On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Periodic solutions for a Lotka–Volterra mutualism system with several delays

In the present paper, a Lotka–Volterra type mutualism system with several delays is studied. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions of the mutualism system. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions. Our results are different from the existing ones such as those in of Yang et al. [F. Yang, D. Jiang, A. Ying, Existence of positive solution of multidelays facultative mutualism system, J. Eng. Math. 3 (2002) 64–68] and Chen et al. [F. Chen, J. Shi, X. Chen, Periodicity in a Lotka–Volterra facultative mutualism system with several delays, J. Eng. Math. 21 (3) (2004) 403–409].     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

Determination of ultra-trace gold in natural water by graphite furnace atomic absorption spectrophotometry after in situ enrichment with thiol cotton fiber

A simple method of determining ultra-trace Au in natural water was presented by using graphite furnace atomic absorption spectrophotometry (GFAAS) after in situ enrichment with thiol cotton fiber (TCF). The sample solution was adjusted to pH 1.5-2.0 with HCl, then the water sample was passed through a column packed with 0.10-0.20 g TCF and the flow rate was controlled at 20-40 ml min⁻¹. The effects of interferences, such as complexing and oxidizing agents and other elements adsorbed on TCF were overcome by chemical treatments prior to the desorption of Au. The adsorbed Au was adsorbed with 2.0 ml hot acid, then it was extracted with 1.00 ml methyl isobutylketone (MIBK). For a 5 l water sample, the detection limit of Au is 0.02 ng l⁻¹. The relative standard deviation (R.S.D.) for the determination of 1.44 ng l⁻¹ Au was 9.4%.The method was applied to determine ultra-trace Au both in suspended phase and soluble phase in natural water, the concentrations of total Au in natural water samples range from 0.51 to 67.82 ng l⁻¹. The recovery of added 0.50-6.00 ng l⁻¹ Au was 80-95%. The method is useful in prospecting for Au deposits by means of hydrogeochemical methods. The enrichment is carried out in the field, and then the determination of Au is completed later in the laboratory.     

New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping

Some new oscillation criteria are established for the nonlinear damped differential equation (r(t)y′)′+p(t)y′+q(t)f(y)=0 that are different from most known ones in the sense that they are based on a class of new functions Φ(t,s,r) defined in the sequel. Our results are sharper than some previous results which can be seen by the examples at the end of this paper.     

On Romanoff's constant

In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16.     

D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.