Integral Representations,Differentiability Properties and Limits at Infinity for Beppo Levi Functions

The first aim in the present paper is to give an integral representation for Beppo Levi functions on R ⁿ. Our integral representation is an extension of Sobolev's integral representation given for infinitely differentiable functions with compact support. As applications, continuity and differentiability properties of Beppo Levi functions are studied.Our second aim in this paper is to study the existence of limits at infinity for Beppo Levi functions. We also consider the existence of fine-type limits at infinity with respect to Bessel capacities, which yields the radial limit result at infinity.     

A predual of a predual of B_σ and its applications to commutators

A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.     

Combinatorics for Small Ideals on Pkλ

We study the distributivity of the bounded ideal on P_kλ and answer negatively to a question of Johnson in [13]. The size of non-normal ideals with the partition property is also studied.     

Structure of the stochastic layer of a perturbed double-well potential system

The Poincaré mapping of a double-well potential system perturbed by a paramagnetic alternating field is constructed numerically. It can be well described by the whisker mapping approximation. The KAM-tori and the cantori are investigated in terms of the whisker mapping. The width of the stochastic layer increases in discrete steps as the amplitude of the external field increases.     

High-temperature XAFS study of solid and molten SrCl2

The local structure of solid and molten SrCl₂ was investigated by X-ray absorption fine structure technique. According to the curve fitting analysis with assessment of the anharmonic vibration effect, the nearest Sr²⁺-Cl⁻ distance and the coordination number are 2.99 ± 0.01 Å and 6.6 ± 0.2 in molten state. XAFS functions calculated from molecular dynamics simulation results were compared with the experimental XAFS data.     

Sharp-interface limit of the Allen-Cahn action functional in one space dimension

We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic arguments and numerical results have suggested that the limiting action should “count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of scaling. In this paper, we prove that for d = 1, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem. Mathematics Subject Classification (2000) 49J45, 35R60, 60F10     

Third-order optical nonlinearity in regioregular head-to-tail coupled poly(3-Hexylthiophene)

We measured the third-order optical nonlinearity of regioregular head-to-tail coupled poly (3-hexylthiophene) (HT-PHT) and regiorandom poly (3-hexylthiophene) (R-PHT) around exciton resonance using degenerate four wave mixing. The observed value of ∣χ⁽³⁾∣ at the exciton resonance peak of HT-PHT is in the order of 10^-9 esu which is approximately three-fold larger than that of R-PHT. We observed for the first time the enhancement in optical nonlinearity that occurs through the control of regularity of the polymeric structure. Response time of the nonlinearity was also measured using the transient grating method. The decay time of the transient grating in R-PHT and HT-PHT was less than 2 ps.     

Adsorption and biotransformation of 17β-estradiol in biological activated carbon adsorbers

As the first systematic study dealing with the adsorption of estrogens by granular activated carbon (GAC), the removal behavior of 17β-estradiol (E2) and its biotransformation product of estrone (E1) in fixed GAC columns was examined using four biological activated carbon (BAC) columns (BAC-1～BAC-4) generated by coating four GAC columns with detached microorganisms from the riverbed sediment of a representative drinking river water source containing lower content of natural organic matter (NOM). For comparison, parallel adsorption experiments were also performed using another four GAC columns (GAC-1～ GAC-4) packed by strictly following the configurations of four BAC columns. Adsorption experimental results obtained by intermittently spiking E2 over a total running period about 350 days into the river water mixed with or without a peaty water containing higher content of NOM showed that E2 was readily removed by adsorption and the combined adsorption/biodegradation. The vertical profiles of E2 and E1, which have great significance for better understanding and optimization of the adsorption process for removal of human estrogens, were also obtained.