Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Valuation 'accuracy' within the Right to Buy process

Based on surveys undertaken with local authorities and valuers who provide the valuations on which purchase prices for local authority houses under the Right to Buy are based, this paper reports on research which aims to establish the reasons for the differences between the initial valuations provided by the local authority valuers and those provided by the District Valuer on appeal. The paper reports on the reasons why tenants appeal the initial valuation and discusses issues of valuation accuracy, uncertainty and the different and imperfect data available to valuers employed by the organisations involved, as well as the factors within the valuation process, including the absence of any requirement to agree a value, which contribute to the different outcomes.

Planning autonomous vehicles in the absence of speed lanes using lateral potentials

Chaotic traffic, prevalent in many countries, is marked by a large number of vehicles driving with different speeds without following any predefined speed lanes. Such traffic rules out using any planning algorithm for these vehicles which is based upon the maintenance of speed lanes and lane changes. The absence of speed lanes may imply more bandwidth and easier overtaking in cases where vehicles vary considerably in both their size and speed. Inspired by the performance of artificial potential fields in the planning of mobile robots, we propose here lateral potentials as measures to enable vehicles to decide about their lateral positions on the road. Each vehicle is subjected to a potential from obstacles and vehicles in front, road boundaries, obstacles and vehicles to the side and higher speed vehicles to the rear. All these potentials are lateral and only govern steering the vehicle. A speed control mechanism is also used for longitudinal control of vehicle. The proposed system is shown to perform well for obstacle avoidance, vehicle following and overtaking behaviors.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Language in calculation: A core mechanism?

Although there is evidence that exact calculation recruits left hemisphere perisylvian language systems, recent work has shown that exact calculation can be retained despite severe damage to these networks. In this study, we sought to identify a “core” network for calculation and hence to determine the extent to which left hemisphere language areas are part of this network. We examined performance on addition and subtraction problems in two modalities: one using conventional two-digit problems that can be easily encoded into language; the other using novel shape representations. With regard to numerical problems, our results revealed increased left fronto-temporal activity in addition, and increased parietal activity in subtraction, potentially reflecting retrieval of linguistically encoded information during addition. The shape problems elicited activations of occipital, parietal and dorsal temporal regions, reflecting visual reasoning processes. A core activation common to both calculation types involved the superior parietal lobule bilaterally, right temporal sub-gyral area, and left lateralized activations in inferior parietal (BA 40), frontal (BA 6/8/32) and occipital (BA 18) regions. The large bilateral parietal activation could be attributed to visuo-spatial processing in calculation. The inferior parietal region, and particularly the left angular gyrus, was part of the core calculation network. However, given its activation in both shape and number tasks, its role is unlikely to reflect linguistic processing per se. A possibility is that it serves to integrate right hemisphere visuo-spatial and left hemisphere linguistic and executive processing in calculation.

Mid-Holocene monsoons: a multi-model analysis of the inter-hemispheric differences in the responses to orbital forcing and ocean feedbacks

The response of monsoon circulation in the northern and southern hemisphere to 6 ka orbital forcing has been examined in 17 atmospheric general circulation models and 11 coupled ocean–atmosphere general circulation models. The atmospheric response to increased summer insolation at 6 ka in the northern subtropics strengthens the northern-hemisphere summer monsoons and leads to increased monsoonal precipitation in western North America, northern Africa and China; ocean feedbacks amplify this response and lead to further increase in monsoon precipitation in these three regions. The atmospheric response to reduced summer insolation at 6 ka in the southern subtropics weakens the southern-hemisphere summer monsoons and leads to decreased monsoonal precipitation in northern South America, southern Africa and northern Australia; ocean feedbacks weaken this response so that the decrease in rainfall is smaller than might otherwise be expected. The role of the ocean in monsoonal circulation in other regions is more complex. There is no discernable impact of orbital forcing in the monsoon region of North America in the atmosphere-only simulations but a strong increase in precipitation in the ocean–atmosphere simulations. In contrast, there is a strong atmospheric response to orbital forcing over northern India but ocean feedback reduces the strength of the change in the monsoon although it still remains stronger than today. Although there are differences in magnitude and exact location of regional precipitation changes from model to model, the same basic mechanisms are involved in the oceanic modulation of the response to orbital forcing and this gives rise to a robust ensemble response for each of the monsoon systems. Comparison of simulated and reconstructed changes in regional climate suggest that the coupled ocean–atmosphere simulations produce more realistic changes in the northern-hemisphere monsoons than atmosphere-only simulations, though they underestimate the observed changes in precipitation in all regions. Evaluation of the southern-hemisphere monsoons is limited by lack of quantitative reconstructions, but suggest that model skill in simulating these monsoons is limited.

Analyzing lateral root development: how to move forward

Roots are important to plants for a wide variety of processes, including nutrient and water uptake, anchoring and mechanical support, storage functions, and as the major interface between the plant and various biotic and abiotic factors in the soil environment. Therefore, understanding the development and architecture of roots holds potential for the manipulation of root traits to improve the productivity and sustainability of agricultural systems and to better understand and manage natural ecosystems. While lateral root development is a traceable process along the primary root and different stages can be found along this longitudinal axis of time and development, root system architecture is complex and difficult to quantify. Here, we comment on assays to describe lateral root phenotypes and propose ways to move forward regarding the description of root system architecture, also considering crops and the environment.

