On a problem of Zygmund

It is proved that there exists an integrable function on [0, 1]² whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 749–762, November, 1998.     

超模的同构定理

本文利用模论导出超模的三个同构定理,同时,给出超模的Jordan-Holder定理,最后,探讨了超模的基本关系∈~*,并研究其性质．     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

The preparation and X-ray structural study of complexes that catalyze isocyanate cyclotrimerization

A 11-complex of trinitrophenol with benzyldimethylamine (1) and a 111-complex, the product of the interaction of benzyldimethylamine, glycidyl phenyl ether, and phenol (2), have been synthesized and characterized by means of X-ray analysis. Complex1 is a precursor for the catalysts of selective isocyanate cyclotrimerization, while complex2 is one of those catalysts. In the crystal structure complex1 forms H-bonded cationic-anionic aggregates with proton transfer from phenol to the N-atom of the tertiary amine. Complex2 crystallizes as a monohydrate (2a) with a strong H-bond between the quaternary ammonium and phenolic components, and exists in crystals in the form of globular H-bonded dimeric hydrates. Possible pathways of dissociation of complex2a are discussed. The data obtained may be used as a basis for further interpretation of the regularities of cyclotrimerization of isocyanates catalyzed by complexes of this type.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 92–97, January, 1993.     

太阳CO 4.6微米红外成像观测

太阳红外光谱中蕴含着丰富的物理信息,其中CO 4.6μm波段是具有代表性的分子谱带,其形成于温度极小区附近,对研究太阳物理具有极其重要的意义。为获得CO 4.6μm波段太阳单色像,本文建立了一套全反射太阳红外成像观测系统。该系统采用定天镜跟踪引光,通过成像反射镜将太阳成像于3~5μm波段红外相机的焦平面上,该相机采用的是国产HgCdTe焦平面阵列器件。同时,为提高信噪比,提出了一种有效计算平场提取观测目标的方法,并利用该方法获得了CO 4.6μm波段的太阳单色像。     

Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.