Synthesis and structures of nitroxyalkyl methylphosphonates

The reactions of ethylene glycol mononitrate and glycerol 1,3-dinitrate with methylphosphonic dichloride afforded new nitroxyalkyl methylphosphonates.     

A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given.     

An Enumerative Geometry for Magic and Magilatin Labellings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from set systems to rational linear forms. Dedicated to the memory of Claudia Zaslavsky, 1917–2006 Received August 10, 2005     

On the structure of finite coverings of compact connected groups

Finite-sheeted covering mappings onto compact connected groups are studied. We show that for a covering mapping from a connected Hausdorff topological space onto a compact (in general, non-abelian) group there exists a topological group structure on the covering space such that the mapping becomes a homomorphism of groups. To prove this fact we construct an inverse system of covering mappings onto Lie groups which approximates the given covering mapping. As an application, it is shown that a covering mapping onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by degree of the mapping. We also get a criterion for triviality of coverings in terms of means and prove that each finite covering of G is equivalent to a polynomial covering.     

Application of Electron-Shelving Detection via 423 nm Transition in Calcium-Beam Optical Frequency Standard

A new scheme of small compact optical frequency standard based on thermal calcium beam with application of 423 nm shelving detection and sharp-angle velocity selection detection is proposed. Combining these presented techniques, we conclude that a small compact optical frequency standard based on thermal calcium beam will outperform the commercial caesium-beam microwave dock, like the 5071 Cs clock （from Hp to Agilent, now Symmetricom company）, both in accuracy and stability.     

TRANILAST ^1H^13CNMR谱分析及其结构的鉴定

本文用COSY,CHCOR等二维核磁共振技术对TRANILAST,2[]3-(3.4-二甲基苯基)1-氧代-2-丙烯基]氨基]苯甲到进行了~1H、~(13)C NMR谱数据分析及归属,并结合~(13)C弛豫时间T_1 及变温实验对合成产品进行了结构鉴定.     

Molecular dynamics simulations on the structures and properties of ε-CL-20-based PBXs ——Primary theoretical studies on HEDM formulation design

Five polymer bonded explosives (PBXs) with the base explosive ε-CL-20 (hexanitrohexaazaisowurtzi- tane), the most important high energy density compound (HEDC), and five polymer binders (Estane 5703, GAP, HTPB, PEG, and F2314) were constructed. Molecular dynamics (MD) method was employed to investigate their binding energies (Ebind), compatibility, safety, mechanical properties, and energetic properties. The information and rules were reported for choosing better binders and guiding formula- tion design of high energy density material (HEDM). According to the calculated binding energies, the ordering of compatibility and stability of the five PBXs was predicted as ε-CL-20/PEG > ε-CL-20/ Estane5703 ≈ε-CL-20/GAP > ε-CL-20/HTPB > ε-CL-20/F2314. By pair correlation function g(r) analyses, hydrogen bonds and vdw are found to be the main interactions between the two components. The elasticity and isotropy of PBXs based ε-CL-20 can be obviously improved more than pure ε-CL-20 crystal. It is not by changing the molecular structures of ε-CL-20 for each binder to affect the sensitivity. The safety and energetic properties of these PBXs are mainly influenced by the thermal capability (C°p) and density (ρ) of binders, respectively.     

On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

Prospective and retrospective analyses under logistic regression models

In logistic case-control studies, Prentice and Pyke (Biometrika 66 (1979) 403-411) showed that valid point estimators of the odds-ratio parameters and their standard errors may be obtained by fitting the prospective logistic regression model to case-control data. Wang and Carroll (Biometrika 80 (1993) 237-241; J. Statist. Plann. Inference 43 (1995) 331-340) generalized Prentice and Pyke's (Biometrika 66 (1979) 403-411) results to robust logistic case-control studies. In this paper, we extend the results of Prentice and Pyke (Biometrika 66 (1979) 403-411) and Wang and Carroll (Biometrika 80 (1993) 237-241; J. Statist. Plann. Inference 43 (1995) 331-340) to a class of statistics and a class of unbiased estimating equations. We present some results on simulation and on the analysis of two real datasets.     

Tropical Weyl Group Action via Point Configurations and τ-Functions of the q-Painlevé Equations

Starting from certain point sets in the projective plane, we construct a tropical (or subtraction-free birational) representation of Weyl groups over the field of τ-functions. In particular, our construction includes E ₈ ⁽¹⁾ , E ₇ ⁽¹⁾ , E ₆ ⁽¹⁾ and D ₅ ⁽¹⁾ as affine cases; each of them gives rise to the q-difference Painlevé equation.