The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H ²-norm. To this end, an explicit Lyapunov function as a weighted and squared H ²-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H ²-exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C ¹-norm are derived.

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.

Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasilinear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions of Lipschitz solutions to the Cauchy problem and proves the existence and uniqueness of solutions.

The authors mainly study the Hausdorff operators on Euclidean space ℝ ⁿ. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces $H\dot K_q^{\alpha ,p} (\mathbb{R}^n )$ than their performance on the Hardy spaces H ^p(ℝ ⁿ) when 0 < p < 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.

Let X ₁,X ₂, ... be a sequence of dependent and heavy-tailed random variables with distributions F ₁, F ₂, ... on (−∞,∞), and let τ be a nonnegative integer-valued random variable independent of the sequence {X _k, k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities $S_n = \sum\limits_{k = 1}^n {X_k }$ and $S_{(n)} = \mathop {\max }\limits_{1 \leqslant k \leqslant n} S_k$ for n > 1, and their randomized versions S _τ and S _(τ) are studied. Some applications to the risk theory are presented.

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.

This paper is a continuation of the study of the algebraic speed for Markov processes. The authors concentrate on algebraic decay rate for the transient birth-death processes. According to the classification of the boundaries, a series of the sufficient conditions for algebraic decay is presented. To illustrate the power of the results, some examples are included.

The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds. It is also shown that the energy minimizing maps are smooth, when the target manifolds have no focal points.

In this paper, Schwarz-Pick estimates for high order Fréchet derivatives of holomorphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Schwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.

Consider the following heteroscedastic semiparametric regression model: $y_i = X_i^T \beta + g\left( {t_i } \right) + \sigma _i e_i , 1 \leqslant i \leqslant n,$ where {X _i, 1 ≤ i ≤ n} are random design points, errors {e _i, 1 ≤ i ≤ n} are negatively associated (NA) random variables, σ _i ² = h(u _i), and {u _i} and {t _i} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the nonparametric component g (t) and the variance function h (u) are given. Under some general conditions, the strong convergence rate of these wavelet estimators is $O\left( {n^{ - \tfrac{1}{3}} \log n} \right)$. Hence our results are extensions of those results on independent random error settings.

Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation invariant differential operator $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }$ called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators $\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }$ and $\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }$ which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }$. In this paper, Teodorescu operators for the Hermitian Dirac operators $\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }$ and $\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }$ are constructed. Moreover, the structure of the Euclidean and Hermitian Teodorescu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators issuing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed.