耦合mKdV系统的非奇异正子解、负子解及复子解

研究从二层流体模型中导出的变系数耦合mKdV模型,利用达布变换法,并依据系统中Lax对的谱参数的性质,给出了耦合mKdV系统的正子解、负子解、复子解及这些解的具体结构图形.其中所得到的耦合mKdV系统的正子解、负子解和复子解都是解析的,而复子解可看作一种形式的周期波解.

子午弧长正反解幂级数公式的简单形式

采用幂级数减缩法对一组可算至任意精度的子午弧长正反解幂级数展开式进行减缩 ,得出适用于全球的减缩公式以及适用于我国的减缩公式。减缩式不仅形式简单、使用方便 。

Initial Value Problem of Singular n-Laplacian Equation

To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.

Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems

The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.

Representations and Classification of Traveling Wave Solutions to sinh-Grdon Equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.

Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.

Several Properties of p-w-hyponormal Operators

In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.

On the Representation of Some Subnormal Operators

Let T be pure subnormal operator. In this paper necessary and sufficiert conditions that T=N+K are given,where N is normal, K is quasinormal and NK=KN.

Positive Solutions of p-Laplacian Functional Difference Equations

In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.

Aircraft attitude estimation of MEMS sensor based on modified particle filter

The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.

Electronic-Positron （Pairino＇s） Structure of Nuclear Substance （Matter）

Decrease or enlargement of the number of pairinos in nuclei and as free nucleons, pairinos, electrinos, positpinos is a factor of destabilization in the matter and or environment. For the benefit of a electronic-positron structure the representations about an annihilation of the electronic-positron pairs, formation in substance electronic-positron of pairs under activity action of a gamma radiation, electronic and positron character of a beta radiation in nuclei are worked. Terminology： positrino, electrino, pairino. The new mechanism of a physical phenomenon, well explored to the present moment, with the conventional interpretation - mechanism of an annihilation of a free positron on electrons of substance is offered. That is the conventional point of view is those, that during annihilation the electron bums down, disappears or is transmuted into a gamma-quantum. In opinion of the author any facts or the proofs of such interpretation do not exist. The following mechanism therefore is offered： an electron and positron at coming together are discharged by two gamma-quantum and form pairino （unloaded electron - positron state with gravitational mass ＂m＂ about 2 eV, with compensation by electric charge, about an electrino by positrino interaction）; that is the mechanism ＂cold＂ （low, is less than 10 KeV, energies） synthesis of pairino. The given mechanism of phenomenon of annihilation is more realistic.

Optimizing pyrolysis of resin carbon for anode of lithium ion batteries

Pyrolytic resin carbon anode for lithoum ion batteries was prepared from thermosetting phenolic resin. Pyrolysis of the primary phenolic resin and the dewatered one was studied by thermal gravimetric analysis. Structures and characteristics of the carbon materials were determined by X-ray diffraction, Brunauer-Emmer-Teller surface area analysis and electrochemical measurements. With the increase of pyrolyzing temperature and soaking time, the resin carbon material has larger crystallite sizes of L_c and L_a, lower specific surface area, smaller irreversible capacity and higher initial coulombic efficiency. The pyrolyzing temperature and soaking time are optimized to be 1050℃ and 2h. The resin carbon anode obtained under the optimum conditions shows good electrochemical performances with reversible capacity of 387mA·h/g and initial coulombic efficiency of 69.1%.

New Multiple Soliton-like and Periodic Solutions for （2＋l）-Dimensional Canonical Generalized KP Equation with Variable Coefficients

In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.

FM Space Depend on Operator T and the Normal Solvability of Operator Polynomial P（T）

In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.

A Note on Generalized Aluthge Transformation for p-hyponormal and Log-hyponormal Operators

We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.

New Explicit Exact Solutions for the （2＋1）-Dimensional Higher-Order Broer-Kaup System

Using the modified extended tanh-function method,explicit and exact traveling wave solutions for the(2+1)-dimensional higher-order Broer-Kaup(HBK)system,comprising new soliton-like and period-form solutions,are obtained.

Shocks and Solitons in Ultradense Degenerate Electron-Positron-Ion Plasmas

The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger （dKdVB） equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar （cylindrical and spherical） geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.

Synthesis of ITQ-2 Zeolites and Catalytic Performance in n-Dodecane Cracking

ITQ-2 zeolites were prepared by sequential alkali-swelling and ultrasonic-delamination of precursor MCM-22 and characterized by X-ray powder diffraction, scanning electron microscopy, nitrogen adsorption-desorption, ammonia temperature-programmed desorption and in-situ Fourier-transform infrared spectroscopy. The delamination induced a change in the morphology of ITQ-2 zeolites from aggregated thin platelets to scattered platelets, together with a significant increase in external specific surface area, which reached a plateau at the ultrasonic treatment time of 3 h. The catalytic cracking of n-dodecane over ITQ-2 zeolites was evaluated with ITQ-2 coated on the inside wall of a tubular reactor at 550 ℃ and 4 MPa. The sample obtained by ultrasonic treatment of 3 h （ITQ-2-3） gave the highest initial conversion of n-dodecane, whereas those of 5 h and I h gave the conversion even lower than MCM-22, which was in agreement with the trend of the ratio of strong Lewis acid to the total acid amount. Although the amount of cokes deposited on ITQ-2-3 was larger than that on MCM-22, the former deactivated slowly, suggesting that a large external specific surface area benefits the stability of zeolite coatings,

Significant contributions of the petroleum industry to volatile organic compounds and ozone pollution:Insights from year-long observations in the Yellow River Delta

The petroleum industry is a significant source of anthropogenic volatile organic compounds(VOCs),but up to now,its exact impact on urban VOCs and ozone(O_(3))remains unclear.This study conducted year-long VOC ob-servations in Dongying,China,a petroleum industrial region.The VOCs from the petroleum industry(oil and gas volatilization and petrochemical production)were identified by employing the positive matrix factorization model,and their contribution to O_(3) formation was quantitatively evaluated using an observation-based chemical box model.The observed annual average concentration of VOCs was 68.6±63.5 ppbv,with a maximum daily av-erage of 335.3 ppbv.The petroleum industry accounted for 66.5%of total VOCs,contributing 54.9%from oil and gas evaporation and 11.6%from petrochemical production.Model results indicated that VOCs from the petroleum industry contributed to 31%of net O_(3) production,with 21.3%and 34.2%contributions to HO_(2)+NO and RO_(2)+NO pathways,respectively.The larger impact on the RO_(2) pathway is primarily due to the fact that OH+VOCs ac-count for 86.9%of the primary source of RO_(2).This study highlights the critical role of controlling VOCs from the petroleum industry in urban O_(3) pollution,especially those from previously overlooked low-reactivity alkanes.

Multiple Positive Solutions to a Nonlinear Two-point Boundary Value Problem with p-Laplacian

By a simple application of a new three functionals fixed point theorem, sufficient conditions axe obtained to guarantee the existence of at least three positive solutions for p-Laplacian equation： （φp（u′））′ ＋ α（t）f（t,u（t）） = 0 subject to nonlinear boundary value conditions. An example is presented to illustrate the theory.