Optimal design of gears contact interface modification for an objective as minimum impact resistance of initial meshing-in time domain

Meccanica - In gear pair actual alternating meshing process, the comprehensive errors of the transmission system and the thermal elastic deformation of the teeth body cause the gears in the meshing...     

Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

Comparative investigation of up-conversion luminescence in Tm/Yb-codoped germanate-niobic and germanium-bismuth glasses: effect of phonon density on up-conversion emission

Tm³⁺/Yb³⁺-codoped germanate-niobic (GN) and germanium-bismuth (GB) glasses have been synthesized by conventional melting and quenching method. Intense blue and weak red emissions centered at 477 and 650 nm, corresponding to the transitions ¹G₄→³H₆ and ¹G₄→³H₄, respectively, were observed at room temperature. The possible up-conversion mechanisms are discussed and estimated. GN glass showed a weaker up-conversion emission than GB glass, which is inconsistent with the prediction from the difference of maximum phonon energy between GN and GB glasses. In this paper, Raman spectroscopy was employed to investigate the origin of the difference in up-conversion luminescence in the two glasses. Compared with phonon side-band spectroscopy, Raman spectroscopy extracts more information including both phonon energy and phonon density. For the first time, our results reveal that, besides the maximum phonon energy, the phonon density of host glasses is also an important factor in determining the up-conversion efficiency.     

DIFFUSION-DRIVEN INSTABILITY IN THE GIERER-MEINHARDT MODEL OF MORPHOGENESIS

In this paper, we consider the Gierer-Meinhardt model of morphogenesis. It is shown that the homogeneous equilibrium solution and the homogeneous periodic solution become diffusively unstable if the diffusion coefficients of the two substances are chosen suitably.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.