“孤平”新解

近体诗十分讲究格律,"孤平"是律诗(包括长律和律绝)的大忌。然而,何谓"孤平"则众说纷纭。目前,对"孤平"具有代表性的解释有两种,一种以王力先生为代表的解释;一种以启功先生为代表的解释。因两派观点均有值得商榷的地方,故提出"句中无两平相连者为孤平"的新解,并明确此类"孤平"的救法,以供学界参考。

Isoflurane preserves energy balance in isolated hepatocytes during in vitro anoxia/reoxygenation

AIM: To investigate the protective effect of isoflurane on energy balance in isolated hepatocytes during in vitro anoxia/reoxygenation, and to compare isoflurane with halothane. METHODS: Hepatocytes freshly isolated from fed rats were suspended in Krebs-Henseleit buffer, and incubated in sealed flasks under O2/CO2 or N2/CO2 (95%/5%, V/V) for 30 or 60 min, followed by 5 or 10 min of reoxygenation, with an added volatile anesthetic or not. ATP, ADP, and adenosine monophosphate in hepatocytes were determined by high performance liquid chromatography, and energy charge was calculated. RESULTS: During 30 min of anoxia, the energy charge and total adenine nudeotide steadily increased with the isoflurane dose from 0 to 2 minimum alveolar anesthetic concentration (MAC), then decreased from 2 to 3 MAC. In short incubations (30-35 min) at 1 MAC isoflurane, energy charge modestly decreased during anoxia, which was partially prevented by isoflurane and completely reversed by reoxygenation, and total adenine nudeotide did not decrease. In long incubations (60-70 min), both energy charge and total adenine nudeotide greatly decreased during anoxia, with partial and no reversal by reoxygenation, respectively. Isoflurane partly prevented decreases in both energy charge and total adenine nudeotide during anoxia and reoxygenation. In addition, 1 MAC isoflurane obviously increased ATP/ADP, which could not be changed by 1 MAC halothane. CONCLUSION: Isoflurane partially protects isolated hepatocytes against decreases in both energy charge and total adenine nudeotide during short (reversible) or long (irreversible) anoxia.

An Estimation of Internal Soliton Forces on a Pile in the Ocean

Internal soliton forces on oil-platform piles in the ocean are estimated with the Morison Formula. Different from sur- face wave forces, which change only in magnitude along a pile, internal soliton forces can be distributed over the entire pile in the water and they change not only in magnitude but also in direction with depth. Our calculations show that the maximum total force caused by a soliton with its associated current of 2.1 m s-1 is nearly equal to the maximum total force exerted by a surface wave with a wavelength of 300 m and a wave-height of 18 m. The total internal soliton force is large enough to affect the operations of marine oil platforms and other facilities. Therefore, the influence of internal solitons should not be neglected in the design of oil platforms.

Three Types of Expression in Dark-Soliton Perturbation Theory Based on Squared Jost Solutions

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.

Some Special Types of Solitary Wave Solutions for （3＋1）-Dimensional Jimbo-MiwaEquation

Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.

Nonpropagating Solitary Waves in （2＋1）-Dimensional Nonlinear Systems

By means of extended homogeneous balance method and variable separationapproach, quite a general variable separation solution of the (2+l)-dimensionalBroer-Kaup-Kupershmidt equation is derived. From the variable separation solution and by selectingappropriate functions, a new class of (2+1)-dimensional nonpropagating solitary waves are found. Thenovel features exhibited by these new structures are first revealed.

Oscillating Solitons for （2＋1）-Dimensional Nonlinear Models

Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.

Numerical Soliton and Oscillating Wave Solutions for Flierl-Petviashvili Equation in Plasmas

Numerical axisymmetric soliton and oscillating wave solutions for the Flierl-Petviashvili equation in plasmas are presented. Solution branch paradigm and examples are given. Some implications of results to ion drift wave as well as force-free field of magnetic equilibrium are briefly discussed.

Vortex Spatial Solitons to a Nonlinear Schrodinger Equation with Varying Coefficients

Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation （NLSE） with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.

A New Auto-Backlund Transformation and Two-Soliton Solution for (3+l)-Dimensional Jimbo-Miwa Equation

Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.

