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This article describes a generalization to a model of recidivism proposed earlier by Maltz and McCleary (1977). This modification allows the model to better fit data on recidivism that the earlier authors presented. The mathematical and logical derivation of the new model are presented as are two methods of parameter estimation. The efficacy of the model is demonstrated on Taylor's (1971) data set and is compared with earlier efforts. It is found that the old model's fit is more than 16 times worse than that ofthe new model.

The pole assignment problem has been subject for research for a long time. For single-input single-output systems this problem is well understood but for multi-input multi-output systems the pole assignment problem is more complex. In this thesis a parameterization of state feedback gains for pole assignment is characterized with respect to completeness, redundancy and existence. In order to make a systematic examination of this parameterization a number of classes are introduced. This parameterization depends on two matrices that can be regarded as design parameters. In the thesis it is shown how the degree of freedom in the pole assignment problem for multi-input systems is characterized by these two matrices. It turns out that the properties of the parameterization depends on whether the characteristic polynomials of the open and the closed loop systems are coprime or not. It is shown in the thesis that if the characteristic polynomials are coprime, every possible feedback gain can be parameterized in this way, and in this sense the parameterization is complete. If the characteristic polynomials have factors in common the parameterization is not complete. In the thesis the shortcomings of the parameterization for this case are characterized. The design parameters seem to offer a greater degree of freedom than what can be offered in the pole assignment problem. This indicates a certain degree of overparameterization. This redundancy in the design parameters is characterized in the thesis. The parameterization implies that a certain matrix is invertible. Necessary conditions for when this matrix is invertible are given in terms of the two design parameters. It is shown that this matrix is invertible for almost every value of the design parameters when the characteristic polynomials are coprime, and hence that the parameterized gains are generally applicable. The parameterization and its properties are illustrated on a linear model of the military aircraft JAS Gripen.

The change in the state of sky from cloudy to cloudless (or vice versa) comprises an additional phase called 'transition zone,' in which the characteristics of the particle suspension lay between those corresponding to pure clouds and atmospheric aerosols. This phase, however, is usually considered, in atmospheric monitoring and modeling, as an area containing either aerosol or thin clouds. A sensitivity analysis has been performed to assess the longwave radiative effects resulting from different approximations to the transition zone for three radiation parameterizations included in the Weather Research and Forecasting Model. The parameterizations produce important differences (up to 60 W m−2) between radiative effects of optically thin layers of aerosols and clouds (as surrogates for transition zone suspensions) in the longwave region, both at the top and bottom of the atmosphere. Also, differences are greater if the suspension of particles is located at higher altitudes, but smaller in high humidity conditions ; This study is funded by the Spanish Ministry of Economy and Competitiveness (project NUBESOL, CGL2014‐55976‐R), Spanish Ministry of Science and Innovation (project NUBESOL‐2, PID2019‐105901RB‐I00), and University of Girona (project PONTUdG2019/05). Babak Jahani holds a FI‐AGAUR PhD grant (2018FI_B_00830) provided by the Government of Catalonia (Universities and Research Secretariat) and the European Union