A Relationship Between the Conditional <Emphasis Type="Italic">g</Emphasis>-Evaluation System and the Generator <Emphasis Type="Italic">g</Emphasis> and Its Applications

In this paper, under the most elementary conditions on a backward stochastic differential equation （BSDE for short） introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of ＂process＂, based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.     

ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved, with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.     

Nonlinear Doob-Meyer Decomposition for General Filtration

The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.     

SMALLEST g-SUPERSOLUTION FOR BSDE WITH CONTINUOUS DRIFT COEFFICIENTS

91. IntroductionSince the result of monotonic lied theorem of BSDE and its aPPlication to nonlinearDoolyMeyer decomposition theorem, the smallest g-supersolution with a constraint on (Y, Z)(see [1]), some developments have been done, for example, in 14], where by a penallzationmethod, Chen and Peng discussed nonlinear Doob-Meyer decomposition theorem ash theBSDE introduced by Duffie and EPsteinI3]. In [51 Lin discussed the smallest g-supersolutionto BSDE with a constraint on (y,z) wi…     

Orthogonality of Generalized (θ,φ)-Derivations on Ideals

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized (θ,φ)-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

理想上的广义$(\theta,\phi)$-导子的正交性

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized （θ,φ）-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

非奇异H-张量的新判定（英文）

H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors. In this paper, some definitions and theorems related to H-tensors are introduced firstly. Secondly, some new criteria for identifying nonsingular H-tensors are proposed, moreover, a new theorem for identifying positive definiteness of even order real symmetric tensors is obtained. Finally, some numerical examples are given to illustrate our results.     

EXISTENCE OF TWO PERIODIC SOLUTIONS TO n-DIMENSIONAL NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEM

In this paper,some suffcient criteria for the existence and the multiplicity of positive periodic solutions to a class of first-order n-dimensional neutral functional differential system are established. Our main results generalize related studies in the previous literatures. The fixed point theorem in cones is required to prove our results.     

Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain

We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation Δu-Vu=g（·,u）, where V and g are Borel measurable functions, required to satisfy suitable assumptions related to a new functional class J. Our approach uses the Schauder fixed point theorem.     

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.     

A Converse Comparison Theorem for <Emphasis Type="Italic">g</Emphasis>-Expectations

With the help of a limit property of solutions of backward stochastic differential equations(BSDEs),this paper establishes a converse comparison theorem for deterministic generators g of BSDEs under the assumption g(t, y, 0) ≡0.     

A Property of <Emphasis Type="Italic">g</Emphasis>-Expectation

This paper proves that, under the hypothesis g(t, 0, 0) ≡ 0 and some natural assumptions, the generator g of a backward stochastic differential equation can be uniquely determined by the corresponding g-expectations with all terminal conditions. The main result of this paper also confirms and extends Peng Shige‘s conjecture.     

Jensen’s Inequality for Backward Stochastic Differential Equations

Abstract Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9]. *Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.     

Notes on symmetric g-functions

A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable. The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China.     

A generalized Henstock-Stieltjes integral involving division functions

We can consider the Riemann-Stieltjes integral dg as an integral of a point function f with respect to an interval function g. We could extend it to the Henstock-Stieltjes integral. In this paper, we extend it to a generalized Stieltjes integral dg of a point function f with respect to a function g of divisions of an interval. Then we prove for this integral the standard results in the theory of integration, including the controlled convergence theorem.      

条件g-期望的矩不等式

找到了几个使条件g-期望的矩不等式在一般意义下成立的关于g和g-期望的充分条件.     

On Λ-generalized closed sets in topological spaces

We introduce new classes of sets called Λ _g -closed sets and Λ _g -open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ _g -closed sets and Λ _g -open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively. Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday     

（g, f）-Factorizations Randomly Orthogonal to a Subgraph in Graphs

Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integervalued functions defined on V(G) such that 2k - 2 ≤g(x)≤f(x) for all x∈V(G). Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg m-1,mf-m 1)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions.     

Orthogonal factorizations of digraphs

Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g ⁻, g ⁺) and ƒ = (ƒ ⁻, ƒ ⁺) be pairs of positive integer-valued functions defined on V(G) such that g ⁻(x) ⩽ ƒ ⁻(x) and g ⁺(x) ⩽ ƒ ⁺(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g ⁻(x) ⩽ id _H (x) ⩽ ƒ ⁻(x) and g ⁺(x) ⩽ od _H (x) ⩽ ƒ ⁺(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let = {F ₁, F ₂,…, F _m} and H be a factorization and a subdigraph of G, respectively. is called k-orthogonal to H if each F _i , 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g ⁻(x), g ⁺(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.