CONVERGENCE OF DOUBLE WALSH-FOURIER SERIES AND HARDY SPACES

It is proved that the maximal operator of the Marczinkiewicz-Fejér meams of a double Walsh-Fourier series is bounded from the two-dimensional dyadic martingale Hardy space H p to L p (2/3<p<∞) and is of weak type (1,1). As a consequence we obtain that the Marczinkiewicz-Fejér means of a function f∈L 1 converge a.e. to the function in question. Moreover, we prove that these means are uniformly bounded on H p whenever 2/3<p<∞. Thus, in case f∈H p , the Marczinkiewicz-Fejér means conv f in H p norm. The same results are proved for the conjugate means, too.

Crack spacing threshold of double cracks propagation for large-module rack

Large-module rack of the Three Gorges shiplift is manufactured by casting and machining, which is unable to avoid slag inclusions and surface cracks. To ensure its safety in the future service, studying on crack propagation rule and the residual life estimation method of large-module rack is of great significance. The possible crack distribution forms of the rack in the Three Gorges shiplift were studied. By applying moving load on the model in FRANC3 D and ANSYS, quantitative analyses of interference effects on double cracks in both collinear and offset conditions were conducted. The variation rule of the stress intensity factor(SIF) influence factor, RK, of double collinear cracks changing with crack spacing ratio, RS, was researched. The horizontal and vertical crack spacing threshold of double cracks within the design life of the shiplift were obtained, which are 24 and 4 times as large as half of initial crack length, c0, respectively. The crack growth rates along the length and depth directions in the process of coalescence on double collinear cracks were also studied.

A Generic Description Model for the Structure of Atomic Nucleus with New Interpretation of the Strong Forces

The present investigation is motivated by finding and developing an easily understandable solution in the context of unified quantum and gravitational theories. Model-based methods are applied, with emphasis on structural descriptions by introducing some strong hypotheses. A subset of the introduced hypotheses led to a surprising understanding of the internal structure and construction of quarks, neutrons, protons and more complex atomic nuclei. The research work therefore focused mainly on the model-based interpretation of subatomic processes. The results obtained so far and presented in this paper are new. They consist of a generic description model for the structure of atomic nuclei. This model contains two important structural links that originate from the initial phase of the cosmological big bang. They hold atomic parts together and are involved in many known nuclear fusion and fission processes. Modifications of them, including the electron-positron annihilation process, are necessary and will be described. A new interpretation of the strong forces from the Standard Model is possible and will be given. In addition, the formation processes for electron and positron particles are considered. Based on the structural relationships, a deeper understanding of matter transformations (transmutations), early cosmological processes and dark matter has been achieved. All challenges of this work are the logical conclusions from the used hypotheses on two structural links. They need to be further investigated and verified by theoretical and experimental works. The postulated particle in this paper, as accompanying product in the electron-positron annihilation, will play a major role for the future investigations.

A Special MJO Event with a Double Kelvin Wave Structure

The second Madden–Julian Oscillation（MJO）event during the field campaign of the Dynamics of the MJO/Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011（DYNAMO/CINDY2011）exhibi ted an unusual double rainband structure.Using a wavenumber-frequency spectral filtering method,we unveil that this double rainband structure arises primarily from the Kelvin wave component.The zonal phase speed of the double rainbands is about 7.9 degree per day in the equatorial Indian Ocean,being in the range of convectively coupled Kelvin wave phase speeds.The convection and circulation anomalies associated with the Kelvin wave component are characterized by two anomalous convective cells,with low-level westerly（easterly）and high（low）pressure anomalies to the west（east）of the convective centers,and opposite wind and pressure anomalies in the upper troposphere.Such a zonal wind–pressure phase relationship is consistent with the equatorial free-wave dynamics.While the freeatmospheric circulation was dominated by the first baroclinic mode vertical structure,moisture and vertical motion in the boundary layer led the convection.The convection and circulation structures derived based on the conventional MJO filter show a different characteristic.For example,the phase speed is slower（about 5.9 degree per day）,and there were no double convective branches.This suggests that MJO generally involves multi-scales and it is incomplete to extract its signals by using the conventional filtering technique.

OPERATORS ON CORNER MANIFOLDS WITH EXIT TO INFINITY

We study （pseudo-）differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are corner degenerate in a specific way. They are described Cmodulo ＇lower order terms＇） by a principal symbolic hierarchy σ（A） = （σψ （A）, σ∧ CA）, σ∧ （A））, where σψ is the interior symbol and σ∧（A） （y, η）, （y, η） ∈ T＊Y／0, the Coperator-valued） edge symbol of ＇first generation＇, cf. [1]. The novelty here is the edge symbol σ∧ of ＇second generation＇, parametrised by （z, ζ） ∈ T＊Z ／ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.