A sufficient condition for Hamiltonian cycles in bipartite tournaments

In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W(n - 3), then T is Hamiltonian, except for four exceptional graphs. This result is shown to be best possible in a sense.     

若干铬(III)含β-二酮混配配合物的冷冻态顺磁共振谱研究

本文对若干新型Cr(β-dik)Cl2Py2混配配合物的冷冻玻璃态顺磁共振谱进行了研究, 运用Powell优化法得了自旋哈密顿参数g、D、E值, 并利用这些参数计算和绘制了共振磁场位置与角度变化图, 结果表明这套参数的确定是合理的.     

Invariant Foliation of Dynamical Spacetimes

We present a gauge-theoretical derivation of the Frobenius foliation condition. It is based on a nonlinear coset realization of the Poincaré group, implying the time component ⁰ of the coframe to be invariant. By means of the unitary gauge fixing of the boosts, three Goldstone-like degrees of freedom of ⁰ are eliminated. The remaining Higgs-like boson, satisfying the foliation condition, plays the role of time.     

Energy and Angular Momentum ofthe Weak Gravitational Waves on the Schwarzschild Background — Quasilocal Gauge-invariant Formulation

A four-dimensional spherically covariantgauge-invariant quasilocal framework for theperturbation of the Schwarzschild metric is given. Animportant ingredient of the analysis is the concept ofquasilocality, which does duty for the separation ofangular variables in the usual approach. A precise andfull analysis for the mono-dipole part ofthe theory is presented. Direct construction (from theconstraints) of the reduced canonical structure for theinitial data and explicit formulae for thegaugeinvariants are proposed. The reduced symplecticstructure explains the origin of the axial and polarinvariants. This enables one to introduce an energy andangular momentum for the gravitational waves, which isinvariant with respect to the gauge transformations. Anexplicit expression for the energy and new proposition for angular momentum is introduced, inparticular, compatibility of theChristodoulou-Klainerman S.A.F. condition withwell-possedness of our functionals is checked. Bothgenerators (energy and angular momentum) represent quadratic approximation ofthe adm nonlinear formulae in terms of the perturbationsof the Schwarzschild metric. The previously knownresults are presented in a new geometric andself-consistent way. Both degrees of freedom fulfill thegeneralized scalar wave equation. For the axial degreeof freedom the radial part of the equation correspondsto the Regge-Wheeler result and for the polar one we get the Zerilli result.