On the Flag f-vector of a Graded Lattice with Nontrivial Homology

It is proved that the Boolean algebra of rank n minimizes the flag f-vector among all graded lattices of rank n, whose proper part has nontrivial top-dimensional homology. The analogous statement for the flag h-vector is conjectured in the Cohen-Macaulay case.     

Affine lines on ℚ-homology planes with logarithmic Kodaira dimension -∞

In the present paper, we study a topologically contractible irreducible algebraic curve C on a ℚ-homology plane S with We determine such a pair (S,C) when and C is smooth. Moreover, we prove that if C is not smooth, then C has exactly one singular point and theMakar-Limanov invariant of S is trivial. An erratum to this article is available at .     

Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term

We investigate the asymptotic behaviour as p → ∞ of sequences of positive weak solutions of the equation $$\left\{\begin{array}{l}-\Delta_p u = \lambda\,u^{p-1}+ u^{q(p)-1}\quad {\rm in}\quad \Omega,\\ u = 0 \quad {\rm on}\quad \partial\Omega,\end{array} \right.$$ where λ > 0 and either 1 < q(p) < p or p < q(p), with ${{\lim_{p\to\infty}{q(p)}/{p}=Q\neq1}}$ . Uniform limits are characterized as positive viscosity solutions of the problem $$\left\{\begin{array}{l}\min\left\{|\nabla u (x)| - \max\{\Lambda\,u (x),u ^Q(x)\}, -\Delta_{\infty}u (x)\right\} = 0 \quad {\rm in} \quad \Omega,\\ u = 0\quad {\rm on}\quad \partial\Omega.\end{array}\right.$$ for appropriate values of Λ > 0. Due to the decoupling of the nonlinearity under the limit process, the limit problem exhibits an intermediate behavior between an eigenvalue problem and a problem with a power-like right-hand side. Existence and non-existence results for both the original and the limit problems are obtained.     

On a class of totally topologically transitive skew products defined on cells in ℝ n,n ≥ 2

Mathematical Notes - We obtain sufficient conditions for total topological transitivity (transitivity of all iterations) for a class of C 3 skew products defined on cells in ? n , n ≥ 2.     

Numerical solution of a variational problem with L∞ functionals

We consider the problem which consists in finding an optimal Lipschitz extension to the domain Ω of functions that verify the restriction u = g on ∂Ω. This work deals with the numerical approximations of the problem in dimension two. Using a discretization procedure based on finite differences method we obtain a large scale non smooth convex minimization problem, which is solved via Variable Metric Hibrid Proximal Point Method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Completion of ■~2 with a Conformal Metric as a Closed Surface

In this paper, we obtain some asymptotic behavior results for solutions to the prescribed Gaussian curvature equation. Moreover, we prove that under a conformal metric in ■~2, if the total Gaussian curvature is 4π, the conformal area of ■~2 is finite and the Gaussian curvature is bounded, then ■~2 is a compact C~(1,α)surface after completion at ∞, for any α∈(0, 1). If the Gaussian curvature has a H?lder decay at infinity, then the completed surface is C~2. For radial solutions, the same regularity holds if the Gaussian curvature has a limit at infinity.     

The φ-Group for n Submodules Systems as a Generalization of the K-Theory

In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indecomposable systems of n subspaces.     

Interpolation for a subclass of H ∞

We introduce and characterize two types of interpolating sequences in the unit disc \(\mathbb {D}\) of the complex plane for the class of all functions being the product of two analytic functions in \(\mathbb {D}\) , one bounded and another regular up to the boundary of \(\mathbb {D}\) , concretely in the Lipschitz class, and at least one of them vanishing at some point of \(\overline {\mathbb {D}}\) .     

On the Stabilizer of the Automorphism Group of a 4—valent Vertex—transitive Graph with Odd—prime—power Order

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^κ（κ≥1） and let A be the full automorphism group of X.In this paper,we prove that the stabilizer Av of a vertex v in A is a 2-group if p≠5,or a {2,3}-group if p=5.Furthermore,if p=5|Av| is not divisible by 3^2.As a result ,we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p^κ(κ≥1） is at most 1-arc-transitive for p≠5 and 2-arc-transitive for p=5.     

Nontrivial solution of a quasilinear elliptic equation with critical growth in ℝn

Suppose Δ_n u = div (¦ ?u ¦^n-2?u) denotes then-Laplacian. We prove the existence of a nontrivial solution for the problem $$\left\{ \begin{gathered} - \Delta _n u + \left| u \right|^{n - 2} u = \int {(x,u)u^{n - 2} in \mathbb{R}^n } \hfill \\ u \in W^{1,n} (\mathbb{R}^n ) \hfill \\ \end{gathered} \right.$$ wheref(x, t) =o(t) ast → 0 and ¦f(x, t)¦ ≤C exp(α_n¦t¦^n/(n-1)) for some constantC > 0 and for allx∈?;t∈? with α_n =nω _n ^1/(n-1) , ω_n = surface measure ofS ^n-1.     

Plasticity as the Γ-limit of a Nonlinear Dislocation Energy with Mixed Growth

We consider a model for straight parallel edge dislocations with a nonlinear elastic energy with mixed growth. By means of Γ-convergence we show that the suitably rescaled energy converges to a strain-gradient plasticity model. As a tool we proof a generalized rigidity estimate which bounds the distance of a field with non-vanishing curl to a specific rotation by the distance to all rotations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

This paper is concerned with the finite-time quantized H_∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H_∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.     

Joint torsion of Toeplitz operators with H∞ symbols

We give a new² index theorem for the basic example of Toeplitz operators on the circle. The joint torsion, a non zero complex valued analytic index, of a pair of Fredholm Toeplitz operatorsT andT withH symbols is computed by residues in the disk, and is determined by a monodromy integral which specifies the isomorphism class of a flat line bundle on the circle. When the symbols and are rational a product of joint torsions identifies the isomorphism class of the bundle inH ¹ (S ¹,C ^*), and the identification extends by rational approximation to the case of smooth symbols defined on the circle.Partially supported by National Science Foundation grants to both authors.     

On （α,β）-Metrics of Scalar Flag Curvature with Constant S-curvature

In this paper, we study （α,β）-metrics of scalar flag curvature on a manifold M of dimension n （n 〉 3）. Suppose that an （α,β）-metric F is not a Finsler metric of Randers type, that is, F ≠k1 V√α^2 ＋ k2β^2 ＋ k3β, where k1 〉 0, k2 and k3 are scalar functions on M. We prove that F is of scalar flag curvature and of vanishing S-curvature if metric. In this case, F is a locally Minkowski and only if the flag curvature K = 0 and F is a Berwald metric.     

A family of translation planes of order q 2m+1 with two orbits of length 2 and q 2m+1−1 on l ∞

A class of translation planes of order q ^2m+1, where q is an odd prime power and m1, is constructed. If m=1, then this class is contained in the class of order q ³ constructed by Hiramine [5]. These planes of order q ^2m+1 are of dimension 2m+1 over their kernels. If q ^2m+13³, then the linear translation complements of these planes have two orbits of length 2 and q ^2m+1–1 on l and this class contains many planes which are not generalized André planes. If q ^2m+1= 3³, then each plane of this class is isomorphic to the Hering plane of order 27.Dedicated to Professor Tuyosi Oyama on his 60th birthday