Further explorations on bridged 1,2,4-trioxanes

Three new bicyclo[3.2.1]-type 1,2,4-trioxanes have been designed and synthesized. One of them demonstrates better tolerance of the intramolecular hemiketals to steric crowding in hydroperoxidation. The other represents a prototype for possible manipulation of the transient radicals generated in cleavage reactions. A new substitution pattern in the bridged system is explored through synthesis of the third molecule. The configurations of all stereogenic centers in the bridged system can be effectively controlled by the chirality of the allyl alcohol as illustrated by the enantioselective synthesis of the fourth molecule. Finally, similar bicyclo[3.3.1]-type 1,2,4-trioxanes are shown very difficult to be synthesized because of the involvement of a conformer with two substituents at axial positions at the same time.     

NMR SPECTROSCOPIC STUDY ON COPOLYMER OF ETHYLENE-NORBORNENE

A series of ethylene-norbornene copolymers were synthesised using VO (OEt) Cl_2/Al_2Et_3Cl_3 catalytic system and their structure was characterized by ~1H-NMR, ~1H-~1HCOSY NMR and ~(13)C-NMR. Assignments of NMR spectra were given and discussed indetail.     

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H²(D) and the Fock space g².The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.     

Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations

Numerical Algorithms - This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity...     

A Review of Results on Axially Symmetric Navier-Stokes Equations,with Addendum by X. Pan and Q. Zhang

In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail.In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors.     

The critical exponent of degenerate parabolic systems

The Cauchy problemu _t=u +v ^p ,v _t =v +u ^q is studied, wherex R ^N , 0 <t < and ,,p andq, are positive exponents. It is proved that ifp,q 1 and 1 <pq < 1 + 2 max(p + ,q + )/n then every nontrivial non-negative solution is not global in time; whereaspq > 1 + 2 max(p + , q + )/n then there exist both positive global solutions and non-global solutions. In addition, the decaying in time of solutions tou _t,=u inR ⁿ × (0, ), an equation which occurs naturally in our study of above systems, is studied and solutions with the fastest decaying in time are constructed.     

Regularity of minimizers of non-isotropic integrals of the calculus of variations

The regularity of the minimizers of a special type of non-isotropic variational minimization problem is studied. The particularity of the potential of energy is that it has different growth rate with respect to different parts of the derivatives of the function. In particular, the model treated in this paper can be described as $$\Phi (Du) = |\partial _1 u|^2 + |\partial _2 u|^2 + |\partial _3 u|^2 + |\partial _3 u - |^p .$$ By using a result of P.Marcellini (cf. [4]) and perturbation method, it is proved that the minimizer of the Dirichlet boundary value problem is a function of W _loc ^{1, ∞} .