Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

A review of the spatial economics of non-timber forest product extraction: implications for policy

Patterns of forest cover and forest degradation determine the size and types of ecosystem services forests provide. Particularly in low-income countries, nontimber forest product (NTFP) extraction by rural people, which provides important resources and income to the rural poor, contributes to the level and pattern of forest degradation. Although recent policy, particularly in Africa, emphasizes forest degradation, relatively little research describes the spatial aspects of NTFP collection that lead to spatial degradation patterns. This paper reviews both the spatial empirical work on NTFP extraction and related forest degradation patterns, and spatial models of behavior of rural people who extract NTFPs from forest. Despite the impact of rural people's behavior on resulting quantities and patterns of forest resources, spatial–temporal models/patterns rarely inform park siting and sizing decisions, econometric assessments of park effectiveness, development projects to support conservation, or REDD protocols. Using the literature review as a lens, we discuss the models' implications for these policies with particular emphasis on effective conservation spending and leakage.

An assessment of the MODIS collection 5 leaf area index product for a region of mixed coniferous forest

Canopy leaf area index (LAI), defined as the single-sided leaf area per unit ground area, is a quantitative measure of canopy foliar area. LAI is a controlling biophysical property of vegetation function, and quantifying LAI is thus vital for understanding energy, carbon and water fluxes between the land surface and the atmosphere. LAI is routinely available from Earth Observation (EO) instruments such as MODIS. However EO-derived estimates of LAI require validation before they are utilised by the ecosystem modelling community. Previous validation work on the MODIS collection 4 (c4) product suggested considerable error especially in forested biomes, and as a result significant modification of the MODIS LAI algorithm has been made for the most recent collection 5 (c5). As a result of these changes the current MODIS LAI product has not been widely validated. We present a validation of the MODIS c5 LAI product over a 121 km2 area of mixed coniferous forest in Oregon, USA, based on detailed ground measurements which we have upscaled using high resolution EO data. Our analysis suggests that c5 shows a much more realistic temporal LAI dynamic over c4 values for the site we examined. We find improved spatial consistency between the MODIS c5 LAI product and upscaled in situ measurements. However results also suggest that the c5 LAI product underestimates the upper range of upscaled in situ LAI measurements.

The impact of price promotions on producer strategies in markets with large product heterogeneity

Although current research indicates that increasing the number of options has negative effects on the cognitive ability of consumers, little understanding has been given to the consequences on producers and their strategic behavior. This article tests whether a large portfolio of products is beneficial to producers by observing UK consumer response to price promotions. The article shows that discounts induce mainly segment switching (74% of the total impact), with a limited effect on stockpiling (26%) and no impact on purchase incidence. Consequently, consumers prefer to “follow the discount” rather than purchase multiple units of the same wine. This result seems to explain the current structure of the market, and suggests that discounts may conflict with segment loyalty, a situation that disfavors producers, particularly in very populated segments. Results also casts doubts on the economic sustainability of competition based on an intense product differentiation in the wine sector.

Competition and product survival in the UK car market

The paper examines the extent to which inter- and intra-firm competition influenced the survival of cars in the UK market between 1971 and 1998. It is shown that, while competition influenced product survival in all market segments within the UK car market, the nature of that competition differed between them. In the small family and large family car segments, intra-firm competition dominated inter-firm competition. In contrast, in the luxury/sports car segment only inter-firm competition conditions resulted in product survival. Evidence was also found that the luxury/sports car segment has grown more competitive over time and that firms marketing products in the family car segments have become considerably more successful at avoiding the effects of intra-firm competition.

Tax principles, product differentiation and the nature of competition

We analyze the choice between the origin and destination principles of taxation when there is product differentiation and Bertrand competition. If taxes are redistributed to consumers and demand is linear the origin principle dominates the destination principle whatever the degree of product differentiation and extent of economic integration. With nonlinear demand the origin principle dominates if there is sufficient economic integration. When the social value assigned to tax revenue is higher than the private value, the destination principle dominates for intermediate values of product differentiation and economic integration. The same results are also shown to hold with Cournot competition.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

The influence of markets and policy on spatial patterns of non-timber forest product extraction

When villagers extract resources, such as fuelwood, fodder, or medicinal plants from forests, their decisions over where and how much to extract are influenced by market conditions, their particular opportunity costs of time, minimum consumption needs, and access to markets. This paper develops an optimization model of villagers’ extraction behavior that clarifies how, and under what conditions, policies that create incentives such as improved returns to extraction in a buffer zone might be used instead of adversarial enforcement efforts to protect a forest’s pristine ‘‘inner core.’’

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev

An experimental validation of hypothetical WTP for a recyclable product

Using a within-subject experiment, we compare hypothetical and real willingness to pay (WTP) for an improvement in the recyclability of a product. Subjects are faced with a real payment scenario after they have responded to a hypothetical question. Contrary to most of the results obtained in similar studies, at apopulation level, there are no significant median differences between actual and hypothetical stated values of WTP. However,within-subject comparisons between hypothetical and actual values indicate that subjects stating a low (high) hypothetical WTP tend to underestimate (overestimate) the value of their actual contributions.

Adaptive behavior by single-product and multiproduct price setting firms in experimental markets

We focus on the learning dynamics in multiproduct price-setting markets, where firms use past strategies and performance to adapt to the corresponding equilibrium.