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SCIENCE CHINA Mathematics
05 April 2016, Vol. 59, No. 5


 
Hot Paper More »   
Correlation functions of gauged linear σ-model
TIAN Gang, XU GuangBo
SCIENCE CHINA Mathematics, 2016, 59(5): 823-838
DG Poisson algebra and its universal enveloping algebra
LÜ JiaFeng, WANG XingTing, ZHUANG GuangBin
SCIENCE CHINA Mathematics, 2016, 59(5): 849-860
Large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations
LIU QiHuai, LI XinXiang, YAN Jun
SCIENCE CHINA Mathematics, 2016, 59(5): 875-890
A smoothing trust region filter algorithm for nonsmooth least squares problems
CHEN XiaoJun, DU ShouQiang, ZHOU Yang
SCIENCE CHINA Mathematics, 2016, 59(5): 999-1014
 
Current Issue Archive Accepted Online First Special Topic View by Fields
  SCIENCE CHINA Mathematics--2016, 59(5)   Published: 05 April 2016
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Correlation functions of gauged linear σ-model Hot!

TIAN Gang, XU GuangBo
SCIENCE CHINA Mathematics, 2016, 59(5): 823-838 | doi:10.1007/s11425-016-5134-5
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This is the second paper in a series following Tian and Xu (2015), on the construction of a mathematical theory of the gauged linear σ-model (GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified γ-spin curve.

Articles

A characterization of Burniat surfaces with K2=4 and of non nodal type

SHIN YongJoo
SCIENCE CHINA Mathematics, 2016, 59(5): 839-848 | doi:10.1007/s11425-015-5090-5
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Let S be a minimal surface of general type with pg(S) = 0 and KS2 = 4. Assume the bicanonical map φ of S is a morphism of degree 4 such that the image of φ is smooth. Then we prove that the surface S is a Burniat surface with K2 = 4 and of non nodal type.

Articles

DG Poisson algebra and its universal enveloping algebra Hot!

LÜ JiaFeng, WANG XingTing, ZHUANG GuangBin
SCIENCE CHINA Mathematics, 2016, 59(5): 849-860 | doi:10.1007/s11425-016-5127-4
Full Text: PDF (196 KB)  
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We introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by Aue. We show that Aue has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over Aue. Furthermore, we prove that the notion of universal enveloping algebra Aue is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

Articles

Applications of balanced pairs

LI HuanHuan, WANG JunFu, HUANG ZhaoYong
SCIENCE CHINA Mathematics, 2016, 59(5): 861-874 | doi:10.1007/s11425-015-5094-1
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Let (X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to (X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y (resp. Y-coresolution dimension of X) is finite, then the bounded homotopy category of Y (resp. X) is contained in that of X (resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.

Articles

Large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations Hot!

LIU QiHuai, LI XinXiang, YAN Jun
SCIENCE CHINA Mathematics, 2016, 59(5): 875-890 | doi:10.1007/s11425-015-5102-5
Full Text: PDF (221 KB)  
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We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM (Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general convergence result for viscosity solutions and adherence of the graph as t → ∞.

Articles

The periodic unfolding method for the heat equation in perforated domains

DONATO Patrizia, YANG ZhanYing
SCIENCE CHINA Mathematics, 2016, 59(5): 891-906 | doi:10.1007/s11425-015-5103-4
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We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil (2001).

Articles

Sharp constants for a class of multilinear integral operators and some applications

WU Di, YAN DunYan
SCIENCE CHINA Mathematics, 2016, 59(5): 907-920 | doi:10.1007/s11425-015-5120-3
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We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.

Articles

Real-valued valuations on Sobolev spaces

MA Dan
SCIENCE CHINA Mathematics, 2016, 59(5): 921-934 | doi:10.1007/s11425-015-5101-6
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Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified. The centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be Lp-norms raised to p-th power (up to suitable multipication scales).

Articles

A new proof of a theorem of Petersen

YANG YiHu, ZHANG Yi
SCIENCE CHINA Mathematics, 2016, 59(5): 935-944 | doi:10.1007/s11425-015-5091-4
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Let M be an n-dimensional complete Riemannian manifold with Ricci curvature ≥ n - 1. By developing some new techniques, Colding (1996) proved that the following three conditions are equivalent: 1) dGH(M, Sn) → 0; 2) the volume of M Vol(M) → Vol(Sn); 3) the radius of MM) →π. By developing a different technique, Petersen (1999) gave the 4th equivalent condition, namely he proved that the n + 1-th eigenvalue of M, λn+1(M) → n, is also equivalent to the radius of M, rad(M) →π, and hence the other two. In this paper, we use Colding's techniques to give a new proof of Petersen's theorem. We expect our estimates will have further applications.

Articles

Strong laws of large numbers for sub-linear expectations

CHEN ZengJing
SCIENCE CHINA Mathematics, 2016, 59(5): 945-954 | doi:10.1007/s11425-015-5095-0
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We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.

Articles

Dynamic bivariate normal copula

LIAO Xin, PENG Liang, PENG ZuoXiang, ZHENG YanTing
SCIENCE CHINA Mathematics, 2016, 59(5): 955-976 | doi:10.1007/s11425-015-5114-1
Full Text: PDF (1166 KB)  
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Normal copula with a correlation coefficient between -1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, Hüsler and Reiss (1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by Hüsler and Reiss (1989). A simulation study and real data analysis are presented too.

Articles

Composite quantile regression estimation for P-GARCH processes

ZHAO Biao, CHEN Zhao, TAO GuiPing, CHEN Min
SCIENCE CHINA Mathematics, 2016, 59(5): 977-998 | doi:10.1007/s11425-015-5115-0
Full Text: PDF (254 KB)  
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We consider the periodic generalized autoregressive conditional heteroskedasticity (P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator. The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions. The proposed methodology is also illustrated by VaR on stock price data.

Articles

A smoothing trust region filter algorithm for nonsmooth least squares problems Hot!

CHEN XiaoJun, DU ShouQiang, ZHOU Yang
SCIENCE CHINA Mathematics, 2016, 59(5): 999-1014 | doi:10.1007/s11425-015-5116-z
Full Text: PDF (315 KB)  
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We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.

Articles

Strategically supported cooperation in dynamic games with coalition structures

WANG Lei, GAO HongWei, PETROSYAN Leon, QIAO Han, SEDAKOV Artem
SCIENCE CHINA Mathematics, 2016, 59(5): 1015-1028 | doi:10.1007/s11425-016-5131-8
Full Text: PDF (196 KB)  
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The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments. From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.

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