Science China Mathematics
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On triangular algebras with noncommutative diagonals
Science China Mathematics - Tập 51 - Trang 1937-1944 - 2008
We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.
Invariant integral and statistical equations of paraxial light beam transmission in free space
Science China Mathematics - Tập 40 - Trang 546-554 - 1997
The statistical behavior of arbitrary paraxial light beams propagating in free space is investigated by using the Hermite-Gaussian expansion method and Fock’s representation. A series of equivalent Gaussian parameters for paraxial beam and the statistical equations for these parameters are presented. The optical transmission problem in quasi-far field region is studied. The so-called general Hermi......
Preparation of very long and open aligned carbon nanotubes
Science China Mathematics - Tập 43 - Trang 210-216 - 2000
Very long and open aligned carbon nanotubes that reach about 2 mm long, an order of magnitude longer than previously reached, have been prepared by chemical vapor deposition over silica dioxide substrates on the surface, where iron/silica nano-composite particles are evenly positioned. The nanotubes are naturally opened at the bottom ends. The growth mechanism of the very long and openended nanotu......
Experimental studies of axial magnetic fields generated in ultrashort-pulse laser-plasma interaction
Science China Mathematics - Tập 43 - Trang 1312-1317 - 2000
The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction.
Remarks on the rank properties of formal CR maps
Science China Mathematics - Tập 49 - Trang 1477-1490 - 2006
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
Multi-dimensional versions of a formula of Popoviciu
Science China Mathematics - Tập 50 - Trang 285-291 - 2007
In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s × (s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of......
Noise control and utility: From regulatory network to spatial patterning
Science China Mathematics - - 2020
Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network congurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilit......
Problem of invariant subspaces in C*-algebras
Science China Mathematics - - 2002
Let A be a separable simple C*-algebra. For each ;) on A such that π(a) has a non-trivial invariant subspace in Hπ.
Elliptic genera of homogeneous spin manifolds and theta functions identities
Science China Mathematics - Tập 48 - Trang 1637-1645 - 2005
By Witten rigidity theorem and the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, the elliptic genus of a homogeneous spin manifold G/H can be expressed as a sum of theta functions quotients over the Weyl group of G. Consequently, we obtain several classes of combinatorial identities of theta functions.
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