Derivations with large separating subspace

In his famous paper The image of a derivation is contained in the radical, Marc Thomas establishes the (commutative) Singer-Wermer conjecture, showing that derivations from a commutative Banach algebra to itself must map into the radical. The proof goes via first showing that the separating subspace of a derivation on must lie in the radical of . In this paper, we exhibit discontinuous derivations on a commutative unital Fréchet algebra such that the separating subspace is the whole of . Thus, the situation on Fréchet algebras is markedly different from that on Banach algebras.

     

Fréchet-Urysohn spaces in free topological groups

Let and be respectively the free topological group and the free Abelian topological group on a Tychonoff space . For every natural number we denote by () the subset of () consisting of all words of reduced length . It is well known that if a space is not discrete, then neither nor is Fréchet-Urysohn, and hence first countable. On the other hand, it is seen that both and are Fréchet-Urysohn for a paracompact Fréchet-Urysohn space . In this paper, we prove first that for a metrizable space , () is Fréchet-Urysohn if and only if the set of all non-isolated points of is compact and is Fréchet-Urysohn if and only if is compact or discrete. As applications, we characterize the metrizable space such that is Fréchet-Urysohn for each and is Fréchet-Urysohn for each except for . In addition, however, there is a first countable, and hence Fréchet-Urysohn subspace of () which is not contained in any (). We shall show that if such a space is first countable, then it has a special form in (). On the other hand, we give an example showing that if the space is Fréchet-Urysohn, then it need not have the form.

     

Van der Pauw resistivity measurements on evaporated thin films of cadmium arsenide, Cd3As2

Cadmium arsenide is a II-V semiconductor, exhibiting n-type intrinsic conductivity with high mobility and narrow bandgap. It is deposited by thermal evaporation, and has shown the Schottky and Poole-Frenkel effects at high electric fields, but requires further electrical characterisation. This has now been extended to low-field van der Pauw lateral resistivity measurements on films of thickness up to 1.5 μm. Resistivity was observed to decrease with increasing film thickness up to 0.5 μm from about 3 × 10⁻³ Ω m to 10⁻⁵ Ω m, where the crystalline granular size increases with film thickness. This decrease in resistivity was attributed to a decrease in grain boundary scattering and increased mobility. Substrate temperature during deposition also influenced the resistivity, which decreased from around 10⁻⁴ Ω m to (10⁻⁵ to 10⁻⁶) Ω m for an increase in substrate deposition temperature from 300 K to 423 K. This behaviour appears to result from varying grain sizes and ratios of crystalline to amorphous material. Resistivity decreased with deposition rate, reaching a minimum value at about 1.5 nm s⁻¹, before slowly increasing again at higher rates. It was concluded that this resulted from a dependence of the film stoichiometry on deposition rate. The dependence of resistivity on temperature indicates that intercrystalline barriers dominate the conductivity at higher temperatures, with a hopping conduction process at low temperatures.     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Singularity of the specific heat of two-dimensional random Ising models

The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random Ising models. A phase diagram relating strength of the randomness and temperature is also presented. Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998     

Evolutionary operation-factorial design technique for optimization of conversion of mixed agroproducts into gallic acid

This article presents the optimization of gallic acid production using filamentous fungi from tannin-rich mixed substrates taking into account the interaction effects of six variable process parameters. The methodology adopted for optimization was the evolutionary operation (EVOP)-factorial design technique. This technique combines the factorial method for designing experiments with the EVOP methodology for analyzing the experimental results systematically and arriving at conclusions according to its decision-making procedure. Standard deviation and error limits based on 95% confidence were calculated according to the relationship given in the literature. It was found that the best combinations of the process parameters at the optimum levels were 30°C, 80% relative humidity, pH 5.0, 48-h incubation period, 3 mL of induced inoculum, and 35 g of mixed substrate, resulting in a gallic acid yield of 94.8% under modified solid-state fermentation.     

Short-time plasma surface modification of HDPE powder in a Plasma Downer Reactor - process, wettability improvement and ageing effects

The effectiveness of improving the wettability of HDPE powders within less than 0.1 s by plasma surface modification in a Plasma Downer Reactor is investigated. A correlation is revealed between the XPS results (O/C-ratio) and the wettability (contact angle, polar surface tension by capillary rise method). The O₂-content in the plasma feed gas has been adjusted for best wettability properties. XPS results indicate the formation of CO and COOH functional groups on the powder surface. The O/C-ratio increased from 0.0 (no oxygen on the non-treated powder) up to 0.15 for the plasma treated HDPE powder surface. With pure O₂-plasma treatment, a water contact angle reduction from >90° (no water penetration into the untreated PE powder) down to 65° was achieved. The total surface free energy increased from 31.2 to 45 mN/m. Ageing of treated powders occurs and proceeds mostly within the first 7 days of storage. Contact angle measurements and O1s/O2s intensity ratio data support that ageing is mainly a diffusion-controlled process. Nevertheless, XPS results show the presence of oxygen functional groups even after 40 days, which explains why the powder is still dispersible in water without any addition of surfactants.     

LOCV calculation for the uniform electron fluid at finite temperature

The free energy of the homogeneous electron fluid at finite temperature is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of cluster expansion series the three-body cluster terms are calculated with the LOCV correlation functions. The results agree reasonably with those of Monte Carlo, coupled-cluster, perturbational expansion etc, techniques at zero temperature. The flashing and critical temperatures as well as the critical exponent are found to be about 0.6, 1.3 eV and 0.384 respectively. A similar liquid-gas phase transition to that of nuclear matter and liquid He³ is observed. Received 15 April 2002 / Received in final form 19 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: modarres@khayam.ut.ac.ir     

Weak compactness of certain sets of measures

For a compact Hausdorff space and a Montel Hausdorff locally convex space , let being the uniform topology. We determine the necessary and sufficient conditions for an equicontinuous to be -compact. Special results are obtained when is an -space or a -Stonian space.

     

Dielectric relaxation,ac and dc conductivities in the fullerenes C60 and C70

The complex conductivity in polycrystalline C₆₀ and C₇₀ has been investigated for frequencies 20 Hz≤ν≤10⁶ Hz and temperatures 10 K≤T≤750 K. The high-frequency dielectric constants ε_α= 2.6±0.1(C₆₀) and ε_∞= 4.6±0.1 (C₇₀) were deduced from these experiments. The observed low temperature relaxation process in C₆₀ fits well into the relaxation dynamics of the C₆₀ molecules as determined by many other experimental techniques operating on very different time scales. In addition to the study of the dipolar relaxation process, the dc and ac conductivities were determined. From the temperature dependence of the dc conductivities energy barriers of E_G=1.75±0.1 eV (C₆₀) and E_G=1.7±0.1 eV (C₇₀) were estimated. In C₇₀ we found indications for small polaron tunneling.