Search

Let ( T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote by ω( x, f) and P( f) the ω-limit set of x under f and the set of periodic points of f, respectively. Write Ω( x, f) = { y| there exist a sequence of points x ∈ T and a sequence of positive integers n < n < ··· such that lim x = x and lim $$f^{n_{k}}$$ ( x ) = y}. In this paper, we show that the following statements are equivalent: (1) f is equicontinuous. (2) ω( x, f) = Ω( x, f) for any x ∈ T. (3) ∩ f ( T) = P( f), and ω( x, f) is a periodic orbit for every x ∈ T and map h: x → ω( x, f) ( x ∈ T) is continuous. (4) Ω( x, f) is a periodic orbit for any x ∈ T. [ABSTRACT FROM AUTHOR]

Let Gi be closed Lie groups of U(n), Ωi be bounded Gi-invariant domains in ℂn which contains 0, and O(ℂn)Gi = ℂ, for i = 1, 2. It is known that if f: Ω1 →} Ω2 is a proper holomorphic mapping, and f−1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f. [ABSTRACT FROM AUTHOR]

In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained. [ABSTRACT FROM AUTHOR]

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. [ABSTRACT FROM AUTHOR]

Let I be a compact interval of real axis ℝ, and (I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that Pn = (x0, x1,..., xn) is a return trajectory of f and that p ∈ [minPn, maxPn] with p ∈ f(p). In this paper, we show that if there exist k (≥ 1) centripetal point pairs of f (relative to p) in {(xi; xi+1): 0 ≤ i ≤ n − 1} and n = sk + r (0 ≤ r ≤ k − 1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r > 0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to I. [ABSTRACT FROM AUTHOR]

Let G be a graph and f: G → G be a continuous map. Denote by h( f), P( f), AP( f), R( f) and ω( x, f) the topological entropy of f, the set of periodic points of f, the set of almost periodic points of f, the set of recurrent points of f and the ω-limit set of x under f, respectively. In this paper, we show that the following statements are equivalent: (1) h( f) > 0. (2) There exists an x ∈ G such that ω( x, f) ∩ P( f) ≠ Ø and ω( x, f) is an infinite set. (3) There exists an x ∈ G such that ω( x, f) contains two minimal sets. (4) There exist x, y ∈ G such that ω( x, f) − ω( y, f) is an uncountable set and ω( y, f) ∩ ω( x, f) ≠ Ø. (5) There exist an x ∈ G and a closed subset A ⊂ ω( x, f) with f( A) ⊂ A such that ω( x, f) − A is an uncountable set. (6) R( f) − AP( f) ≠ Ø. (7) f|() is not pointwise equicontinuous. [ABSTRACT FROM AUTHOR]

In this paper, we generalize Rees-Shishikura's theorem to the class of geometrically finite rational maps. [ABSTRACT FROM AUTHOR]

Let S be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S , and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C. [ABSTRACT FROM AUTHOR]

Let H be a Hilbert space with dim H ≥ 2 and Z ∈ B( H) be an arbitrary but fixed operator. In this paper we show that an additive map Φ: B( H) → B( H) satisfies Φ( AB) = Φ( A) B = AΦ( B) for any A, B ∈ B( H) with AB = Z if and only if Φ( AB) = Φ( A) B = AΦ( B), ∀ A, B ∈ B( H), that is, Φ is a centralizer. Similar results are obtained for Hilbert space nest algebras. In addition, we show that Φ( A ) = AΦ( A) = Φ( A) A for any A ∈ B( H) with A = 0 if and only if Φ( A) = AΦ( I) = Φ( I) A, ∀ A ∈ B( H), and generalize main results in Linear Algebra and its Application, 450, 243-249 (2014) to infinite dimensional case. New equivalent characterization of centralizers on B( H) is obtained. [ABSTRACT FROM AUTHOR]

Let R be a unital *-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP = 0 implies A = 0 and AR(I − P) = 0 implies A = 0. In this paper, it is shown that a surjective map Φ: R → R is strong skew commutativity preserving (that is, satisfies Φ( A)Φ( B)−Φ( B)Φ( A) * = AB− BA * for all A,B ∈ R) if and only if there exist a map f: R→ Z( R) and an element Z ∈ Z( R) with Z = I such that Φ( A) = ZA + f( A) for all A ∈ R, where Z( R) is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime *-rings and von Neumann algebras with no central summands of type I are characterized. [ABSTRACT FROM AUTHOR]

A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color. In this paper, it is proved that if G is a planar graph with Δ( G) ≥ 7 and without chordal 7-cycles, then G has a (Δ( G)+1)-total-coloring. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the general solution and stability of the Jensen-cubic functional equation $$f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} + {y_2}} \right) + f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} - {y_2}} \right)$$ = f( x, y+ y)+ f( x, y− y)+6 f( x, y)+ f( x, y+ y) + f( x, y− y) + 6 f( x, y). [ABSTRACT FROM AUTHOR]

This paper studies the quasisymmetric mappings on Moran sets. We introduce a generalized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure. [ABSTRACT FROM AUTHOR]

In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B. Moreover, the distortion theorem of spirallike mappings is obtained. [ABSTRACT FROM AUTHOR]

In this article, we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings. Then we use it to obtain an asymptotically Koebe type distortion theorem, a coefficients estimate, a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings. At last, we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings. [ABSTRACT FROM AUTHOR]

Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression. [ABSTRACT FROM AUTHOR]

Let p ≥ 2 be a prime number and ℤp be the ring of p-adic intergers. Let G be a semigroup generated by infinitely many contractive maps on pℤp. It is shown that if G satisfies the open tiling conditions, then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on pℤp. As an application, we can generalize p-adic Khinchin's Theorem and p-adic Lochs' Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation. [ABSTRACT FROM AUTHOR]

Let X be a Banach space over F(=RorC) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B0(X) the set spanned by N(X). We give a structure result to the additive maps on FI+B0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI+B0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A−1 +ϕ(T)I for all T∈FI+B0(X) or Φ(T) = cAT* A−1 + ϕ(T)I for all T∈FI+B0(X), where c is a nonzero scalar, A is a τ-linear bijective transformation for some automorphism τ of F and ϕ is an additive functional. In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. [ABSTRACT FROM AUTHOR]

Let S be a smooth minimal projective surface of general type with pg(S) = q(S) = 1, KS2 = 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. [ABSTRACT FROM AUTHOR]

Let Alg ℒ be a J -subspace lattice algebra on a Banach space X and M be an operator in Alg ℒ. We prove that if δ: Alg ℒ → B( X) is a linear mapping satisfying δ( AB) = δ( A) B + Aδ( B) for all A,B ∈ Alg ℒ with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras. [ABSTRACT FROM AUTHOR]

Let A be a factor. For A, B ∈ A, define by [ A, B] = AB − BA* the skew Lie product of A and B. In this article, it is proved that a map Φ: A → A satisfies Φ([[ A, B], C]) = [[Φ( A), B], C] + [[ A, Φ( B)], C] + [[ A, B], Φ( C)] for all A, B, C ∈ A if and only if Φ is an additive *-derivation. [ABSTRACT FROM AUTHOR]

Let X be a Peano continuum having a free arc. If X admits a sensitive open map, then X either is homeomorphic to the closed interval [0, 1], or is homeomorphic to the unit circle S. [ABSTRACT FROM AUTHOR]

We study the long time behavior of J-flows on toric manifolds. By introducing the transition maps between moment maps, we get a quasilinear parabolic system for J-flows. Some basic estimates for transition maps are obtained. [ABSTRACT FROM AUTHOR]