Pointwise Estimates for a Class of Oscillatory Integrals and Related Lp–Lq Estimates

In this article we establish pointwise estimates for a class of oscillatory integrals related to the fundamental solution of the dispersive equation ∂_t u − iP (D_x)u = 0, where P(D_x) is a differential operator whose symbol P(ξ) is a real polynomial in one variable. Then we use such pointwise estimates to establish L^p–L^q estimates for the solution of this equation.     

Heisenberg群上一类左不变LPDO的局部基本解及局部可解性

In this paper it is proved that local fundamental solution exists in some space W^m(H_n) (m∈Z), if the left invariant differential operator on the Heisenberg group H_n satisfies certain condition. The main results are:l.Let L be a left invariant differential operator on H_n. If there exist R≥0, r,s∈R and operators {B_λ|λ∈Γ_R} ∈V^s(Γ_R, M^r) such that, for almost all λ∈Γ_R, B_λ is the right inverse of Ⅱ_λ(L), then there exists E∈W^m(H_n) (when m≥0 or m even) or E∈W^m-1(H_n) (when m<0 and odd) such that LE =δ(near the origie) Where m=min([r],-[2s]-n-2); 2. Let L(W,T) be of the form (3.1). If there exist R≥0 and r,s∈R such that when |λ|≥R,(?) and C_λ≥ C|λ|^x(C>0), then the same conclusion as above holds with m=min(-[2r]-n-2,[-2s]-n-2).     

Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

The Synthesis and 31P NMR Spectral Studies of Cyclophosphazenes

A modified method for preparing large-scale quantities of pure hexachlorocyclophosphazene (N₃P₃Cl₆) and octachlorocyclotetraphosphazene (N₄P₄Cl₈), phosphorus pentachloride with ammonium chloride, in the presence of zinc chloride, has been developed. The time of the reaction and the quantities of the catalyst are also studied. It is found that the optimum reaction time is 1.5 h and by-products are remarkably reduced by addition of 10% zinc chloride. As indicated by the ³¹ P NMR spectra, the synthesis and separation of cyclophosphazenes can be accomplished in moderate yield of tetramer (39%) and good yield of trimer (83%).     

Synthesis and characterization of folic acid‐modified carboxymethyl chitosan‐ursolic acid targeted nano‐drug carrier for the delivery of ursolic acid and 10‐hydroxycamptothecin

Carboxymethyl chitosan (CMCS), as a water‐soluble, biocompatible, and biodegradable polymer, is an excellent carrier for a sustained drug delivery system. In this study, a amphiphilic carboxymethyl chitosan‐ursolic acid nano‐drug carrier modified by folic acid (FPCU) were prepared, and then the nano‐drug carrier wrapped another anticancer drug 10‐hydroxycamptothecin were self‐assembled into nanoparticles (FPCU/HCPT NPs). The FPCU/HCPT NPs had a suitable size, high drug loading efficiency of ursolic acid (6.4%) and 10‐hydroxycamptothecin (14.1%). The drug release study in vitro indicated that the nanoparticles have obviously sustained effect and pH sensitive behaviors, the drug release amount was higher at pH 5.5 than at pH 7.4. in vitro and in vivo study showed that the nanoparticles displayed a high antitumor efficiency to tumor cells compared with free drug. The nano delivery system as a carrier for ursolic acid (UA) and 10‐hydroxycamptothecin (HCPT) has good application prospects in cancer treatment.     

Strong-Base-Assisted Synthesis of a Crystalline Covalent Triazine Framework with High Hydrophilicity via Benzylamine Monomer for Photocatalytic Water Splitting

Methods to synthesize crystalline covalent triazine frameworks (CTFs) are limited and little attention has been paid to development of hydrophilic CTFs and photocatalytic overall water splitting. A route to synthesize crystalline and hydrophilic CTF-HUST-A1 with a benzylamine-functionalized monomer is presented. The base reagent used plays an important role in the enhancement of crystallinity and hydrophilicity. CTF-HUST-A1 exhibits good crystallinity, excellent hydrophilicity, and excellent photocatalytic activity in sacrificial photocatalytic hydrogen evolution (hydrogen evolution rate up to 9200 μmol g⁻¹ h⁻¹). Photocatalytic overall water splitting is achieved by depositing dual co-catalysts in CTF-HUST-A1, with H₂ evolution and O₂ evolution rates of 25.4 μmol g⁻¹ h⁻¹ and 12.9 μmol g⁻¹ h⁻¹ in pure water without using sacrificial agent.     

一类半线性积分微分方程初边值问题的爆破解和全局解

本文研究初边值问题的爆破解和全局解，证明了在ｆ的凸性假设和一定的增长性假定下解在有限时刻爆破，而在ｆ的其他假设下证明了全局解的存在性。     

Refined Composite Multi-Scale Reverse Weighted Permutation Entropy and Its Applications in Ship-Radiated Noise

Ship-radiated noise is one of the important signal types under the complex ocean background, which can well reflect physical properties of ships. As one of the valid measures to characterize the complexity of ship-radiated noise, permutation entropy (PE) has the advantages of high efficiency and simple calculation. However, PE has the problems of missing amplitude information and single scale. To address the two drawbacks, refined composite multi-scale reverse weighted PE (RCMRWPE), as a novel measurement technology of describing the signal complexity, is put forward based on refined composite multi-scale processing (RCMP) and reverse weighted PE (RWPE). RCMP is an improved method of coarse-graining, which not only solves the problem of single scale, but also improves the stability of traditional coarse-graining; RWPE has been proposed more recently, and has better inter-class separability and robustness performance to noise than PE, weighted PE (WPE), and reverse PE (RPE). Additionally, a feature extraction scheme of ship-radiated noise is proposed based on RCMRWPE, furthermore, RCMRWPE is combined with discriminant analysis classifier (DAC) to form a new classification method. After that, a large number of comparative experiments of feature extraction schemes and classification methods with two artificial random signals and six ship-radiated noise are carried out, which show that the proposed feature extraction scheme has better performance in distinguishing ability and stability than the other three similar feature extraction schemes based on multi-scale PE (MPE), multi-scale WPE (MWPE), and multi-scale RPE (MRPE), and the proposed classification method also has the highest recognition rate.     

Uniqueness of weak solution to the generalized magneto-hydrodynamic system

We study uniqueness of weak solution for the generalized incompressible magneto-hydrodynamic (GMHD) system with suitable \(\beta \) , and we prove that the weak solutions are unique in the class \(L^{\frac{2\beta }{2\beta -1+r}}(0,T;B^{r}_{\infty ,\infty })\) with \(r\in (1-2\beta ,1]\) .