On the error-sum function of Lüroth series

We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function.     

ON THE ERROR-SUM FUNCTION OF ALTERNATING LǖIROTH SERIES

The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.     

On a property specific to the tent map

Let a set {X_λ; λ  Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace X_λ to define a map g_Xλ:X_λ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω₀, ω₁, ω₂, … of X_λ, λ  Λ, we can find an initial point x₀  ω₀ such that g_ω0(x₀)ω₁,g_ω1(g_ω0(x₀))ω₂,…. The conditions are successfully applied to a closed cover of a weak self-similar set.     

Making the Tent function complex

This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.     

一般三角帐篷映射混沌性与两种混沌互不蕴含性

将三角帐篷映射推广为一般的n-三角帐篷映射,并且借助于一般Bernoulli移位映射,Banks定理与Li-Yorke定理,首先证明：对于任意的正整数n,n-三角帐篷映射既是Devaney混沌的,也是Li-Yorke混沌的.然后,利用所得到的结果,通过实例展示：Devaney混沌与Li-Yorke混沌的互不蕴含性.     

On statistical properties of the lyapunov exponent of the generalized skew tent map

The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index are obtained. A sufficient condition for weakly mixing of the chaotic generalized skew tent map is derived, and the asymptotic distribution of its Lyapunov exponent is provided.     

On the smooth Feshbach-Schur map

A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum electrodynamics. We analyze and clarify its algebraic and analytic properties, and we generalize it to non-selfadjoint partition operators χ and .     

Unimodal maps as boundary restrictions of two-dimensional full-folding maps

It is shown that every unimodal map is realized as a restriction of a simple map defined on the unit disc to a part of its boundary. Our two-dimensional map is called a full-folding map, which is defined generally on a compact metric space. It is a generalization of the full tent map in that it has two homeomorphic inverse maps and thus every non-critical point has two inverse images.     

On a coupled logistic map with large strength

In this paper, a class of diffusive coupled logistic map with large strength is considered. Depending on the parameter of the logistic family and the strength of coupling, we show the existence of a forward invariant curve which determines, in some sense, the boundary of the set whose points have unbounded orbit.     

The uniform laws of large numbers for the tent map

The tent map is an ergodic map defined on the unit interval. This paper considers the asymptotic behaviors of the various processes generated by the tent map. We get the uniform versions of law of large numbers for the tent map. An application to Monte Carlo integration is provided.     

一类迭代序列Cesaro平均收敛的条件

该文给出了帐篷映射产生的迭代序列Cesaro平均收敛的条件．研究了它与实数二进展式度量性质之间的联系．     

On the pluricanonical map of threefolds of general type

Let be a smooth minimal threefold of general type and let be an integer . Assume that the image of the pluricanonical map of is a curve. Then a simple computation shows that is necessarily or . When with a numerical condition or when , we obtain two inequalities and , where is the irregularity of and is the Euler characteristic of .

     

On the tropical Torelli map

We construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties, working in the category of (what we call) stacky fans. We define the tropical Torelli map between these two moduli spaces and we study the fibers (tropical Torelli theorem) and the image of this map (tropical Schottky problem). Finally we determine the image of the planar tropical curves via the tropical Torelli map and we use it to give a positive answer to a question raised by Namikawa on the compactified classical Torelli map.     

On the decomposition map for symmetric groups

Let R ^d be the ℤ-module generated by the irreducible characters of the symmetric group . We determine bases for the kernel of the decomposition map. It is known that R ^d ⊗ _ℤ F is isomorphic to the radical quotient of the Solomon descent algebra when F is a field of characteristic zero. We show that when F has prime characteristic and I _br ^d is the kernel of the decomposition map for prime p then R ^d /I _br ^d ⊗ _ℤ F is isomorphic to the radical quotient of the p-modular Solomon descent algebra. To the memory of Manfred Schocker.     

On a piecewise-smooth map arising in ecology

In this paper, we study a two-dimensional piecewise smooth map arising in ecology. Such map, containing two parameters d and β, is derived from a model describing how masting of a mature forest happens and synchronizes. Here d is the energy depletion quantity and β   is the coupling strength. Our main results are the following. First, we obtain a “weak” Sharkovskii ordering for the map on its nondiagonal invariant region for a certain set of parameters. In particular, we show that its Sharkovskii ordering is the natural number (resp., the positive even number) for β>1$\beta >1$ (resp., 0<β<1$0<\beta <1$). Second, we obtain a region of parameter space for which its corresponding global dynamics can be completely characterized.     

On convergence of function series

, a _n f _n (x) . .