Convenient construction of tetrahedral finite elements for the quasi-harmonic equation

It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Relations between chronic regulatory focus and future time perspective: Results of a cross-lagged structural equation model

Future time perspective - the way individuals perceive their remaining time in life - importantly influences socio-emotional goals and motivational outcomes. Recently, researchers have called for studies that investigate relationships between personality and future time perspective. Using a cross-lagged panel design, this study investigated effects of chronic regulatory focus dimensions (promotion and prevention orientation) on future time perspective dimensions (focus on opportunities and limitations). Survey data were collected two times, separated by a 3. month time lag, from 85 participants. Results of structural equation modeling showed that promotion orientation had a positive lagged effect on focus on opportunities, and prevention orientation had a positive lagged effect on focus on limitations.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

A note on the analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration

The analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration for the degenerate case of decaying constants being equal is given from the point of view of understanding the non-existence of the “degenerate modes”. This analysis also shows that there exist well defined “degenerate points” on the dispersion curve with electromagnetic fields varying linearly over small distances taken away from the interface.

A universal equation to predict methane production of forage-fed cattle in Australia

The methods for estimating methane emissions from cattle as used in the Australian national inventory are based on older data that have now been superseded by a large amount of more recent data. Recent data suggested that the current inventory emissions estimates can be improved. To address this issue, a total of 1034 individual animal records of daily methane production (MP) was used to reassess the relationship between MP and each of dry matter intake (DMI) and gross energy intake (GEI). Data were restricted to trials conducted in the past 10 years using open-circuit respiration chambers, with cattle fed forage-based diets (forage >70%). Results from diets considered to inhibit methanogenesis were omitted from the dataset. Records were obtained from dairy cattle fed temperate forages (220 records), beef cattle fed temperate forages (680 records) and beef cattle fed tropical forages (133 records). Relationships were very similar for all three production categories and single relationships for MP on a DMI or GEI basis were proposed for national inventory purposes. These relationships were MP (g/day) = 20.7 (±0.28) × DMI (kg/day) (R2 = 0.92, P < 0.001) and MP (MJ/day) = 0.063 (±0.008) × GEI (MJ/day) (R2 = 0.93, P < 0.001). If the revised MP (g/day) approach is used to calculate Australia’s national inventory, it will reduce estimates of emissions of forage-fed cattle by 24%. Assuming a global warming potential of 25 for methane, this represents a 12.6 Mt CO2-e reduction in calculated annual emissions from Australian cattle.