On the Same $n$-Types for the Wedges of the Eilenberg-Maclane Spaces

Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X~((n)) and X′~((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 a_2 ··· a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].)     

Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.     

A Serrin criterion for compressible nematic liquid crystal flows

This paper is concerned with a simplified system, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. We establish a blowup criterion for three‐dimensional compressible nematic liquid crystal flows, which is analogous to the well‐known Serrin's blowup criterion for three‐dimensional incompressible viscous flows. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear simulations of vesicle wrinkling

In this paper, we study nonlinear wrinkling dynamics of a vesicle in an extensional flow. Motivated by the recent experiments and linear theory on wrinkles of a quasi‐spherical membrane, we are interested in examining the linear theory and exploring wrinkling dynamics in a nonlinear regime. We focus on a quasi‐circular vesicle in two dimensions and show that the linear analytical results are qualitatively independent of the number of dimensions. Hence, the two‐dimensional studies can provide insights into the full three‐dimensional problem. We develop a spectral accurate boundary integral method to simulate the nonlinear evolution of surface tension and the nonlinear interactions between flow and membrane morphology. We demonstrate that for a quasi‐circular vesicle, the linear theory well predicts the characteristic wavenumber during the wrinkling dynamics. Nonlinear results of an elongated vesicle show that there exist dumbbell‐like stationary shapes in weak flows. For strong flows, wrinkles with pronounced amplitudes will form during the evolution. As far as the shape transition is concerned, our simulations are able to capture the main features of wrinkles observed in the experiments. Interestingly, numerical results reveal that, in addition to wrinkling, asymmetric rotation can occur for slightly tilted vesicles. The mathematical theory and numerical results are expected to lead to a better understanding of related problems in biology such as cell wrinkling. Copyright © 2013 John Wiley & Sons, Ltd.     

A Schwarz Lemma at the Boundary of Hilbert Balls

In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B′in separable complex Hilbert spaces H and H′, respectively. It is found that if the mapping f ∈ C~(1+α)at z_0∈ ?B with f(z_0) = w_0∈ ?B′, then the Fr′echet derivative operator Df(z_0) maps the tangent space Tz_0(?B~n) to Tw_0(?B′), the holomorphic tangent space T_(z_0)~(1,0)(?B~n) to T_(w_0)~(1,0)(?B′),respectively.     

A Landesman-Lazer Type Theorem for Periodic Solutions of the Resonant Asymmetric ρ-Laplacian Equation

In this paper, we give a Landesman-Lazer type theorem for periodic solutions of the asymmetric 1-dimensional p-Laplacian equation -（｜x＇｜^p-2x＇）＇=λ｜x｜^p-2x＋＋μ｜x｜^p-2x-＋f（t,x）with periodic boundary value.     

具有BMO系数的拟线性椭圆方程解的BMO估计

We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A(x,Du) = div(|F|~(p-2)F) under the BMO smallness of the nonlinearity,that is |F|~(p-2)F∈BMO implies that Du ∈BMO.     

Zero-Hopf Bifurcation at the Origin and Infinity for a Class of Generalized Lorenz System

In this paper, the zero-Hopf bifurcations are studied for a generalized Lorenz system. Firstly, by using the averaging theory and normal form theory, we provide sufficient conditions for the existence of small amplitude periodic solutions that bifurcate from zero-Hopf equilibria under appropriate parameter perturbations. Secondly, based on the Poincar{\''e} compactification, the dynamic behavior of the generalized Lorenz system at infinity is described, and the zero-Hopf bifurcation at infinity is investigated. Additionally, for the above theoretical results, some related illustrations are given by means of the numerical simulation.     

在微重力条件下无限长方柱中的自然对流*

为了研究在宇宙空间微重力环境中.自然对流对流体运动的影响,将变量展成Grashof的摄动级数,使用摄动理论将Navier-Stokes方程组简化成:关于温度T的Poisson方程,关于流函数ψ的非齐次biharmonic方程.选取一无限长封闭方柱体,假定在柱体边界上预先给定一种线性温度分布,使用数值计算方法求解上述简化方程组,得到各阶流函数和各阶温度值,进而详细地研究了方柱中流体的运动状况,分析和讨论了某些参数,如Grashof数和Prandtl数对流体运动的影响,最后将计算结果与由未简化方程推算的结果进行比较,证实近似方法正确地简化了复杂的流体运动过程,并且可以推广、运用到三维问题上.     

