Three classes of smooth Banach submanifolds in B(E,F)

Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F) RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments

By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with multiple deviating arguments, a new result on the existence of periodic solutions is obtained.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.     

Fuzzy Model of Regional Economic Competitiveness in GIS Spatial Analysis: Case Study of Gansu, Western China

After more than 20 years of impressive development since the economic reforms in 1978, today western China is facing an increasing development gap between its regions, particularly between urban and rural areas. Using the fuzzy comprehensive evaluation model, this paper aims to demonstrate the evolution of the economic competitiveness levels base on two categories of geographical unity in the province of Gansu located in Northwest China between 2000 and 2004. The results of fuzzy modeling are integrated into GIS spatiotemporal analyses in order to identify the spatial variation of each significant change in terms of the regional economic development. Our research effectively illustrates that there is a particular spatial dynamic of the economic development from region to region. Although the cities have improved very well in their economic competitiveness, the rural areas and minority regions still have a lot of progress to be achieved.     

Protection of iron corrosion by stearic acid and stearic imidazoline self-assembled monolayers

A type of stearic imidazoline (IM) inhibitor was prepared using stearic acid (SA) and diethylenetriamine (DETA) as raw materials. The monolayers of IM and SA were assembled on the iron surface. The electrochemical characterization of stearic acid (SA) and stearic imidazoline (IM) on an oxide free iron surface had been studied. The monolayers of IM inhibitor were characterized by electrochemical impedance spectroscopy (EIS), electrochemical polarization curves, double layer capacitance, X-ray photoelectron spectroscopy (XPS) and molecular simulation. The results of electrochemical studies had illustrated that the inhibition efficiency of IM was higher than SA. XPS showed that the IM molecules adsorbed on the iron surface. The molecular simulation calculations showed that the IM molecules were tilted at an angle on the iron surface.