Elementary Quadrature for the Riccati equation

Using suitable transformation in combination with a specific Riccati-type equation solvable, the problem of solving Riccati equation can be transformed into that of a quasi-Abel equation of the second kind. By the extended Julia’s integrability condition, the general solutions of Riccati equation in the form of elementary quadrature are obtained, which contains numerous. This method opens up a new prospect for the study of nonlinear differential equations by analytical method.

An efficient algorithm for non-rigid object registration

An efficient algorithm for registration of two non-rigid objects based on geometrical transformation of the template object to target object is proposed. The transformation is considered as warping of the template onto the target. To choose the most suitable transformation from all possible warps, a registration algorithm should satisfy deformation constraints referred to as regularization of non-rigid objects. In this work, we use variational functionals for affine transformations. With the help of computer simulation, the proposed method for searching the optimal geometrical transformation is compared with that of common algorithms.

Bilinearization and fractional soliton dynamics of fractional Kadomtsev-Petviashvili equation

Kadomtsev-Petviashvili equation is a mathematical model with many important applications in fluids. In this paper, a local fractional Kadomtsev-Petviashvili equation with Lax integrability is derived and solved by extending Hirota?s bilinear method. More specifically, the local fractional Kadomtsev-Petviashvili equation is derived from a local fractional Lax equation. With the help of a suitable transformation, the local fractional Kadomtsev-Petviashvili equation is then bilinearized. Based on the bilinearized form, n-soliton solution with Mittag-Leffler functions is obtained. In order to gain more insights into the fractional n-soliton solution, the velocity of the fractional one-soliton solution is simulated. It is shown that the velocity of the fractional one-soliton changes with the fractional order.

Ergodicity of Markov chain Monte Carlo with reversible proposal

We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

A Novel Method for Rotor Field-Oriented Control of Single-Phase Induction Motor

This paper presents a novel rotor field-oriented control (RFOC) method for asymmetrical single-phase induction motor (SPIM). It is shown in this paper that by using a suitable transformation matrix (TM) for stator current variables, the asymmetrical equations of SPIM are transformed into symmetrical equations. Based on this similarity, a novel vector conrol technique for SPIM is presented. Performance of the proposed method is assessed using MATLAB/SIMULINK software. Simulation results showed the excellence speed and torque responses obtained using the proposed technique.

Nash's Bargaining Formula Revisited

The note consists of showing the marginal rates of substitution (MRS) explicitly in Nash's product formula and contract curve given by the Jacobian determinant, which otherwise are contained therein only implicitly. Two simple examples from duopoly and bilateral monopoly are used to show the MRS's explicitly in the mathematical structure of the bargaining game. We learn from the note that, while the MRS's are implicit in the mathematical structure of the game, the MRS's after suitable transformation can be shown explicitly in the product formula and contract curve. This MRS showing puts the structure of the game in a context familiar to economists.

Genetic variation among lambs in peripheral IgE activity against the larval stages ofTeladorsagia circumcincta

SUMMARYIgA and IgE activity againstTeladorsagia circumcinctawas investigated in a flock of Texel lambs following natural, mixed nematode infection among lambs. The distribution of IgA activity was similar to a gamma distribution whereas IgE activity was different. Box-Cox analysis demonstrated that X0·25was a suitable transformation to normalise IgE responses. The transformed IgE activity was under moderate to strong genetic control. Nine different allergens were identified by proteomic analysis. Tropomyosin was selected for further analysis. IgE activity against tropomyosin was moderately heritable and associated with decreased egg counts and with reduced body weight at the time of sampling.