On Banach spaces with few spreading models

If the set of spreading models of a Banach space is countable (up to equivalence), then it cannot contain a strictly increasing infinite chain of spreading models generated by normalized weakly null sequences. Moreover, such a space must have a spreading model which is `close' to or for some .

     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

Cauchy’s residue theorem for a class of real valued functions

Let [a, b] be an interval in ℝ Rand let F be a real valued function defined at the endpoints of [a, b] and with a certain number of discontinuities within [a, b]. Assuming F to be differentiable on a set [a, b] | E to the derivative f, where E is a subset of [a, b] at whose points F can take values ±∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that KH-vt ∝ _a ^b f = F(b) − F(a), where KH-vt denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate the theory.     

Underwater speech communications with a modulated laser

A novel speech communications system using a modulated laser beam has been developed for short-range applications in which high directionality is an exploitable feature. Although it was designed for certain underwater applications, such as speech communications between divers or between a diver and the surface, it may equally be used for air applications. With some modification it could be used for secure diver-to-diver communications in the situation where untethered divers are swimming close together and do not want their conversations monitored by intruders. Unlike underwater acoustic communications, where the transmitted speech may be received at ranges of hundreds of metres omnidirectionally, a laser communication link is very difficult to intercept and also obviates the need for cables that become snagged or broken. Further applications include the transmission of speech and data, including the short message service (SMS), from a fixed installation such as a sea-bed habitat; and data transmission to and from an autonomous underwater vehicle (AUV), particularly during docking manoeuvres. The performance of the system has been assessed subjectively by listening tests, which revealed that the speech was intelligible, although of poor quality due to the speech algorithm used. PACS 42.55.Px; 42.60.By; 42.62.-b     

A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

Journal of Mathematical Chemistry - A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear (2?+?1)-dimensional...     

Novel use of mesoporous aluminas as supports for Cp2ZrCl2 and Cp*ZrMe3: Ethylene polymerization and formation of polyethylene nanofibers

Mesoporous aluminas with average pore sizes of 4.3–7.8 nm were prepared by anodization of an aluminum film (AAO), and by a sol–gel templating method (TPL). In addition to a commercial alumina and sulfated TPL, the aluminas were used as supports for cyclopentadienyl zirconocene dichloride (Cp₂ZrCl₂) and trimethyl(η5‐pentamethylcyclopentadienyl)zirconium (Cp*ZrMe₃) and tested in the polymerization of ethylene. The metallocenes supported on the alumina prepared with the templating method and its sulfated modification exhibited polymerization activities of 440 and 350 kg_PE/(mol_Zr × h × bar), respectively, comparable to that obtained with silica‐supported metallocenes (390 kg_PE/(mol_Zr × h × bar)). The acid site distribution of the aluminas was studied with FTIR and temperature programmed desorption (TPD) of pyridine, and also the amount of medium and strong acid sites was determined gravimetrically from the adsorption of pyridine. Relative to the surface area, AAO with the highest amount of acid sites (2.10 μmol_py/m) adsorbed Cp₂ZrCl₂ and Cp*ZrMe₃ the most. Study of the polymers' morphology with a scanning electron microscope revealed polyethylene nanofibers in all the polymer samples, also in those obtained from the reference polymerizations with homogeneous Cp₂ZrCl₂ and Cp*ZrMe₃. This finding suggests that a catalyst support with a tubular pore structure is not a prerequisite for the formation of polymer nanofibers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4002–4012, 2007     

Breathing noise elimination in through-water speech communication between divers

Breathing noise and bubble noise are the main factors affecting the subjective quality of through-water speech signals in communications between divers wearing full-face masks or aural-nasal masks. Only breathing noise is considered here, which can be gated out by applying a combination of zero-crossing detection and energy measurements to noisy speech signals above predetermined threshold values. The signals are picked up by a microphone placed close to the diver's mouth in the air cavity of the mask. Results were obtained during diving trials with four different types of masks.     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

Binding energies of donor impurities in modulation-doped double quantum wells under an electric field

In this study, we have investigated theoretically the binding energies of shallow donor impurities in modulation-doped GaAs/Al_0.33Ga_0.67As double quantum wells (DQWs) under an electric field which is applied along the growth direction for different doping concentrations as a function of the impurity position. The electronic structure of modulation-doped DQWs under an electric field has been investigated by using a self-consistent calculation in the effective-mass approximation. The results obtained show that the carrier density and the depth of the quantum wells in semiconductors may be tuned by changing the doping concentration, the electric field and the structure parameters such as the well and barrier widths. This tunability gives a possibility of use in many electronic and optical devices.     

The diamagnetic susceptibilities of donors in quantum wells with anisotropic effective mass

The diamagnetic susceptibility of a hydrogenic donor placed in Si, Ge and GaAs quantum wells with infinite confinement potential which have different effective mass anisotropy parameters (γ=_m⊥/_m∥$\gamma =m_{\perp }/m_{\parallel }$) has been investigated as a function of the well sizes. The binding energies of the donor have also been computed using a trial wave function with two parameters in the framework of the effective mass approximation. It has been observed that the diamagnetic susceptibility of the donor in the anisotropic materials converges rapidly to the bulk limit as the well size increases.