Analytical solutions of N‐person games

The possibility of analytical solutions of N‐person games is presented. A simple formula provides valuable information about the outcomes of such games with linear payoff functions and Pavlovian agents. Experiments performed with our simulation tool for the multiagent stag hunt dilemma game are presented. For the case of Pavlovian agents the game has nontrivial but remarkably regular solutions. If both payoff functions are linear and the real solutions of Eq. (2) are both positive, then the analytical solutions are remarkably accurate. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Open retractions onto n-ods

We characterize dendrites which admit an open retraction onto an arbitrary n-od. The paper contains also several corollaries and two problems concerning the subject     

Representation of molecules by atomic charges: A new population analysis

For the calculation of atomic charges in molecules, a new fast procedure based on extended Mulliken population analysis is presented. The reliability of the new population analysis is tested within the AM1 approximation and the results are compared in detail with those obtained by different methods reported in the literature.     

Semispectroscopic and quantitative structure-property relationship estimates of the equilibrium and vibrationally averaged structure and dipole moment of 1-buten-3-yne

Systematic quantum chemical calculations have been performed to obtain precise estimates of the equilibrium and vibrationally averaged molecular structure and electric dipole moment of vinylacetylene (VA, 1-buten-3-yne). Anharmonic (cubic and semi-diagonal quartic) MP2/cc-pVTZ force fields in normal coordinates were computed to account for anharmonic vibrational effects, including zero-point contributions to the rotational constants and the electric dipole moment. A simultaneous weighted least-squares structural refinement was performed, resulting in the best semispectroscopic estimate of the re structure of VA. The refinement was based on experimentally measured ground-state rotational constants of two isotopologs of VA corrected to equilibrium values using MP2/cc-pVTZ vibration-rotation interaction constants and all-electron CCSD(T)/aug-cc-pVTZ structural constraints. The semispectroscopic re structure of VA agrees excellently with the high-level CCSD(T)/aug-cc-pVTZ ab initio structure. The most dependable, CCSD(T)/cc-pVQZ//CCSD(T)/aug-cc-pVTZ equilibrium electric dipole moment of VA, in D, is mua= 0.4088, mub= 0.0004, and muc= 0. The vibrationally corrected a-component of 0.4214 D is in excellent agreement with one of the available experimental values. The present analysis shows that mub is negligible even after vibrational correction. A simple quantitative structure-property relationship (QSPR) model resulted in a highly similar estimate, 0.45 D, for the electric dipole moment of VA.     

Vector algebra and molecular symmetry: a tribute to Professor Josiah Willard Gibbs

Vector algebra, as developed by Josiah Willard Gibbs, is much simpler than matrix or tensor algebra, therefore, it is more suitable to introduce the students of chemistry into the wonderful world of molecular symmetry. A program based on elementary vector algebra has been written to determine all symmetry elements and symmetry operations of rigid molecular structures. The program also contains data for 57 point groups common in chemistry. Therefore, it automatically supplies the particular point group to which the structure belongs. Since the locations of the nuclei related to the symmetry elements are also revealed by the program, even the detailed notation of the framework group of the molecular structure can be deduced. The program can be a great help in determining the symmetries of the normal modes of vibration, too.     

优化固氮活性模型信息研究—双齿配体DPPE和DPPM对固氮酶促反应的影响

报道了某些双齿配体对固氮酶促反应影响的研究结果．发现１，２－双（二苯基磷）－乙烷（ＤＰＰＥ）对固氮酶酶促乙炔还原反应有促进作用，但同时又抑制了固氮酶的放氢反应。而比ＤＰＰＥ少一个－ＣＨ２－链的双（二苯基磷）－甲烷（ＤＰＰＭ）却不能表现出对固氮酶促乙炔还原活力的促进作用．对照固氮酶ＭｏＦｅ－蛋白Ｘ－光衍射结构分析结果和量子化学近似计算所导出的固氮酶活性中心结构模型提出了ＤＰＰＥ促进酶促乙炔还原反应的一种可能的解释．