Abstract:
Due to absorption of the earth, the seismic data has lower resolution and could not get the precise information. At the same time, one- way wave equation methods have many advantages in seismic forward modeling than full way equation, for example, high calculation efficiency, less memory. In this paper, we combine the quality factor Q with the SSF operator using one-way wave equation to realize wave-field extrapolation arithmetic used for viscoelastic medium. Then, we realize viscoelastic medium nonzero-offset seismic pre-stack forward modeling by one-way equation based on positioning principle, mathematical geophone principle and equal-time stacking principle. Finally, we use elastic and viscoelastic arithmetic to image for viscoelastic forward modeling and comparison. Numerical examples show that viscoelastic medium pre-stack forward decreases the deep reflection wave energy significantly, with the thick axis and narrow band and the lower resolution.Migration with viscoelastic arithmetic has achieved amplitude recovery, and the seismic data resolution also has been enhanced.

Abstract:
The meiotic process of pollen mother cells in Dianthus chinensis L. was observed by traditional squash method. The results showed that abnormal phenomena, such as bivalent separated in advance, chromosomes scattered outside equatorial plate, lagging chromosomes and chromosome uneven separation, occurred in the process of meiosis. The meiotic process of D. chinensis was generally normal due to abnormality rate at different development stages below 3%. The chromosome number of D. chinensis was 2n=2x=30.

Abstract:
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition rigorously proves the following: (\textit{ii}) that the particles satisfy \textit{only} a node coalescence condition; (\textit{iii}) that irrespective of their charge or statistics, the particles cannot coalesce; (\textit{iv}) that the particles cannot cross each other, and must be ordered; (\textit{v}) the particles are therefore distinguishable; (\textit{vi}) as such their statistics are not significant; (\textit{vii}) conclusions similar to those of the spin-statistics theorem of quantum field theory are arrived at via non-relativistic quantum mechanics; (\textit{viii}) the noninteracting system \textit{cannot} be employed as the lowest-order in a perturbation theory of the interacting system. (\textit{ix}) Finally, the coalescence condition for particles with the short-ranged delta-function interaction and \textit{arbitrary} external potential energy, is also derived. These particles can coalesce and cross each other.

Abstract:
Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schr{\"o}dinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electron-nucleus cusp condition, we prove that the effective electron -interaction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on the assumption of finiteness of this potential energy at a nucleus. We further demonstrate the criticality of the electron-nucleus cusp condition to such theories by example of the Hydrogen molecule. We show thereby that both model system effective electron-interaction potential energies, as determined from densities derived from accurate wave functions, will be singular at the nucleus unless the wave function satisfies the electron-nucleus cusp condition.

Abstract:
In this paper we construct such a set of `degenerate' Hamiltonians $\hat{H}$, which differ by an `intrinsic' constant but represent different physical systems yet possess the same ground state density. . Thus, although the proof of Hohenberg-Kohn (HK) theorem is independent of whether the constant $C$ is additive or intrinsic, its applicability is restricted to excluding the case of the latter. This constitutes the corollary to the theorem.The corollary has also been extended to the time-dependent version of the HK theorem.

Abstract:
The treatment of degenerate states within Kohn-Sham density functional theory (KS-DFT) is a problem of longstanding interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory (Q-DFT). We describe the Q-DFT of \textit{both} ground and excited degenerate states, and for the cases of \textit{both} pure state and ensemble v-representable densities. This then further provides a rigorous physical interpretation of the density and bidensity energy functionals, and of their functional derivatives, of the corresponding KS-DFT. We conclude with examples of the mappings within Q-DFT.

Abstract:
We have derived the integral form of the cusp and node coalescence conditions satisfied by the wavefunction at the coalescence of two charged particles in $D \geq 2$ dimension space. From it we have obtained the differential form of the coalescence conditions. These expressions reduce to the well-known integral and differential coalescence conditions in $D = 3$ space. It follows from the results derived that the approximate Laughlin wavefunction for the fractional Quantum Hall Effect satisfies the node coalescence condition. It is further noted that the integral form makes evident that unlike the electron-nucleus coalescence condition, the differential form of the electron-electron coalescence condition cannot be expressed in terms of the electron density at the point of coalescence. From the integral form, the integral and differential coalescence conditions for the pair-correlation function in $D\geq 2$ dimension space are also derived. The known differential form of the pair function cusp condition for the uniform electron gas in dimensions $D = 2,3$ constitute a special case of the result derived.

Abstract:
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momentum. The proofs differ from the original HK proof, and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function.

Abstract:
The spatial distribution of aerosol was analyzed by the measured data with PMS rented from Beijing weather modification in October 2009.The relations of aerosol distribution characteristics with inversion layer and relative humidity were discussed.The results show that there was significant difference in the vertical distribution of aerosol.The inversion layer and relative humidity have a great impact on the distribution of aerosol.Nearby the inversion layer and higher relative humidity,there was a accumula...