A finite volume scheme for a model coupling free surface and pressurised flows in pipes

A model is derived for the coupling of transient free surface and pressurized flows. The resulting system of equations is written under a conservative form with discontinuous gradient of pressure. We treat the transition point between the two types of flows as a free boundary associated to a discontinuity of the gradient of pressure. The numerical simulation is performed by making use of a Roe-like finite volume scheme that we adapted to such discontinuities in the flux. The validation is performed by comparison with experimental results.     

Analysis and finite element approximation of a coupled,continuum pipe‐flow/Darcy model for flow in porous media with embedded conduits

We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. The mathematical well‐posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two‐dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1242–1252, 2011     

Self-similar turbulent boundary layer in pressure gradient

Self-similar flows in a turbulent boundary layer when the free-stream velocity is specified as a power function of longitudinal coordinate are investigated. The self-similar formulation not only simplifies solving of the problem by reducing the equations of motion to ordinary differential equations but also provides a mean for formulating closure conditions. It is shown that for the class of flows under consideration that depend on three governing parameters the dimensionless mixing length is a function of the normalised distance from the wall and the exponent in the law specifying the free-stream velocity distribution in the outer region and a universal function of local Reynolds number in the wall region, the latter corollary being true even when the skin friction vanishes. In calculations this function is set to be independent of pressure gradient, which gives the results very close to experimental data. There exist four different self-similar flow regimes. Each regime is related to its similarity parameter, one of which is the well-known Clauser equilibrium parameter and the other three are established for the first time. In case of adverse pressure gradient when the exponent lies within certain limits, which depend on Reynolds number, the problem has two solutions with different values of the boundary layer thickness and skin friction, which points out the possibility of hysteresis in near-separating flow. Separation occurs not at the minimum value of the exponent that corresponds to the strongest adverse pressure gradient but at a higher one whose dependence on Reynolds number is calculated in the paper. The results of the theory are in good agreement with experimental data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary Regularity for Minimal Graphs of Higher Codimensions

In this paper, the authors derive H¨older gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets of Euclidean space under some suitable conditions.     

Boundedness of Commutators of θ-Type Calderόn-Zygmund Operators on Non-homogeneous Metric Measure Spaces

Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L~∞(μ) into RBMO(μ) and from H_(at)~(1,∞)(μ) into L~1(μ), respectively.As a consequence of these results, they establish the L~p(μ) boundedness of the commutators on the non-homogeneous metric spaces.     

On the GF(p) Linear Complexity of Hall's Sextic Sequences and Some Cyclotomic-Set-Based

Klapper (1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over $GF(2)$, but these sequences have very low linear complexities when considered as sequences over $GF(p)(p$ is an odd prime). This linear complexity of a binary sequence when considered as a sequence over $GF(p)$ is called $GF(p)$ complexity. This indicates that the binary sequences with high $GF(2)$ linear complexities are inadequate for security in the practical application, while, their $GF(p)$ linear complexities are also equally important, even when the only concern is with attacks using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register synthesis and bch decoding, {\it IEEE Transactions on Information Theory}, {\bf 15}(1), 1969, 122--127]. From this perspective, in this paper the authors study the $GF(p)$ linear complexity of Hall''s sextic residue sequences and some known cyclotomic-set-based sequences.     