Neural stem cells and cell replacement therapy: making the right cells

The past few years have seen major advances in the field of NSC (neural stem cell) research with increasing emphasis towards its application in cell-replacement therapy for neurological disorders. However, the clinical application of NSCs will remain largely unfeasible until a comprehensive understanding of the cellular and molecular mechanisms of NSC fate specification is achieved. With this understanding will come an increased possibility to exploit the potential of stem cells in order to manufacture transplantable NSCs able to provide a safe and effective therapy for previously untreatable neurological disorders. Since the pathology of each of these disorders is determined by the loss or damage of a specific neural cell population, it may be necessary to generate a range of NSCs able to replace specific neurons or glia rather than generating a generic NSC population. Currently, a diverse range of strategies is being investigated with this goal in mind. In this review, we focus on the relationship between NSC specification and differentiation and discuss how this information may be used to direct NSCs towards a particular fate.

Housing or property? The dynamics of housing policy and property principles in the right to buy

This paper examines the interplay and tension between housing law and policy and property law, in the specific context of the right to buy (RTB). It focuses on funding arrangements between the RTB tenant and another party. It first examines how courts determine the parties' respective entitlements in the home, highlighting the difficulty of categorising, under traditional property law principles, a contribution in the form of the statutory discount conferred on the RTB tenant. Secondly, it considers possible exploitation of the RTB scheme, both at the macro level of exploitation of the policy underpinning the legislation and, at the micro level, of exploitation of the tenant. The measures contained in the Housing Act 2004 intended to curb exploitation of the RTB are analysed to determine what can be considered to be legitimate and illegitimate uses of the scheme. It is argued that, despite the government's implicit approval, certain funding arrangements by non-resident relatives fail to give effect to the spirit of the scheme.

Simulations of the impact of orbital forcing and ocean on the Asian summer monsoon during the Holocene

The importance of orbital forcing and ocean impact on the Asian summer monsoon in the Holocene is investigated by comparing simulations with a fully coupled ocean–atmosphere general circulation model (FOAM) and with the atmospheric component of this model (FSSTAM) forced with prescribed modern sea-surface temperatures (SSTs). The results show: (1) the ocean amplifies the orbitally-induced increase in African monsoon precipitation, makes somewhat increase in southern India and damps the increase over the southeastern China. (2) The ocean could change the spatial distribution and local intensity of the orbitally-induced latitudinal atmospheric oscillation over the southeastern China and the subtropical western Pacific Ocean. (3) The orbital forcing mostly enhances the Asian summer precipitation in the FOAM and FSSTAM simulations. However, the ocean reduces the orbitally-induced summer precipitation and postpones the time of summer monsoon onset over the Asian monsoon region. (4) The orbital forcing considerably enhances the intensity of upper divergence, which is amplified by ocean further, over the eastern hemisphere. But the divergence is weaker in the FOAM simulations than in the FSSTAM simulations when the orbital forcing is fixed. (5) The orbital forcing can enhance the amplitude of precipitation variability over the subtropical Africa, the southeastern China and northwestern China, inversely, reduce it over central India and North China in the FOAM and FSSTAM simulations. The ocean obviously reduces the amplitude of precipitation variability over most of the Asian monsoon regions in the fixed orbital forcing simulations. (6) The areas characterized by increased summer precipitation in the long-term mean are mostly characterized by increased amplitude of short-term variability, whereas regions characterized by decreased precipitation are primarily characterized by decreased amplitude of short-term variability. However, the influences of orbital forcing or dynamical ocean on regional climate depend on the model.

Intercomparison of simulated global vegetation distribution in response to 6 kyr BP orbital forcing

The response of ten atmospheric general circulation models to orbital forcing at 6 kyr BP has been investigated using the BIOME model, which predicts equilibrium vegetation distribution, as a diagnostic. Several common features emerge: (a) reduced tropical rain forest as a consequence of increased aridity in the equatorial zone, (b) expansion of moisture-demanding vegetation in the Old World subtropics as a consequence of the expansion of the Afro–Asian monsoon, (c) an increase in warm grass/shrub in the Northern Hemisphere continental interiors in response to warming and enhanced aridity, and (d) a northward shift in the tundra–forest boundary in response to a warmer growing season at high northern latitudes. These broadscale features are consistent from model to model, but there are differences in their expression at a regional scale. Vegetation changes associated with monsoon enhancement and high-latitude summer warming are consistent with palaeoenvironmental observations, but the simulated shifts in vegetation belts are too small in both cases. Vegetation changes due to warmer and more arid conditions in the midcontinents of the Northern Hemisphere are consistent with palaeoenvironmental data from North America, but data from Eurasia suggests conditions were wetter at 6 kyr BP than today. The models show quantitatively similar vegetation changes in the intertropical zone, and in the northern and southern extratropics. The small differences among models in the magnitude of the global vegetation response are not related to differences in global or zonal climate averages, but reflect differences in simulated regional features. Regional-scale analyses will therefore be necessary to identify the underlying causes of such differences among models.