New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

The pivotal aim of the present work is to find the numerical solution for fractional Benney–Lin equation by using two efficient methods, called q ‐homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three‐dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.     

微重力环境下无限长柱体内角毛细流动解析近似解研究

应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度.     

Functors of the category of abelian sheaves on regular affine scheme

In this short paper, we prove that ifR is a regular local ring of unequal characteristic, then there exists an additive covariant functorG from the category of abelian sheaves on SpecR to the category of abelian groups such that id _R (G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.     

A Compact Space Is Homotopy Equivalent to a CW-Complex If and Only If It Is an Absolute Neighborhood h-Retract

It is proved that a compact space is homotopy equivalent to a CW-complex if and only if it is an absolute neighborhood h-retract.     

The Convergence of (~γ)s(b0hn - h1bn-1)

This paper computes the Thom map on γ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of b2,0, from which it is proved that (~γ)s(b0hn - h1bn-1) for 2 ≤ s ＜ p - 1 are permanent cycles in the ASS.     

关于非线性规划问题的组合同伦内点法

文[1]在条件(C1)、(C2)和(C3)之下，利用组合同伦内点法讨论了非凸非线性规划问题K—K—T点的存在性，本文对条件(C2)和(C3)进行了改进和处理。     

Systems of Inclusions Involving Fredholm Operators of Nonnegative Index and Nonconvex-Valued Maps

We study the existence of solutions to a system of two inclusions involving Fredholm operators of nonnegative (Fredholm) index and the so-called c-admissible maps: upper semicontinuous maps with values being continuous images of cell-like sets. The presented approach resembles the substitution technique, i.e. applies the so-called solution map. The appearance of the ‘dimension defect’ reflecting the nonnegativity of Fredholm indices requires the use of algebraic tools based on the cohomotopy theory, different from the usual homological ones present in the fixed point theory. An application to boundary value problems is provided as well as the brief exposition of basic facts from the cohomotopy theory. Mathematics Subject Classifications (2000) 47H04, 47A53, 55M20, 55Q55, 34A60.     

关于映射同伦类的拓扑熵

设ｆ：Ｔ＾ｍ→Ｔ＾ｍ为ｍ维环面自映射，Ｎ＾∞（ｆ）是ｆ的渐近Ｎｉｅｌｓｅｎ数，本文应用Ｎｉｅｌｓｅｎ不动点理论，给出了ｌｏｇＮ＾∞（ｆ）是ｆ的同伦类的拓扑熵的最好下界的一个充要条件；并通过在齐性空间上引入等价度量，将此结论推广到了幂零流形自映射的情形。     

EQUIVARIANT SELF EQUIVALENCES OF PRINCIPAL FIBRE BUNDLES

Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known.     

TheK-theory of AF embeddings of the rational rotation algebras

Our main result is the construction of an embedding ofC(T²) into an approximately finite-dimensionalC ^*-algebra which induces an injection onK ₀(C(T²)). The existence of this embedding implies that Cech cohomology cannot be extended to a stable, continuous homology theory forC ^*-algebras which admits a well-behaved Chern character. Homotopy properties ofC ^*-algebras are also considered. For example, we show that the second homotopy functor forC ^*-algebras is discontinuous. Similar embeddings are constructed for all the rational rotation algebras, with the consequence that none of the rational rotation algebras satisfies the homotopy property called semiprojectivity.