中国邮路问题的一个解法

本给出中国邮路问题的一个解法。虽然它仍只是初始方案，但因考虑了问题的足够信息，因而这种方案至少拉近了与最优解的距离。     

Some Properties of an Operator on L^∞（△） and Its Applications

In this paper, we introduce an operator Hμ（z） on L^∞（△） and obtain some of its properties. Some applications of this operator to the extremal problem of quasiconformal mappings are given. In particular, a sufficient condition for a point r in the universal Teichmfiller space T（△） to be a Strebel point is obtained.     

The Problem of Periodic Solutions for a Class of Dynamical System（Ⅱ）

51.IntroductionLetK:R"XR"-Rbeasmoothfunctionwithi)K(q,p)isevenandstrictlyconvexinP,VqeR"lii)K(q,6)=o,VqeR".Supl>oseV=R"-Rbeasmoothfunction,t:R"-R"'(,n<)l)beaSubmersiveoperator.WIlereR",R,.arendimensionalEducli(leanspace,qeR",PeR",C(q)=(C,(q),C,(q),-.'C.,(q)).DenoteH(q,p)=K(q,p) V(q).Throughoutthispaper,weletZ(=(q,p))=6betheequilibriumpointofthefollowingsystem-ForoperatorC,wedefinethespeedoperatorofCisWhere,CisconsideredCorr,rristl1e1>rojeclionoperatorfromR"XR,,toI{.,anddf(z)…     

PANCYCLICITY IN LINE GRAPHS

1IntroductionWeuseBondyandMurtyl3]forterminologyand..ta'ti..notdefinedhereandconsidersimpleconnectedgraphsonly.AcircuitCofagraphGisanontrivialconnectedeuleriansubgraphofG.Aspanningcircuit,orbrieflyS-circuit,ofagraphGisacircuitthatcontainsallvenicesofG.AdominatingcircuitorD-circuitofGisacircuitsuchthateveryedgeofGisincidentwithatleastonevertexofthecircuit.AgraphofordernispancyclicifitcontainsallcyclesoflengthIfor3515n.IfCisacircuitofG,thenP(C)denotesthenumberOfedgesofGincidentwithatleas…     

Two Hamiltonian cycles

If the line graph of a graph G decomposes into Hamiltonian cycles, what is G? We answer this question for decomposition into two cycles.     

Hamilton cycles in line graphs of 3-hypergraphs

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.     

Molecular structure and conformation of 2,3-dichloro-1-propene as determined by gas-phase electron diffraction

The molecular structure and conformation of 2,3-dichloro-1-propene have been determined by gas-phase electron diffraction at nozzle temperatures of 24, 90 and 273°C. The molecules exist as a mixture of two conformers with the chlorine atoms anti (torsion angle ∠φ = 0°) or gauche (∠φ = 109°) to each other and with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ was found to be 0.55 (0.08), 0.49 (0.08) and 0.41 (0.10) at 24, 90 and 273°, respectively. These values correspond to an energy difference with estimated standard deviation ΔE° = E°_g-E°_a = 0.7 ± 0.3 kcal mol^?1 and an entropy difference ΔS° = S°_g-S°_a = 0.6 ± 0.9 cal mol^?1 K^?1. Some of the diffraction results, together with spectroscopic observations, permit the evaluation of an approximate torsional potential function of the form 2V = V₁ (1 - cos φ) + V₂ (1 - cos 2φ) + V₃ (1 - cos 3φ); the results are V₁ = 4.4 ± 0.5, V₂ = ?2.9 ± 0.5 and V₃ = 4.8 ± 0.2, all in kcal mol^?1. The results at 24°C for the distance (r_a) and angle (∠_α) parameters, with estimated uncertainties of 2σ, are: r(C_sp²-H) = 1.098(0.020)Å, r(C_sp³-H) = 1.103(0.020)Å, r(CC) = 1.334(0.009)Å, r(C-C) = 1.504(0.013)Å, r(C_sp²-Cl) = 1.752(0.021)Å, r(C_sp³-Cl) = 1.776(0.020)Å, ∠C-CC = 127.6(1.1)°, ∠C_sp³-C_sp²-Cl = 110.2(1.0), ∠C_sp²-C_sp³-Cl = 113.1(1.2)°, ∠H-C_sp³-H = 109.5° (assumed), ∠CC-H = 120.0° (assumed) and ∠φ = 108.9(3.4)°.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Alternative routes to equivalent classical models of a quantum system

<正>Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechanical behavior from the quantum formalism.We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dynamical algebras.Alternative coarse-grained systems generate different evolutions of the same physical quantities,and the difference becomes negligible only in the appropriate macro-limit.