The authors consider one specific kind of heat transfer problems in a three-dimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary (or corrosion) by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.

This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]: A flow through a duct should be considered as a steady, isentropic, irrotational flow with cylindrical symmetry and should be determined by solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted Hölder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.

Let A be a unital AF-algebra (simple or non-simple) and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that α _*0 ^J = id _{K 0}(A). The author proves that A ⋊ _α ℤ has tracial rank zero.

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in ℂ ^N+1 near the origin, and the connected component containing the identity transformation of all locally holomorphic automorphisms of these hypersurfaces near the origin.

For a given self-similar set E ⊂ ℝ ^d satisfying the strong separation condition, let Aut(E) be the set of all bi-Lipschitz automorphisms on E. The authors prove that “f ∈ Aut(E): blip(f) = 1” is a finite group, and the gap property of bi-Lipschitz constants holds, i.e., inf“blip(f) ≠ 1: f ∈ Aut(E)” > 1, where lip(g) = and blip(g) = max(lip(g), lip(g ⁻¹)).

This paper deals with the standing wave for a Hamiltonian nonlinear wave equation which can be viewed as a representative of the class of equations of interest. On the one hand, by proving a compactness lemma and solving a variational problem, the existence of the standing wave with ground state for the aforementioned equation is proved. On the other hand, the authors derive the instability of the standing wave by applying the potential well argument, the concavity method and an invariant region under the solution flow of the Cauchy problem for the equation under study, and the invariance of the region aforementioned can be shown by introducing an auxiliary functional and a supplementary constrained variational problem.

The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U, which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges. Also, some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.

This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semiconductivity, superconductivity, electromagnetic waves, electrolyte and electrode materials, etc.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model (due to Baltagi 1995) to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator (WPLSE) and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator (PLSE), and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator (LPE). The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Carroll (2000), ignoring the correlation structure entirely and “pretending” that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups. Some simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.

Let “X _ni” be an array of rowwise negatively associated random variables and $T_{nk} = \sum\limits_{i = 1}^k {i^\alpha X_{ni} } $ for α ≥ −1, $S_{nk} = \sum\limits_{\left| i \right| \leqslant k} {\varphi \left( {\tfrac{i}{{n^\eta }}} \right)\tfrac{1}{{n^\eta }}X_{ni} } $ for η ∈ (0, 1], where ϕ is some function. The author studies necessary and sufficient conditions of $\sum\limits_{n = 1}^\infty {A_n P\left( {\mathop {max}\limits_{1 \leqslant k \leqslant n} \left| {T_{nk} } \right| > \varepsilon B_n } \right) < \infty and \sum\limits_{n = 1}^\infty {C_n P\left( {\mathop {\max }\limits_{0 \leqslant k \leqslant m_n } \left| {S_{nk} } \right| > \varepsilon D_n } \right) < \infty } } $ for all ɛ > 0, where A _n, B _n, C _n and D _n are some positive constants, m _n ∈ ℕ with m _n/n ^η → ∞. The results of Lanzinger and Stadtmüller in 2003 are extended from the i.i.d. case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented.