A sharp estimate of positive integral points in6-dimensional polyhedra and a sharp estimate of smooth numbers

Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

CLINICAL OBSERVATION ON TREATMENT OF ACUTE BRONCHITIS PRIMARILY WITH PRICKING-CUPPING ON BACK-SHU POINTS

To observe the clinical effect of treatment of acute bronchitis primarily with prickingcupping method on Back-shu points. Methods. The patients of acute bronchitis were randomly divided into 2 groups. In the observation group, there were 36 cases, who were treated with the integrated traditional Chinese and western medicine, primarily the pricking-cupping method on Back-shu points; while in the control group, there were 29 cases who were given the conventinal treatment of western medicine. All the 2 groups were treated for 7 days as one treating course. Results： The total effective rate of the observation group was 97.2% while that of the control group was 82,8%, so there is a significant difference between them. On the first and third days the clinical manifestations were more satisfactorily improved in the treatment group than in the control group （P 〈 0.01） and on the fifth and seventh days, the comparison showed no significant difference （P〉0.05）. Conclusion： The treatment of acute bronchitis by means of the integrated traditional Chinese and western medicine primarily with pricking-cupping method on Back-shu points is of marked therapeutic effect, simple manipulation, and little untoward effects, thus claiming the unique advantage.

THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION

The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma￣[2], Ihe isolated wave in transmission line￣[3], and the isolated wave in the bound-ary surface of the divided layer fluid￣[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.

Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees

Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical method to solve PDE on manifold.In the paper,we propose a method called point integral method(PIM)to solve the Poisson-type equations from point clouds.Among different kinds of PDEs,the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important.In PIM,the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function.This featuremakes the integral equation easy to be discretized frompoint cloud.In the paper,we explain the derivation of the integral equations,describe the point integral method and its implementation,and present the numerical experiments to demonstrate the convergence of PIM.

Multi-stage expansion planning of energy storage integrated soft open points considering tie-line reconstruction

With the rapid development of flexible interconnection technology in active distribution networks(ADNs),many power electronic devices have been employed to improve system operational performance.As a novel fully-con-trolled power electronic device,energy storage integrated soft open point(ESOP)is gradually replacing traditional switches.This can significantly enhance the controllability of ADNs.To facilitate the utilization of ESOP,device loca-tions and capacities should be configured optimally.Thus,this paper proposes a multi-stage expansion planning method of ESOP with the consideration of tie-line reconstruction.First,based on multi-terminal modular design characteristics,the ESOP planning model is established.A multi-stage planning framework of ESOP is then presented,in which the evolutionary relationship among different planning schemes is analyzed.Based on this framework,a multi-stage planning method of ESOP with consideration of tie-line reconstruction is subsequently proposed.Finally,case studies are conducted on a modified practical distribution network,and the cost-benefit analysis of device and multiple impact factors are given to prove the effectiveness of the proposed method.

Entire curves,integral sets and principal bundles

We compare the behaviour of entire curves and integral sets,in particular in relation to locally trivial fiber bundles,algebraic groups and finite ramified covers over semi-abelian varieties.

On orders in number fields: Picard groups, ring class fields and applications

We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group.As an application, we give criteria of the integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.