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Bài báo này bao gồm hai phần. Ở phần đầu tiên, chúng tôi đề cập đến mối quan hệ giữa bậc, bậc thấp và số lần hướng Julia của các hàm toàn phần. Ở phần thứ hai, chúng tôi nghiên cứu sự tồn tại của các nghiệm của một lớp hàm meromorphic. Lớp hàm meromorphic này có một nền tảng vật lý thú vị.

The structure of the set S of shiftable points of wavelet subspaces is researched in this paper. We prove that S = ℝ or $$ S = \frac{1} {q}\mathbb{Z} $$ where q∈ℕ. The spectral and functional characterizations for the shiftability are given. Furthermore, the nonharmonic wavelet bases are discussed.

The space-time monopole equation is the reduction of anti-self-dual Yang-Mills equations in ℝ2,2 to ℝ2,1. This equation is a non-linear wave equation, and can be encoded in a Lax pair. An equivalent Lax pair is used by Dai and Terng to construct monopoles with continuous scattering data, and then the equation can be linearized by the scattering data, allowing one to use the inverse scattering method to solve the Cauchy problem with rapidly decaying small initial data. In this paper, we use the terminology of holomorphic bundle and transversality of certain maps, parametrized by initial data, to give more initial data, with which we can use scattering method to solve the Cauchy problem of the monopole equation up to gauge transformation.

The paper provides integral representations for solutions to a certain first order partial differential equation natural arising in the factorization of the Lamé—Navier system with the help of Clifford analysis techniques. These representations look like in spirit to the Borel—Pompeiu and Cauchy integral formulas both in three and higher dimensional setting.

In clinical studies, it is often that the medical treatments take a period of time before having an effect on patients and the delayed time may vary from person to person. Even though there exists a rich literature developing methods to estimate the time-lag period and treatment effects after lag time, most of these existing studies assume a fixed lag time. In this paper, we propose a hazard model incorporating a random treatment time-lag effect to describe the heterogeneous treatment effect among subjects. The EM algorithm is used to obtain the maximum likelihood estimator. We give the asymptotic properties of the proposed estimator and evaluate its performance via simulation studies. An application of the proposed method to real data is provided.

In this paper, under the most elementary conditions on a backward stochastic differential equation (BSDE for short) introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of "process", based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.

We give expansions about the Gumbel distribution in inverse powers of n and log n for M n , the maximum of a sample size n or n+1 when the j-th observation is $\mu (\tfrac{j} {n}) + e_j $ , µ is any smooth trend function and the residuals {e j } are independent and identically distributed with $P(e > r) \approx \exp ( - \delta x)x^{d_0 } \sum\limits_{k = 1}^\infty {c_k x^{ - k\beta } } $ as x→∞. We illustrate practical value of the expansions using simulated data sets.

The authors consider the simple random walk on the in.nite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of trees. A sufficient condition is established for Galton–Watson trees.

We consider the g–function related to a class of radial functions which gives a characterization of the L p –norm of a function on the Heisenberg group.