测度链上非线性微分方程的三正解(英文)

运用文 [1 ]中的Leggett Williams不动点定理 ,我们给出了测度链上的非线性微分方程-xΔΔ(t) =f(t,x(σ(t) ) ) ,t∈ [a,b]关于两点边值条件αx(a) - βxΔ(a) =0 ,γx(σ(b) ) +δxΔ(σ(b) )

带有积分边值条件的分数阶微分方程正解的存在性

运用推广的Leggett-Williams不动点定理,得到了带有积分边值条件的分数阶微分方程的三正解的存在性结果,并通过例子验证给出结果的有效性。

Application of 3D AVO Interpretation Technique to Lithological Reservoir in the Hongze Area

In the Hongze Area, the reservoirs vary rapidly laterally and are controlled by many factors, such as structure, lithology, oil source, and so on. S-wave well log curves are calculated from an equation derived from multiple-attribute regression analysis of RT, DT, GR, and DEN logs. Representative P-and S-wave velocities and Poisson＇s ratio are statistically computed for oil and water bearing reservoir rock, shale, and calcareous shale in each well. The averaged values are used for AVO forward modeling. Comparing the modeling results with actual seismic data limit the possible AVO interpretations. Well and seismic data are used to calibrate inverted P-wave, S-wave, Poisson＇s ratio, and AVO gradient attribute data sets. AVO gradient data is used for lithofacies interpretation, P-wave data is used for acoustic impedance inversion, S-wave data is used for elastic impedance, and Poisson＇s ratio data is used for detecting oil and gas. The reservoir and hydrocarbon detections are carried out sequentially. We demonstrate that the AVO attributes method can efficiently predict reservoir and hydrocarbon potential.

Existence of Multiple Positive Solutions on the Three Point Boundary Value Problems

In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u＂＋a（t）f（u）=0,t∈[0,1],u（0）=0,au（η）^＊=u（1）.

Direct linear discriminant analysis based on column pivoting QR decomposition and economic SVD

A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.

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.

Existence of Positive Solutions for a Third-Order Three-Point Boundary Value Problem with Semipositone Nonlinearity *

The existence of positive solutions is investigated for following semipositone nonlinear third-order three-point BVP ω''(t) - λf(t,w(t)) = 0, 0 ≤ t ≤ 1, ω(0) = ω'(n) = ω'(1) = 0.

Positive Solutions of a Three-Point Boundary Value Problem

We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].

The Existence of Three Positive Solutions for a Class of Nonlinear Three-Point Boundary Value Problem with p-Laplacian

This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established

Selectively constructing sandwich-like heterostructure of CdS/PbTiO_(3)/TiO_(2)to improve visible-light photocatalytic H_(2)evolution

Fast migration and efficient spatial separation of photogenerated charges in photocatalytic materials are indispensable to efficient solar water splitting reactions.Here,we construct a three-phase heterostructure of CdS/PbTiO_(3)/TiO_(2)by selectively depositing CdS and TiO_(2)at oppositely poled crystal facets of PbTiO_(3)using single-domain ferroelectric PbTiO_(3).The heterostructure has matching band edge alignments and strong interfacial connections at different moieties.The heterostructure combines the interfacial electrical and ferroelectric fields because of their peculiar microstructures,which provide a strong driving force throughout the whole bulk to separate photogenerated charges.Almost two orders of magnitude improvement of visible-light-driven photocatalytic H_(2) production has been realized in CdS/PbTiO_(3)/TiO_(2)compared with bare PbTiO_(3)/TiO_(2),showing the efficiency of charge separation in the heterostructure.The idea of combining ferroelectrics with potential light capture semiconductor provides a paradigm to accurately design charge migration pathways,bringing a step closer to efficient solar water splitting.