Equilibrium statistical theory for nearly parallel vortex filaments

The first mathematically rigorous equilibrium statistical theory for three‐dimensional vortex filaments is developed here in the context of the simplified asymptotic equations for nearly parallel vortex filaments, which have been derived recently by Klein, Majda, and Damodaran. These simplified equations arise from a systematic asymptotic expansion of the Navier‐Stokes equation and involve the motion of families of curves, representing the vortex filaments, under linearized self‐induction and mutual potential vortex interaction. We consider here the equilibrium statistical mechanics of arbitrarily large numbers of nearly parallel filaments with equal circulations. First, the equilibrium Gibbs ensemble is written down exactly through function space integrals; then a suitably scaled mean field statistical theory is developed in the limit of infinitely many interacting filaments. The mean field equations involve a novel Hartree‐like problem with a two‐body logarithmic interaction potential and an inverse temperature given by the normalized length of the filaments. We analyze the mean field problem and show various equivalent variational formulations of it. The mean field statistical theory for nearly parallel vortex filaments is compared and contrasted with the well‐known mean field statistical theory for two‐dimensional point vortices. The main ideas are first introduced through heuristic reasoning and then are confirmed by a mathematically rigorous analysis. A potential application of this statistical theory to rapidly rotating convection in geophysical flows is also discussed briefly. © 2000 John Wiley & Sons, Inc.     

集合论在拟仿紧性中的应用

1977年,刘应明引进拟仿紧性并证明了下述集论拓扑学的结果：在假设$2^{\omega_1}>2^{\omega}$下每一个可分正规的拟仿紧空间是仿紧空间.我们进一步证明假设$2^{\omega_1}>2^{\omega}$等价于每一个可分正规的拟仿紧空间是仿紧空间,获得了拟仿紧性的一个独立性结果.     

Semi-infinite programming duality for order restricted statistical inference models

The equivalence of multinomial maximum likelihood and the isotonic projection problem: $$\inf \left\{ {\sum\limits_{i = 1}^n {p_i \ln (p_i /r_i )|p \in K,a convex} {\mathbf{ }}subset of the probability vectors{\mathbf{ }}p} \right\}$$ can be established using Fenchel's Duality Theorem and subgradient and complementary slackness relationships of convex analysis, all taking place over the real numbers. In this paper non-Archimedean polynomial subgradients (Jeroslow/Kortanek '71, Blair '74, Borwein '80, and Kortanek/Soyster '81) are employed for the case where some of the observed values of the random vector are zero, corresponding to “zero counts in the traditional multinomial setting.” With an appropriate linear semi-infinite programming dual pair it is shown that a vector solves the multinomial problem if and only if it converts to a solution of the isotonic projection problem. The development parallels the one of Robertson/Wright/Dykstra '88, where for the zero counts case the authors adjoin “-∞” to the real numbers and define ln(0)=-∞.     

Surface waves on steady perfect‐fluid flows with vorticity

This is a theory of two‐dimensional steady periodic surface waves on flows under gravity in which the given data are three quantities that are independent of time in the corresponding evolution problem: the volume of fluid per period, the circulation per period on the free stream line, and the rearrangement class (equivalently, the distribution function) of the vorticity field. A minimizer of the total energy per period among flows satisfying these three constraints is shown to be a weak solution of the surface wave problem for which the vorticity is a decreasing function of the stream function. This decreasing function can be thought of as an infinite‐dimensional Lagrange multiplier corresponding to the vorticity rearrangement class being specified in the minimization problem. (Note that functional dependence of vorticity on the stream function was not specified a priori but is part of the solution to the problem and ensures the flow is steady.) To illustrate the idea with a minimum of technical difficulties, the existence of nontrivial waves on the surface of a fluid flowing with a prescribed distribution of vorticity and confined beneath an elastic sheet is proved. The theory applies equally to irrotational flows and to flows with locally square‐integrable vorticity. © 2011 Wiley Periodicals, Inc.     

素数幂、双素数幂阶元的共轭类长的个数为4的 有限群的结构

设群G为一个有限群.如果群G中素数幂、双素幂阶元的共轭类长的集合为{1,p~a,m,p~bm},那么群G是可解的,其中ab为正整数,p为素数且与m互素.进一步,给出了群G/Z(G)的结构,这是对文"Chen R F,Zhao X H.A criterion for a group to have nilpotent p-complements[J].Monatsh Math,2016,179(2):221-225"中定理A主要结论的一个推广.