Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.Siirretty Doriast

Forecasting of operational indicators of grinding tools with the controlled form and orientation of abrasive grains

The interconnection of the abrasive grain front angle parameter with the form, orientation and wear out parameters is investigated. The form of the abrasive grains was estimated by means of form coefficient which represents the relation of diameters of the spheres described around contours of grains, to diameters of the spheres entered in them. The spatial orientation angle of the abrasive grains was defined between main (i.e. the biggest) axis of the grains and the cutting plane. It is established that, depending on an orientation angle at increase in a form coefficient of the abrasive grains can be either an increase or a decrease in the values of their front angles. In most cases, with an increase in a form coefficient of the oriented grinding grains (at orientation angles [theta]=10°-125°) the growth of their front angles is fixed. At tangential orientation of grains ([theta]=0°) and at the close directions of orientation ([theta]=135°-180°) the return picture is observed. Also established that the longer the abrasive grain wears along the main axis and located in the tool body, the larger is its front angle. Besides that, the front angles of the abrasive grains reach the maximum positive values at orientation angles [theta]=2.5°-45°.Dependence of tension in grains during the work with parameters of their form, orientation and depth of embedment in the bundle is investigated. It was found that for all orientation angles of grains their tension significantly increases with an increase in their form coefficient. Besides that it is confirmed that the deeper the grain is in the bundle, the lower the tension is there. Also found that tension is minimal when the grains are tangential orientated. Further on increase the option of the grains in the direction of action of the cutting force follows. Such option of orientation is the most rational both from the point of view of minimization of tension, and for ensuring rational sizes of front angles of the abrasive grains. The rational angle of grain orientation for cutting disc are in range [theta]=65°-75°. The joint analysis of dependences of front angles and tension in grains from factors of their form and orientation allows the prediction of operating characteristics of grinding tools at the design stage for specific tasks and processing conditions

Equations of Rounded-Edge Profile for a Ring Gear in a Wave Reducer with Intermediate Rolling Elements

The paper considers geometrical parameters of a ring gear for a wave gear with rolling elements. A coordinate system is selected. Parametric equations for the ring gear profile are deduced. An equation for rounded edges of the ring gear is developed to increase the transmission efficiency and shorten the ring gear's running-in period. An epicycloidal ring gear profile is plotted in AutoCad. A sample model produced from these calculations is shown. The product is intended for use in the design of a hand-held electric drill on the base of a commutator motor with useful capacity of 1 kW

Stability of the bicriteria Boolean investment problem subject to extreme optimism and pessimism criteria

We consider the bicriteria investment Boolean problem of finding the Pareto set based on efficiency and risk criteria. The quantitative stability characteristics of the problem are investigated, and lower and upper bounds for a stability radius are obtained for the case where portfolio and financial market state spaces are endowed with the Hölder metric. Calculation of these bounds provides investors with a deeper insight into the specific problem of facilitating financial decisions more reliably in uncertain environments

Multicriteria investment problem with Savage's risk criteria: Theoretical aspects of stability and case study

A discrete variant of a multicriteria investment portfolio optimization problem with Savage's risk criteria is considered. One of the three problem parameter spaces is endowed with Hölder's norm, and the other two are endowed with Chebyshev's norm. The lower and upper attainable bounds on the stability radius of one Pareto optimal portfolio are obtained. We illustrate the application of our theoretical results by modeling a relevant case study.</p

Balancing fast-rotating parts of hand-held machine drive

The article considers the issues related to the balancing of fast rotating parts of the hand-held machine drive including a wave transmission with intermediate rolling elements, which is constructed on the basis of the single-phase collector motor with a useful power of 1 kW and a nominal rotation frequency of 15000 rpm. The forms of balancers and their location are chosen. The method of balancing is described. The scheme for determining of residual unbalance in two correction planes is presented. Measurement results are given in tables

Quantum computing with spin qubits in semiconductor structures

We survey recent work on designing and evaluating quantum computing implementations based on nuclear or bound-electron spins in semiconductor heterostructures at low temperatures and in high magnetic fields. General overview is followed by a summary of results of our theoretical calculations of decoherence time scales and spin-spin interactions. The latter were carried out for systems for which the two-dimensional electron gas provides the dominant carrier for spin dynamics via exchange of spin-excitons in the integer quantum Hall regime.Comment: 18 pages in PD