In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based o...In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.展开更多
The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two g...The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.展开更多
In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality(see[1,4])of meromorphic functions to algebroid functions.
In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients....In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.展开更多
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two ...Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω,F, P) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.展开更多
Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT(D) are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h (μ) ...Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT(D) are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h (μ) 〈 h* (μ) for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT(D).展开更多
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we ...Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.展开更多
In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that ...In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.展开更多
It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel ray...It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel rays in Teich(S)and their embeddings in Teich(S),we show that the 1 st-strata space of the augmented Teichmüller space Teich(S)can be embedded in the augmented Teichmüller space Teich(S)isometrically.Furthermore,we show that Φπ induces an isometric embedding from the set Teich(S)B(∞)consisting of Busemann points in the horofunction boundary of Teich(S)into Teich(S)B(∞)with the detour metric.展开更多
We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠...We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other roots.We show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of f.We prove several notable properties and present an application of D_(2).展开更多
Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk(V) denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by includ...Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk(V) denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk(V) independently with probability p, and let Q be a given set of q "bad" tuple assignments. An instance I = (C, Q) is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tupie assignment in Q. Suppose that θ, q 〉 0 are fixed and ε=ε(n) 〉 0 be such in 2 that ε Inn/ In Inn → ∞. Let k ≥ (1 + θ) log2 n and let p0 = ln2/qn^k-1. We prove thatlim∞ P[I issatisfiable] ={1,p≤(1-ε)p0, 0,p≥(1+ε)p0.展开更多
Compressed sensing is a new signal acquisition method that acquires signal in a compressed form and then recovers the signal by the use of computational tools and techniques.This means fewer measurements of signal are...Compressed sensing is a new signal acquisition method that acquires signal in a compressed form and then recovers the signal by the use of computational tools and techniques.This means fewer measurements of signal are needed and thus it will save huge amount of time and storage space.We,in this paper,consider the compressed sensing of sparse integer-valued signal(referred as "q-states signal" throughout the paper).In order to accelerate the speed of reconstruction,we adopt the sparse rather than dense measurement matrices.Using methods and tools developed in statistical physics,we locate the reconstruction limit for L 0-reconstruction method and propose a belief propagationbased algorithm that can deal with instance with large size and its typical reconstruction performance are also analyzed.展开更多
A cell-centered Lagrangian scheme is developed for the numerical simula-tion of wave propagations in one dimensional(1D)elastic-plasticflow.The classical elastic-plastic material model initially proposed by Wilkins is ...A cell-centered Lagrangian scheme is developed for the numerical simula-tion of wave propagations in one dimensional(1D)elastic-plasticflow.The classical elastic-plastic material model initially proposed by Wilkins is adopted.The linear elas-tic model(Hooke’s Law),perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid.The second-order ex-tension of this scheme is achieved by a linear reconstruction method.Various numer-ical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves.Compared with the well-developed operator splitting method used in simulating elastic-plasticflow,this scheme is more accurate due to the con-sideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver.The numerical simulations of typical examples show competitive results.展开更多
文摘In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.
基金supported by National Natural Science Foundation of China(11371045,11301248)
文摘The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.
基金supported by National Natural Science Foundation of China(1047104810771011)the Fundamental Research Funds for the Central Universities
文摘In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality(see[1,4])of meromorphic functions to algebroid functions.
基金supported by the National Natural Science Foundation of China(11371225)National Natural Science Foundation of Guangdong Province(2016A030313686)
文摘In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.
基金Supported by National Natural Science Foundation of China(Grant No.10871016)
文摘Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω,F, P) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.
基金Supported by National Natural Science Foundation of China(Grant No.11371045)
文摘Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT(D) are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h (μ) 〈 h* (μ) for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT(D).
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
基金Supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.
基金supported by National Natural Science Foundation of China(Grant No. 11171015)
文摘In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.
基金Supported by National Natural Science Foundation of China(Grant Nos.11871085,11371045)。
文摘It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel rays in Teich(S)and their embeddings in Teich(S),we show that the 1 st-strata space of the augmented Teichmüller space Teich(S)can be embedded in the augmented Teichmüller space Teich(S)isometrically.Furthermore,we show that Φπ induces an isometric embedding from the set Teich(S)B(∞)consisting of Busemann points in the horofunction boundary of Teich(S)into Teich(S)B(∞)with the detour metric.
基金supported by National Natural Science Foundation of China(Grant Nos.61702025 and 11801101)the Special Fund for Guangxi Bagui Scholar Project+1 种基金Guangxi Science and Technology Program(Grant No.2017AD23056)the Startup Foundation for Advanced Talents in Guangxi University for Nationalities(Grant No.2015MDQD018)。
文摘We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with i<j and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other roots.We show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of f.We prove several notable properties and present an application of D_(2).
基金supported by NSFC(Grant No.11371225)the fund of the State Key Lab of Software Development Environment(Grant No.SKLSDE-2015ZX-05)
文摘Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk(V) denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk(V) independently with probability p, and let Q be a given set of q "bad" tuple assignments. An instance I = (C, Q) is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tupie assignment in Q. Suppose that θ, q 〉 0 are fixed and ε=ε(n) 〉 0 be such in 2 that ε Inn/ In Inn → ∞. Let k ≥ (1 + θ) log2 n and let p0 = ln2/qn^k-1. We prove thatlim∞ P[I issatisfiable] ={1,p≤(1-ε)p0, 0,p≥(1+ε)p0.
文摘Compressed sensing is a new signal acquisition method that acquires signal in a compressed form and then recovers the signal by the use of computational tools and techniques.This means fewer measurements of signal are needed and thus it will save huge amount of time and storage space.We,in this paper,consider the compressed sensing of sparse integer-valued signal(referred as "q-states signal" throughout the paper).In order to accelerate the speed of reconstruction,we adopt the sparse rather than dense measurement matrices.Using methods and tools developed in statistical physics,we locate the reconstruction limit for L 0-reconstruction method and propose a belief propagationbased algorithm that can deal with instance with large size and its typical reconstruction performance are also analyzed.
基金The author would like to thank the referees for the helpful suggestions.This work is supported by National Science Foundation of China(Grants Nos.12002062,91852207,11801036,12002063 and 11972093)NSFC-NSAF Joint Fund(Grants No.U1730118)+1 种基金President Foundation of CAEP(Grant No.YZJJLX2018012)National Key Project(Grant No.GJXM92579).
文摘A cell-centered Lagrangian scheme is developed for the numerical simula-tion of wave propagations in one dimensional(1D)elastic-plasticflow.The classical elastic-plastic material model initially proposed by Wilkins is adopted.The linear elas-tic model(Hooke’s Law),perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid.The second-order ex-tension of this scheme is achieved by a linear reconstruction method.Various numer-ical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves.Compared with the well-developed operator splitting method used in simulating elastic-plasticflow,this scheme is more accurate due to the con-sideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver.The numerical simulations of typical examples show competitive results.