Abstract:
Various kinds of therapies have been clinically applied to treat cervical spondylotic radiculopathy (CSR). However, the evaluation standards of therapeutic effect in different medical institutions are quite different from each other at present, thus bringing about many difficulties in the therapeutic effect evaluation of CSR treatment. Although many CSR-related scales have been developed, none of them could completely represent or reflect the exact curative actualities of CSR in China. Therefore, it is quite essential to establish a comprehensive evaluation scale for the therapeutic effect of CSR. And such evaluation system, in which the estimation of quality of life should be included, will become the developmental direction of CSR research in future.

Abstract:
The chirplet transform is the generalization form of fast Fourier transform , short-time Fourier transform, and wavelet transform. It has the most flexible time frequency window and successfully used in practices. However, the chirplet transform has not inherent inverse transform, and can not overcome the signal reconstructing problem. In this paper, we proposed the improved chirplet transform (ICT) and constructed the inverse ICT. Finally, by simulating the harmonic voltages, The power of the improved chirplet transform are illustrated for harmonic detection. The contours clearly showed the harmonic occurrence time and harmonic duration.

Abstract:
The C42+ molecules with Td or D4h symmetry should take place Jahn-Teller distortion Based on Jahn-Teller effect theory and quantum theory, the Jahn-Teller distortion and the energy level splitting of the T*(e+l2)system for C42+ molecules with Td symmetry are studied in this paper by using the methods of group theory and symmetry analysis. The Hamiltonian of the system is separated into two parts by using unitary shift transformation, one part is the Hamiltonian of not having phonons excited, and the other part is the Hamiltonian of having phonons excited. From this, the ground states and their energies of the system in each minimum are obtained, and the corresponding excited states and their energies are also calculated, the Jahn-Teller distortion of the system is analyzed further by using group theory afterwards. It is found that there are six potential energy minima with C2 symmetry on the potential energy surface of the system because of the vibronic coupling. No matter which minimum the system is in , the original ground energy level of the system is split into three energy levels and the electronic degeneracy of the system is completely lifted, and the energy level interval aroused due to the distortion is enlarged with strengthening of the vibronic coupling strength. The symmetry of C42+ molecules should be lowered to C2 from Td with the Jahn-Teller distortion occurring, the symmetry of the ground electronic state of C42+ molecules is B2 under the group C2 after the Jahn-Teller distortion.

Abstract:
Starting from the standard Hamiltonian describing the optical non-linear process of spontaneous parametric down-conversion, we theoretically show that the generated entangled photon-pairs carry non-negligible orbital angular momentum in the degrees of freedom of relative movement in the type-II cases due to spatial symmetry breaking. We also show that the orbital angular momentum carried by photon-pairs in these degrees of freedom escapes detection in the traditional measurement scheme, which demands development of new techniques for further experimental investigations.

Abstract:
We report the realization of a light source specifically designed for the generation of bright continuous-variable entangled beams and for Heisenberg-limited inteferometry. The source is a nondegenerate, single-mode, continuous-wave optical parametric oscillator in Na:KTP, operated at frequency degeneracy and just above threshold, which is also of interest for the study of critical fluctuations at the transition point. The residual frequency-difference jitter is $\pm$ 150 kHz for a 3 MHz cold cavity half-width at half maximum. We observe 4 dB of photon-number-difference squeezing at 200 kHz. The Na:KTP crystal is noncritically phase-matched for a 532 nm pump and polarization crosstalk is therefore practically nonexistent.

Abstract:
We report the first measurement of the quantum phase-difference noise of an ultrastable nondegenerate optical parametric oscillator that emits twin beams classically phase-locked at exact frequency degeneracy. The measurement illustrates the property of a lossless balanced beam-splitter to convert number-difference squeezing into phase-difference squeezing and, thus, provides indirect evidence for Heisenberg-limited interferometry using twin beams. This experiment is a generalization of the Hong-Ou-Mandel interference effect for continuous variables and constitutes a milestone towards continuous-variable entanglement of bright, ultrastable nondegenerate beams.

Abstract:
We report the experimental demonstration of a heterodyne polarization rotation measurement with a noise floor 4.8 dB below the optical shot noise, by use of the classically phase-locked quantum twin beams emitted above threshold by an ultrastable type-II Na:KTP CW optical parametric oscillator. We believe this is the largest noise reduction achieved to date on optical phase-difference measurements.

Abstract:
In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both diagonal and non-diagonal. For applications, we compute the heat kernel of a Schroedinger operator with terms of lower order, and obtain a globally closed solution to a matrix Riccati equations as a by-product. Besides, we finally recover and generalise several classical results on some celebrated operators.

Abstract:
In this paper, we study Ornstein-Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterise the singularities produced by the potentials by finding explicit geodesics of the operators, and obtain the heat kernels via a probabilistic ansatz. All the formulae are closed.

Abstract:
We show random polymer is diffusive in dimensions 1 and 2 in probability in an intermediate scaling regime. The scale is $\beta= o(N^{-1/4})$ in d=1 and $\beta=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$.