Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.

This paper reviews a less known rational structure on the Siegel modular variety X(N) = Γ(N)ℍ _g over ℚ for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.

This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L ²(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator. Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.

The authors study the asymptotic behavior of the incompressible Navier-Stokes fluid with degree of freedom in the porous medium in ℝ ⁿ with n = 2 or 3. They derive the Darcy law as ε, the character size of the hole, tends to zero. Moreover, the authors obtain the expression of the degree of freedom from the homogenized model.

The author investigates the relationships of some potential objects for a right Markov process and the same objects for the Girsanov transformed process induced by α-excessive function including Revuz measures, energy functionals, capacities and Lévy systems in this paper.

The modular invariants of a family of curves are the degrees of the pullback of the corresponding divisors by the moduli map. The singularity indices were introduced by Xiao (1991) to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In semistable case, the author shows that the modular invariants corresponding to the boundary divisor classes are just the singularity indices. As an application, the author shows that the formula of Xiao for relative Chern numbers is the same as that of Cornalba-Harris in semistable case.

In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable (MDS for short) codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14–3.15, Kai, X., Zhu, S., and Li, P., IEEE Trans. on Inf. Theory, 60(4), 2014, 2080–2086], in the sense that our quantum MDS code has bigger minimum distance.

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space (the inverse limit space) M ^f of f is topologically quasi-stable under C ⁰-small perturbations in the following sense: For any covering endomorphism g C ⁰-close to f, there is a continuous map φ from M ^g to $\mathop \prod \limits_{ - \infty }^\infty M$ such that for any {y _i} _i∈Z ∈ φ(M ^g), y _i+1 and f(y _i) differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense: For any pseudo-orbit {x _i} _i∈ℤ, there is a sequence of points {y _i} _i∈ℤ tracing it, in which y _i+1 is obtained from f(y _i) by a motion along the center direction.

The authors investigate the global existence and asymptotic behavior of classical solutions to the 3D non-isentropic compressible Euler equations with damping on a bounded domain with slip boundary condition. The global existence and uniqueness of classical solutions are obtained when the initial data are near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

Let (H, β) be a Hom-bialgebra such that β ² = id _H. (A, α _A) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category _H ^HYD and (B, α _B) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YD_H ^H. The authors define the two-sided smash product Hom-algebra $\left( {A\natural H\natural B,{\alpha _A} \otimes \beta \otimes {\alpha _B}} \right)$ and the two-sided smash coproduct Homcoalgebra $\left( {A\diamondsuit H\diamondsuit B,{\alpha _A} \otimes \beta \otimes {\alpha _B}} \right)$. Then the necessary and sufficient conditions for $\left( {A\natural H\natural B,{\alpha _A} \otimes \beta \otimes {\alpha _B}} \right)$ and $\left( {A\diamondsuit H\diamondsuit B,{\alpha _A} \otimes \beta \otimes {\alpha _B}} \right)$ to be a Hom-bialgebra (called the double biproduct Hom-bialgebra and denoted by $\left( {A_\diamondsuit ^\natural H_\diamondsuit ^\natural B,{\alpha _A} \otimes \beta \otimes {\alpha _B})} \right)$ are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra $\left( {A\diamondsuit H,{\alpha _A} \otimes \beta } \right)$ to be quasitriangular are given.

Given a connected CW-space X, SNT(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-MacLane 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 McGibbon and Møller (in [McGibbon, C. A. and Møller, 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].)