Synthesis,Structure and Polymorphism of a Novel Two-dimensional Cobalt(Ⅱ)Coordination Polymer Constructed from Citrazinate Ligand

The polymeric Co（Ⅱ） complex[Co（Hdhpc）（py）]n（1）（py = pyridine,H3dhpc =2,6-dihydroxypyridine-4-carboxyl acid） was prepared and characterized.X-ray diffraction data revealed that the compound crystallizes in dimorphic 1α and 1β forms at room and low temperature,respectively.The former crystallizes in the orthorhombic crystal system,space group Pbcm with a =7.209（1）,b = 14.834（3）,c = 15.376（3） A°,V= 1644.3（5）A°3,Z = 4,C（16）H（13）CoN3O4,Mr = 370.22,Dc= 1.496 g/cm^3,F（000） = 756,μ = 1.068 mm^-1,R = 0.0633 and wR = 0.1192.While 1β is attributed to the monoclinic space group C2/c with a = 32.102（4）,b = 7.022,c = 14.945（2）A°,β = 109.052（5）°,V= 3184.4（6） A°3,Z= 8,Dc= 1.544 g/cm^3,F（000） = 1512,μ = 1.103 mm^-1,R = 0.0428 and wR =0.0797.The conformation changes of pyridines between Co-citrazinate planes leading to a reversible single-crystal to single-crystal transformation.The variable temperature magnetic data indicate a weak ferrimagnetism.

Rashba Effect in Presence of Time-Dependent Interaction

Rashba effect in presence of a time-dependent interaction has been considered.Then time-evolution of such a system has been studied by using Lewis–Riesenfeld dynamical invariant and unitary transformation method.So appropriate dynamical invariant and unitary transformation according the considered system have been constructed as well as some special cases have come into this article which are common in physics.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution.The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction.Thus,it is more realistic than the Winkler model,which only represents compressive soil resistance.However,the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation;hence,the beam under inclined loads cannot be considered in the model.In this study,a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model,which tends to disregard the tangential interaction between the beam and the foundation.The horizontal spring reaction is assumed to be proportional to the relative tangential displacement.The governing equation can be deduced by theory of elasticity and Newton’s laws,combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition.Double Fourier transformation is used to simplify the geometric equation into an algebraic equation,thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam.Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution.The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS.Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam.Results are realistic and can be used as reference for future engineering designs.