Optical models of the molecular atmosphere

The use of optical and laser methods for performing atmospheric investigations has stimulated the development of the optical models of the atmosphere. The principles of constructing the optical models of molecular atmosphere for radiation with different spectral composition (wideband, narrowband, and monochromatic) are considered in the case of linear and nonlinear absorptions. The example of the development of a system which provides for the modeling of the processes of optical-wave energy transfer in the atmosphere is presented. Its physical foundations, structure, programming software, and functioning were considered

О построении совместных систем линейных ограничений экономико-математических моделей задач с двухсторонними неравенствами

В статье рассмотрена актуальная проблема построения совместной системы линейных ограничений для экономико–математических моделей, задач с двухсторонними ограничениями на переменные. Приведены примеры и сформулированы условия совместности линейных систем.У статті розглянута актуальна проблема побудови спільної системи лінійних обмежень для економіко–математичних моделей задач із двосторонніми обмеженнями на змінні. Наведені приклади і сформульовані умови спільності лінійних систем.This article deals to the actual problem of building a joint system of linear constraints for economic and mathematical models problems with bilateral constraints on the variables. In applications of the economic models of production systems, lower and upper limits of the values correspond to the minimum and maximum possible values of variables and constraints which are specified explicitly. Such a statement, compared with the traditional when variables imposed only non–negativity condition, is more common and necessary in the construction of econometric models and the solution of practical problems of management and decision–making. Building a joint system of linear constraints and bilateral inequalities carried out on the basis of verification of the fulfillment of conditions: Consistency of a system of linear constraints in Rn ( Kronecker – Capelli theorem) ; Consistency of a system of linear constraints in Rn and in X ≥ 0, by constructing and solving linear programming problem, which determines the consistency in area where X≥ 0; Consistency of a system of linear constraints in the X≥Xmin, by linear coordinate transformations (change of variables X=Xmin+Z, Z≥0 and solving linear programming problem, which determines the consistency at Z ≥ 0 and, that’s why, at the area X≥Xmin); Consistency of a system of linear constraints at X≤Xmax, by checking of the condition Xmax–Xmin=Z, Z≥0. There were given examples of solutions of the problem of determining the consistency of systems of linear constraints and restrictions on the variables in the form of bilateral inequalities

Generalized Schwarzschild's method

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild's method, FEM produces a continuous distribution function (DF) and satisfies the intra element continuity and Jeans equations. The method employs two finite-element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear system of equations, which can be solved for the nodal values of the DF using linear or quadratic programming, or other optimization methods. We illustrate the superior performance of FEM by constructing ergodic and anisotropic equilibrium DFs for spherical stellar systems (Hernquist models). We also show that explicitly constraining the DF by the Jeans equations leads to smoother and/or more accurate solutions with both Schwarzschild's method and FEM.Comment: 14 pages, 7 Figures, Submitted to MNRA

Learning Computer Programs with the Bayesian Optimization Algorithm

The hierarchical Bayesian Optimization Algorithm (hBOA) [24, 25] learns bit-strings by constructing explicit centralized models of a population and using them to generate new instances. This thesis is concerned with extending hBOA to learning open-ended program trees. The new system, BOA programming (BOAP), improves on previous probabilistic model building GP systems (PMBGPs) in terms of the expressiveness and open-ended flexibility of the models learned, and hence control over the distribution of individuals generated. BOAP is studied empirically on a toy problem (learning linear functions) in various configurations, and further experimental results are presented for two real-world problems: prediction of sunspot time series, and human gene function inference

Tools for modelling support and construction of optimization applications

We argue the case for an open systems approach towards modelling and application support. We discuss how the 'usability' and 'skills' analysis naturally leads to a viable strategy for integrating application construction with modelling tools and optimizers. The role of the implementation environment is also seen to be critical in that it is retained as a building block within the resulting system

Optimizing Control of a Power System during an Emergency

Population growth, infrastructure and economy puts pressure and demand on the existing power supplies. It puts strains on the current power systems which causes instabilities in the systems. This is an ongoing challenge which needs an immediate solution. The objective of this thesis is voltage stability. This is examined with the help of constructing a small power system using a programming language called Matlab. Optimization tools provided by Matlab are used to find the maximum possible pre-contingency load, while still maintaining a stable system. To find feasible solutions in Matlab, system models, such as load models and power line models are simplified. The results show that a system which has experienced a fault can successfully recover by using a linear load recovery model and an exponential load recovery model. Certain constraints, such as generator ramping and limitations on the field voltages in the generators are implemented. Feasible olutions are found although constraints might have made it more difficult under the course of this study. These findings are rough approximations of how a small power system can operate. Though, this can give valuable information on how a more complex system might act before and after a contingency as well as suitable recovery paths. Although the thesis is more suited for those who have some knowledge in control or power systems, a reader without a technical background can enjoy the paper too

Achievement test construction using 0-1 linear programming

In educational testing the work of professional test agencies has shown a trend towards item banking. Achievement test construction is viewed as selecting items from a test item bank such that certain specifications are met. As the number of possible tests is large and practice usually imposes various constraints on the selection process, a mathematical programming approach is obvious. In this paper it is shown how to formulate achievement test construction as a 0¿1 linear programming problem. A heuristic for solving the problem is proposed and two examples are given. It is concluded that a 0¿1 linear programming approach fits the problem of test construction in an appropriate way and offers test agencies the possibility of computerizing their services

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure