization is trivial in some sense for getting new solutions, our discussion is still helpful for the study of Wronskian technique.     

Higher-Dimensional KdV Equations and Their Soliton Solutions

A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.     

不同晶形纳米碳酸钙的制备及其表面改性研究进展

本文综述了不同晶形纳米碳酸钙的制备方法、纳米碳酸钙表面改性技术的研究现状以及表面改性方法,分析了目前纳米碳酸钙制备及表面改性技术存在的问题,并对其发展前景作了展望.     

Determining Nuclear Form factor for Detection of Dark Matter in Relativistic Mean Field Theory

In this work, we derive the nuclear form factor for the spin-independent collision between the WIMPs and nucleus in terms of the relativistic mean field (RMF) theory. Comparison with the traditional form factors which are commonly used in literature is given and it is found that our results are slightly above that of the 2PF model by 4% to 8%, but deviate from the Helm form factor by 15% to 25% for the whole recoil energy spectrum of 0 ∽ 100keV. Moreover, taking Xe and Ge as examples, we show the dependenceof the form factor on the recoil energy.     

张弦梁(桁架)结构的找形方法——分级卸载法

对张弦梁(桁架)结构的找形问题进行了深入研究,根据该类结构的受力特点,提出了分级卸载法。该方法无需假定结构零状态几何,而可以一次得到对应于初状态(即预应力态)几何的结构施工放样尺寸(即零状态几何),并通过分级加载对该方法的精度进行了检验。