A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

Maximal functions with polynomial densities in lacunary directions

Given a real polynomial in one variable such that , we consider the maximal operator in ,

0\,,\,i,j\in \mathbb{Z}}\frac{1... ...t f\big (x_{1}-2^{i}p(t),x_{2}-2^{j}p(t)\big )\big \vert\,dt . \end{displaymath}">

We prove that is bounded on for 1$"> with bounds that only depend on the degree of .

     

A filtration of spectra arising from families of subgroups of symmetric groups

Let be a family of subgroups of which is closed under taking subgroups and conjugates. Such a family has a classifying space, , and we showed in an earlier paper that a compatible choice of for each gives a simplicial monoid , which group completes to an infinite loop space. In this paper we define a filtration of the associated spectrum whose filtration quotients, given an extra condition on the families, can be identified in terms of the classifying spaces of the families of subgroups that were chosen. This gives a way to go from group theoretic data about the families to homotopy theoretic information about the associated spectrum. We calculate two examples. The first is related to elementary abelian -groups, and the second gives a new expression for the desuspension of as a suspension spectrum.

     

Characterisation of a nitrogen ECR plasma source for the MBE growth of the dilute nitride semiconductor GaAsN

The use of a nitrogen electron cyclotron resonance (ECR) plasma source has allowed the growth of GaAsN at GaAs substrate temperatures as high as 600 °C, unlike the case for growth using radio frequency (RF) plasma sources, for which there is significant loss of nitrogen at substrate temperatures as low as 480-520 °C. Photoluminescence (PL) intensities are significantly improved at a substrate temperature of 600 °C and are further improved slightly by using an ion trap to extract charged species from the beam. As the trap voltage is increased there is a reduction in the total nitrogen concentration, as measured by secondary ion mass spectrometry (SIMS), and a slight increase in the active nitrogen concentration, as measured by PL. These observations are consistent, for example, with charged and active nitrogen species together being involved in the formation of point defects, however more work is needed to clarify what may well prove to be a complex situation.     

An improved ant colony optimisation heuristic for graph colouring

The focus of this paper is an ant colony optimisation heuristic for the graph colouring problem. We start by showing how a series of improvements enhance the performance of an existing ant colony approach to the problem and then go on to demonstrate that a further strengthening of the construction phase, combined with a tabu search improvement phase, raise the performance to the point where it is able to compete with some of the best-known approaches on a series of benchmark problems.     

α‐Tetraphosphorus Trichalcogenide Diamides and Imides containing both Sulfur and Selenium

Reaction of a mixture of bicyclic phosphorus sulfide selenide iodides α‐P₄S_nSe_3−nI₂ (n = 0–3) with PrⁱNH₂ and Et₃N gave corresponding diamides α‐P₄S_nSe_3−n(NHPrⁱ)₂ (n = 0–3) and imides α‐P₄S_nSe_3−n(μ‐NPrⁱ) (n = 2–3), identified in solution by ³¹P NMR. In one isomer of α‐P₄S₂Se(μ‐NPrⁱ), the C₂ symmetry of imides such as α‐P₄S₃(μ‐NPrⁱ) was broken, allowing relative assignment of ²J NMR couplings to the PNP bridge and the PSP bridge opposite to it. The coupling through the sulfur bridge was found to be reduced to ca. zero, in contrast to previous assumptions for this class of compounds. Ab initio models were calculated at the MPW1PW91/svp level for the sulfide selenide imides and for a selection of bond rotamers of the diamides, and at the MPW1PW91/LanL2DZ(d) level for the sulfide selenide diiodides. Different skeletal isomers were prevalent for the mixed chalcogenide diamides than for the diiodides, showing that exchange of chalcogen between skeletal positions took place in the amination reaction even at room temperature. Similar differences to those observed were predicted by the models, suggesting that equilibrium was attained.     

Measurements of absolute γ-ray intensities in the decays of very neutron rich isotopes of Cd and In

The half lives and the γ-ray branching ratios of neutron rich Cd and In isotopes have been investigated by simultaneous measurements of β- and γ-ray spectra. The results presented contain information on 21 different β-decaying isotopes or isomers of Cd and In in the mass region A=123–129. Four previously unknown or little known isotopes of Cd are reliably characterized for the first time.     

Visual spatial memory is enhanced in female rats (but inhibited in males) by dietary soy phytoestrogens

Background  

In learning and memory tasks, requiring visual spatial memory (VSM), males exhibit superior performance to females (a difference attributed to the hormonal influence of estrogen). This study examined the influence of phytoestrogens (estrogen-like plant compounds) on VSM, utilizing radial arm-maze methods to examine varying aspects of memory. Additionally, brain phytoestrogen, calbindin (CALB), and cyclooxygenase-2 (COX-2) levels were determined.     

Search for anomalous interaction mean free paths of charge, 2≦Z≦18 projectile fragments in emulsions exposed to 1.8 A GeV40Ar ions

⁴⁰Ar-emulsion interactions are studied, to investigate the question of anomalons, in twoG- 5 emulsion stacks. In about 4600 primary interactions, projectile fragments of Z≧2 for all generations have been followed until they interact or leave the stack. After careful estimation of charges of these fragments, variation of their mean free paths is studied as a function of distance from the preceding interaction. Generation effect,N _h dependence and production angle effect are investigated. In addition multi-chain events are analysed separately. Our results do not show anomalons at the 6% level and are consistent with non-occurrence of anomalons. However, this experiment is not sensitive enough to rule out anomalons (with a mfp of the order of 2 to 3 cm) produced at about 1% (or less) level.     

Algebraic thinking with and without algebraic representation: a three-year longitudinal study

An Algebraic Thinking Test was given to 116 students aged 12–14, at the end of each of three years. This age span crosses two levels of school in New Zealand. This test assessed their ability to represent compensation in the four arithmetic operations both numerically and with letters for variables. The analyses of these results, together with the results from separate interviews designed to report individual progress of students in the New Zealand Numeracy Project, showed that students who had developed advanced mental strategies for dealing with additive, multiplicative and proportional operations, were the students who were capable of making full use of the alphanumeric symbols of algebra. These results, taken together with earlier studies by the authors, led to a proposal for a “pathway for algebraic thinking” accessible to all students.