A Mathematical Theory of Full-wave Rectification

The results of a systematic asymptotic analysis of two basicfull-wave rectifier circuits are presented in this paper. Thephysical circuits are modelled by two systems of nonlinear differentialequations which are both singularly perturbed in the limit RC.Here is the angular frequency of the source, R is the resistanceof the load, and C is the capacitance of the circuit. The methodof multiple scales is used to construct the asymptotic behaviourof the solutions as RC. The results contain transient, ripple,and steady-state information. The latter two components simplifyand yield the standard results when the diodes' forward impedanceis small. The analysis of more complicated full-wave rectifiersfollows from the procedure described.     

Piecewise Rational Quadratic Interpolation to Monotonic Data

An explicit representation of a piecewise rational quadraticfunction is developed which produces a monotonic interpolantto given monotonic data. The explicit representation means thatthe piecewise monotonic interpolant is easily constructed andnumerical experiments indicate that the method produces visuallypleasing curves. Furthermore, the use of the method is justifiedby a convergence analysis.     

A Moving Boundary Problem for the Sphere

A new technique is employed to solve a moving boundary problemin a sphere. A transformation is given which considerably simplifiesthe non-linearities associated with the moving boundary andenables an iterative analytic series solution to be found. Threeterms of the series expansion are obtained analytically andnumerically evaluated for comparison with results of previousauthors. Graphs of the motion of the reaction (freezing) frontand concentration (temperature) profiles behind the front aregiven. Also tabulated are the times to complete reaction (freezing)of the particle (that is the time for the moving boundary toreach the centre of the sphere).     

MRCISD calculations of the six lowest valence states of I2 −

Potential curves for the four Hund's case (a) basis electronic states (²Σ, ²Π_g, ²Π_u, and ²Σ⁺) correlating with the I(²P_u) + I^?(¹S_g) dissociation limit have been calculated at the MRCISD level of theory using an all-electron double-zeta basis set augmented with an extensive set of polarization and diffuse functions complete through i angular momentum functions. Transition moments for the dipole allowed transitions between these states are determined as a function of internuclear separation. The four Hund's case (a) curves are used to determine the six Hund's case (c) potential curves which arise when spin-orbit coupling is considered. The rovibrational eigenvalues for each of these six states are determined numerically, and standard spectroscopic constants are determined by fitting the energy of these levels to a Duham series. The results are compared with available experimental and theoretical information.     

FOREST BIOENERGY ADOPTION FOR A RISK‐AVERSE LANDOWNER UNDER UNCERTAIN EMERGING BIOMASS MARKET

Abstract This paper examines a land use problem where a risk‐averse representative landowner is uncertain about the timing and extent of a future biomass market emergence. The risk‐averse landowner is expected to maximize his or her expected utility of net present value from three land uses: agriculture, conventional forestry, and bioenergy forestry. Varying land quality, expected price jumps, and the timing of biomass market emergence are incorporated into the analysis. Under constant risk aversion, the simulation results show that the level of risk aversion has a significant influence on land allocation. The analysis also includes a discussion of how transaction costs affect land use change. The results offer insights into policy making for promoting forest bioenergy market development.