Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Does metabolic compensation explain the majority of less-than-expected weight loss in obese adults during a short-term severe diet and exercise intervention?

Objective: We investigated to what extent changes in metabolic rate and composition of weight loss explained the less-than-expected weight loss in obese men and women during a diet-plus-exercise intervention. Design: 16 obese men and women (41 ± 9 years; BMI 39 ± 6 kg/m2) were investigated in energy balance before, after and twice during a 12-week VLED (565–650 kcal/day) plus exercise (aerobic plus resistance training) intervention. The relative energy deficit (EDef) from baseline requirements was severe (74-87%). Body composition was measured by deuterium dilution and DXA and resting metabolic rate (RMR) by indirect calorimetry. Fat mass (FM) and fat-free mass (FFM) were converted into energy equivalents using constants: 9.45 kcal/gFM and 1.13 kcal/gFFM. Predicted weight loss was calculated from the energy deficit using the '7700 kcal/kg rule'. Results: Changes in weight (-18.6 ± 5.0 kg), FM (-15.5 ± 4.3 kg), and FFM (-3.1 ± 1.9 kg) did not differ between genders. Measured weight loss was on average 67% of the predicted value, but ranged from 39 to 94%. Relative EDef was correlated with the decrease in RMR (R=0.70, P<0.01) and the decrease in RMR correlated with the difference between actual and expected weight loss (R=0.51, P<0.01). Changes in metabolic rate explained on average 67% of the less-than-expected weight loss, and variability in the proportion of weight lost as FM accounted for a further 5%. On average, after adjustment for changes in metabolic rate and body composition of weight lost, actual weight loss reached 90% of predicted values. Conclusion: Although weight loss was 33% lower than predicted at baseline from standard energy equivalents, the majority of this differential was explained by physiological variables. While lower-than-expected weight loss is often attributed to incomplete adherence to prescribed interventions, the influence of baseline calculation errors and metabolic down-regulation should not be discounted.

Is the unigram relevance model term independent? Classifying term dependencies in query expansion

This paper develops a framework for classifying term dependencies in query expansion with respect to the role terms play in structural linguistic associations. The framework is used to classify and compare the query expansion terms produced by the unigram and positional relevance models. As the unigram relevance model does not explicitly model term dependencies in its estimation process it is often thought to ignore dependencies that exist between words in natural language. The framework presented in this paper is underpinned by two types of linguistic association, namely syntagmatic and paradigmatic associations. It was found that syntagmatic associations were a more prevalent form of linguistic association used in query expansion. Paradoxically, it was the unigram model that exhibited this association more than the positional relevance model. This surprising finding has two potential implications for information retrieval models: (1) if linguistic associations underpin query expansion, then a probabilistic term dependence assumption based on position is inadequate for capturing them; (2) the unigram relevance model captures more term dependency information than its underlying theoretical model suggests, so its normative position as a baseline that ignores term dependencies should perhaps be reviewed.

Abatement of energy loss by insulating system and designing automatic water heater

The most suitable temperature range for domestic purposes is about 200C to 260C .Besides, both cold and hot water appear to be essential frequently for industrial purposes. In summer bringing down the water temperature at a comfortable range causes significant energy consumption. This project aims at saving energy to control water temperature by making water tank insulated .Therefore applying better insulation system which would reduce the disparity between the desired temperature and the actual temperature and hence saving energy significantly. Following the investigation, this project used cotton jacket to insulate the tank and the tank was placed under a paddy straw shade with a view to attaining the maximum energy saving. Finally, it has been found that reduction in energy consumption is to be about 50-60% which is quite satisfactory. Since comfortable temperature range varies from person to person this project thus combines insulating effect with automatic water heater.

Real-time power line extraction from unmanned aerial system video images

In this paper a real-time vision based power line extraction solution is investigated for active UAV guidance. The line extraction algorithm starts from ridge points detected by steerable filters. A collinear line segments fitting algorithm is followed up by considering global and local information together with multiple collinear measurements. GPU boosted algorithm implementation is also investigated in the experiment. The experimental result shows that the proposed algorithm outperforms two baseline line detection algorithms and is able to fitting long collinear line segments. The low computational cost of the algorithm make suitable for real-time applications.