Exact Soliton Solutions to a Generalized Nonlinear Schrdinger Equation

The （1＋1）-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general （3＋1）-dimensional nonlinear Schr6dinger equation （NLSE） with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The （3＋1）D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.

CONVEXITY AND SYMMETRY OF TRANSLATING SOLITONS IN MEAN CURVATURE FLOWS

This paper proves that any rotationally symmetric translating soliton of mean curvature flow in R3 is strictly convex if it is not a plane and it intersects its symmetric axis at one point. The authors also study the symmetry of any translating soliton of mean curvature flow in Rn.

A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line

In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem.

Geochemistry of the Middle to Late Permian limestones from the marginal zone of an isolated platform(Laibin,South China)

Major, trace and rare earth elements were measured in 27 samples of the Middle to Late Permian limestones from the Tieqiao section located on the marginal zone of an isolated platform （Laibin, South China）. Shale-normalized REE＋Y patterns of all samples show notably negative Ce anomalies （0.21-0.66, average 0.33）, slightly positive Gd anomalies （1.08-1.30, average 1.20）, and positive Y anomalies with superchondritic Y/Ho ratios （36-91, average 55）, which are consistent with those of modern shallow seawater. Their relative LREEs enrichment with higher NdsN/YbsN ratios （0.58-1.80） than those of modern shallow seawater （0.21-0.50） suggests complicated sources of REEs for all samples. Compared with geochemical features of sediments influenced by terrigenous particles and hydrothermal fluids, it is concluded that ambient shallow seawater was the primary source of REEs in these limestones. Comparing the indicators of REE＋Y elements （ZREE, NdsN/YbsN, Ce/Ce＊, Gd/Gd＊, Eu/Eu＊ and Y/Ho） in limestones with those in bedded cherts from the Tieqiao section, we consider that limestone and bedded chert have similar sources of REE＋Y elements： ambient shallow seawater with more or less hydrothermal fluids. In addition, there is a completely negative correlation between CaCO3 and SiO2 contents in limestones and bedded cherts. These results imply that precipitation of CaCO3 was inhibited by that of SiO2 which was derived mainly from hydrothermal fluid, es- pecially in bedded cherts from the Tieqiao section.

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.

Nonplanar Electrostatic Solitary Waves in a Relativistic Degenerate Dense Plasma

By employing the reductive perturbation technique, the propagation of cylindrical and spherical ion acoustic solitary waves is studied in an unmagnetized dense relativistic plasma, consisting of relativistically degenerate electrons and cold fluid ions. A modified Korteweg-de-Vries equation is derived and its numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate Fermi plasma. Different degrees of relativistic electron degeneracy are discussed and compared. It is found that increasing number density leads to decrease the aznplitude the width of the ion acoustic solitary wave in both the cylindrical and spherical geometries. The relevance of the work to the compact astrophysical objects, particularly white dwarfs is pointed out.

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

The dynamical evolution theory of the isolated oasis system

Assume that an oasis and its surrounding desert consist of an isolated system without mass and energy exchange with the outer environment.The characteristics of oasis evolution have been explored under the condition of system energy conservation.The results show that oasis evolves with two equilibrium states.The first equilibrium suggests a stable expansive and an unstable degraded oasis whereas the second equilibrium indicates a stable shrink and an unstable increase of the oasis area.If one equilibrium state is unstable,the components of the isolated system(oasis and desert) would tend to be no energy exchange and they each reach to energy balance respectively.Oasis would maintain its initial area in this case.Further analyses point out that the two equilibrium states have completely different characteristics.In the first equilibrium state,a higher vegetation albedo,lower soil albedo and larger canopy resistance,and direr soil both contribute to the oasis area expansion,accompanying an excessive large desert soil and vegetation canopy temperature difference(SCTD).In the second equilibrium state,however,a lower vegetation albedo,higher soil albedo and small canopy resistance,and wetter soil benefit the oasis area to stay near its initial value,following a moderate SCTD.The convergent trajectories of the initial values in phase space are influenced by the separatrices of the equilibrium points.Higher temperature is an advantage factor for initial values convergent to the oasis expansion solution.

Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term

The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.

Curvature Estimates of Hypersurfaces in the Minkowski Space

A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.