Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

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, Volume 11 Issue 2

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RESEARCH ARTICLE
Classification of Bott towers by matrix
Qifeng BAI,Fang LI
Front. Math. China. 2016, 11 (2): 255-268.  
https://doi.org/10.1007/s11464-015-0511-x

Abstract   PDF (146KB)

A criterion for the classification of Bott towers is presented, i.e., two ABott towers B?(A) and B?(A') are isomorphic if and only if the matrices A and A' are equivalent. The equivalence relation is defined by two operations on matrices. And it is based on the observation that any Bott tower B?(A) is uniquely determined by its structure matrix A, which is a strictly upper triangular integer matrix. The classification of Bott towers is closely related to the cohomological rigidity problem for both Bott towers and Bott manifolds.

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Classification of irreducible non-zero level quasifinite modules over twisted affine Nappi-Witten algebra
Xue CHEN
Front. Math. China. 2016, 11 (2): 269-277.  
https://doi.org/10.1007/s11464-016-0531-1

Abstract   PDF (108KB)

We obtain that every irreducible quasifinite module with non-zero level over the twisted affine Nappi-Witten algebra is either a highest weight module or a lowest one.

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Minimum distances of three families of low-density parity-check codes based on finite geometries
Yanan FENG,Shuo DENG,Lu WANG,Changli MA
Front. Math. China. 2016, 11 (2): 279-289.  
https://doi.org/10.1007/s11464-016-0530-2

Abstract   PDF (130KB)

Three families of low-density parity-check (LDPC) codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.

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Large and moderate deviations in testing Ornstein-Uhlenbeck process with linear drift
Hui JIANG
Front. Math. China. 2016, 11 (2): 291-307.  
https://doi.org/10.1007/s11464-016-0513-3

Abstract   PDF (161KB)

This paper studies hypothesis testing in the Ornstein-Ulenbeck process with linear drift. With the help of large and moderate deviations for the log-likelihood ratio process, the decision regions and the corresponding decay rates of the error probabilities related to this testing problem are established.

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Geometric characterizations for variational minimizing solutions of charged 3-body problems
Wentian KUANG,Yiming LONG
Front. Math. China. 2016, 11 (2): 309-321.  
https://doi.org/10.1007/s11464-016-0514-2

Abstract   PDF (142KB)

We study the charged 3-body problem with the potential function being (-α)-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the π2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.

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Wakimoto modules for twisted multi-loop algebra of type A1 × A1
Dexin LAN,Xiaoli KONG,Jinglian JIANG
Front. Math. China. 2016, 11 (2): 323-338.  
https://doi.org/10.1007/s11464-015-0493-8

Abstract   PDF (139KB)

We construct a class of modules for the twisted multi-loop algebra of type A1×A1 by applying Wakimoto free bosonic realization. We also discuss the structures and the irreducibility of the Fock space.

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Construction of balanced Boolean functions with high nonlinearity, good local and global avalanche characteristics
Luyang LI,Yujuan SUN,Weiguo ZHANG
Front. Math. China. 2016, 11 (2): 339-352.  
https://doi.org/10.1007/s11464-016-0518-y

Abstract   PDF (138KB)

Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered:high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.

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Irreducible A(1)1 -modules from modules over two-dimensional non-abelian Lie algebra
Genqiang LIU,Yueqiang ZHAO
Front. Math. China. 2016, 11 (2): 353-363.  
https://doi.org/10.1007/s11464-016-0503-5

Abstract   PDF (129KB)

For any module V over the two-dimensional non-abelian Lie algebra b and scalar α∈?, we define a class of weight modules Fα(V) with zero central charge over the affine Lie algebra A(1)1. These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα(V) to be irreducible. In this way, we obtain a lot of irreducible weight A(1)1-modules with infinite-dimensional weight spaces.

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A restriction theorem for Grushin operators
Heping LIU,Manli SONG
Front. Math. China. 2016, 11 (2): 365-375.  
https://doi.org/10.1007/s11464-016-0529-8

Abstract   PDF (131KB)

We study the Grushin operators acting on ?xd1×?td2 and defined by the formula L=-j=1d1?xj2-j=1d1|xj|2k=1d2?tk2. We establish a restriction theorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. Müller [Ann. of Math., 1990, 131: 567–587].

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Generalizations of von Neumann regular rings, PP rings, and Baer rings
Lixin MAO
Front. Math. China. 2016, 11 (2): 377-400.  
https://doi.org/10.1007/s11464-016-0523-1

Abstract   PDF (203KB)

We introduce the notions of IDS modules, IP modules, and Baer* modules, which are new generalizations of von Neumann regular rings, PPrings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer? modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer*modules.

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Injective objects of monomorphism categories
Keyan SONG,Yuehui ZHANG
Front. Math. China. 2016, 11 (2): 401-409.  
https://doi.org/10.1007/s11464-016-0524-0

Abstract   PDF (115KB)

For an acyclic quiver Q and a finite-dimensional algebra A, we give a unified form of the indecomposable injective objects in the monomorphism category Mon(Q,A) and prove that Mon(Q,A) has enough injective objects.

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Domain of attraction of quasi-stationary distribution for one-dimensional diffusions
Hanjun ZHANG,Guoman HE
Front. Math. China. 2016, 11 (2): 411-421.  
https://doi.org/10.1007/s11464-016-0515-1

Abstract   PDF (121KB)

We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and+is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.

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Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces
Jing ZHANG,Huoxiong WU
Front. Math. China. 2016, 11 (2): 423-447.  
https://doi.org/10.1007/s11464-015-0462-2

Abstract   PDF (219KB)

This paper is devoted to investigating the bounded behaviors of the oscillation and variation operators for Calderón-Zygmund singular integrals and the corresponding commutators on the weighted Morrey spaces. We establish several criterions of boundedness, which are applied to obtain the corresponding bounds for the oscillation and variation operators of Hilbert transform, Hermitian Riesz transform and their commutators with BMO functions, or Lipschitz functions on weighted Morrey spaces.

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Waring-Goldbach problems for unlike powers with almost equal variables
Meng ZHANG
Front. Math. China. 2016, 11 (2): 449-460.  
https://doi.org/10.1007/s11464-016-0512-4

Abstract   PDF (140KB)

We prove that almost all positive even integers n can be written as n=p22+p33+p44+p55 with |pkk-N4|N321325+? for 2≤k≤5. Moreover, it is proved that each sufficiently large odd integer N can be represented as N=p1+p22+p33+p44+p55 with |pkk-N5|N321325+?for 1≤k≤5.

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Shift Harnack inequality and integration by parts formula for semilinear stochastic partial differential equations
Shaoqin ZHANG
Front. Math. China. 2016, 11 (2): 461-496.  
https://doi.org/10.1007/s11464-016-0526-y

Abstract   PDF (277KB)

Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F. -Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.

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Free involutive Hom-semigroups and Hom-associative algebras
Shanghua ZHENG,Li GUO
Front. Math. China. 2016, 11 (2): 497-508.  
https://doi.org/10.1007/s11464-015-0448-0

Abstract   PDF (129KB)

We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence, we obtain free Hom-associative algebras generated by a set under the same conditions for the unary operation.

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16 articles