A strictly finitary non-triviality proof for a paraconsistent system of set theory deductively equivalent to classical ZFC minus foundation

The paraconsistent system CPQ-ZFC/F is defined. It is shown using strong non-finitary methods that the theorems of CPQ-ZFC/F are exactly the theorems of classical ZFC minus foundation. The proof presented in the paper uses the assumption that a strongly inaccessible cardinal exists. It is then shown using strictly finitary methods that CPQ-ZFC/F is non-trivial. CPQ-ZFC/F thus provides a formulation of set theory that has the same deductive power as the corresponding classical system but is more reliable in that non-triviality is provable by strictly finitary methods. This result does not contradict G?del's incompleteness theorem because the proof of the deductive equivalence of the paraconsistent and classical systemss use non-finitary methods. Received: 20 July 1998     

Homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity

In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions.     

Compactly Supported Wavelets Through the Classical Umbral Calculus

We explore compactly supported scaling functions of wavelet theory by means of classical umbral calculus as reformulated by Rota and Taylor. We set a theory of orthonormal scaling umbra which leads to a very simple and elementary proof of Lawton's theorem for umbrae. When umbrae come from a wavelet setting, we recover the usual Lawton condition for the orthonormality of the integer translates of a scaling function.     

A semantical proof of the strong normalization theorem for full propositional classical natural deduction

We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.     

Completeness of location families,translated moments,and uniqueness of charges

Summary A sufficient condition for statistical completeness of location families generated by a probability density in euclidean space is given. As an application, completeness of families generated by a symmetric stable law is proved. Our criterion, complementing a classical result of Wiener and recent work of Isenbeck and Rüschendorf, is in terms of regularity of the generating density and zerofreeness of its characteristic function. Its proof rests on a local version of the convolution theorem for Fourier transforms of tempered distributions. A more general version of the criterion is applicable to apparently different problems, as is illustrated by giving a simultaneous proof of a theorem on translated moments by P. Hall and a uniqueness result of M. Riesz in potential theory.     

Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem

We present a new proof of the classical Kirszbraun-Valentine extension theorem. Our proof is based on the Fenchel duality theorem from convex analysis and an analog for nonexpansive mappings of the Fitzpatrick function from monotone operator theory.

     

Symmetrization for Fractional Elliptic and Parabolic Equations and an Isoperimetric Application

This paper develops further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors.This theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic and parabolic equations.The authors extend the theory for the so-called restricted fractional Laplacian defined on a bounded domain Ω of]RN with zero Dirichlet conditions outside of Ω.As an application,an original proof of the corresponding fractional Faber-Krahn inequality is derived.A more classical variational proof of the inequality is also provided.     

Well-posedness for entropy solutions to multidimensional scalar conservation laws with a strong boundary condition

In this paper we give a simple proof of well-posedness of multidimensional scalar conservations laws with a strong boundary condition. The proof is based on a result of strong trace for solutions of scalar conservation laws and kinetic formulation.     

非可加集函数的Lebesgue分解

本文讨论一般的非可加集函数的Lebesgue分解定理,它是经典测度论中相应结果的扩充,同时,也为经典可加测度的Lebessue分解定理提供了另一证明方法.     

高阶波动方程的时空估计与低能量散射

本文研究了高阶波动方程的低能量散射理论，基本工具是高阶线性波动方程解的时空估计．与经典的二阶波动方程解的时空估计证明不同，我们采用泛函分析的方法与待定指标技巧，首次给出了高阶线性波动方程的时空估计，藉此与非线性函数在齐次Ｓｏｂｏｌｅｖ空间中的估计，获得了高阶波动方程的低能量散射结论．与此同时，也得到了具临界增长的高阶波动方程的柯西问题在低能量条件下的整体存在唯一性．     

A simple justification of the singular limit for equatorial shallow‐water dynamics

The equatorial shallow‐water equations at low Froude number form a symmetric hyperbolic system with large variable‐coefficient terms. Although such systems are not covered by the classical Klainerman‐Majda theory of singular limits, the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long‐wave equations as the height and Froude number tend to 0. Their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions. A simpler proof of a slight generalization is presented here in the spirit of the classical theory. © 2008 Wiley Periodicals, Inc.     

From an iteration formula to Poincaré's Isochronous Center Theorem for holomorphic vector fields

We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H. Poincaré, for the condition under which a singularity of a holomorphic vector field is an isochronous center.

     

The classical KAM theorem for Hamiltonian systems via rational approximations

In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-Rüssmann condition, in real-analytic non-degenerate Hamiltonian systems close to integrable. The proof, which uses rational approximations instead of small divisors estimates, is an adaptation to the Hamiltonian setting of the method we introduced in [4] for perturbations of constant vector fields on the torus.     

On an identity from classical invariant theroy

A simple derivation is given of a well-known relation involving the so-called "Cayley Operator" of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics.     

球面S~(d-1)上的广义Ul'yanov型不等式

本文对于单位球面上的经典连续模,给出了一个非常有用的广义Ul'yanov型不等式.该不等式在球面多项式逼近、球面嵌入理论以及球面上函数空间的插值理论等领域有着非常重要的应用.我们的证明基于球面调和多项式展开的新的估计,这些估计本身也具有独立的意义.     

Topos中的Galois联络

In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.     

On a classical theorem in the theory of Fourier integrals

In this note we give a short proof of a classical theorem in the theory of Fourier integrals.

     

Global asymptotic stability of the Goodwin system with repression

We give a global asymptotic stability result for the classical Goodwin system. The proof follows from a combination of the Poincaré–Bendixson property enjoyed by monotone cyclic feedback systems, the theory of compound matrices and comparison techniques from the theory of monotone systems.     

关于Thiele型向量值连分式收敛定理的一个注记

本文利用推广的向量连分式向后递推算法重新给出了文[3]中定理1的证明,并改进了其结果。最后,在稍强的条件下,给出了这一类收敛向量连分式的一个更精致的截断误差估计。     

Some uniform estimates and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows

This paper concerns the global existence and the large time behavior of strong and classical solutions to the two-dimensional (2D) Stokes approximation equations for the compressible flows. We consider the unique global strong solution or classical solution to the 2D Stokes approximation equations for the compressible flows together with the space-periodicity boundary condition or the no-stick boundary condition or Cauchy problem for arbitrarily large initial data. First, we prove that the density is bounded from above independent of time in all these cases. Secondly, we show that for the space-periodicity boundary condition or the no-stick boundary condition, if the initial density contains vacuum at least at one point, then the global strong (or classical) solution must blow up as time goes to infinity.