Performance of arithmetical operations on mobile gadgets using axioms of classical and nonstandard interval analysis

We propose a programming system for calculation of economical standards of regulating banking activity by means of Euclidian and interval arithmetic using mobile gadgets. The program was created by means of Microsoft Visual Studio 2017 Express for Windows Phone using C#. The feature of this programming system is the possibility to be used anywhere: during business negotiations, in the absence of PCs and WiFi, etc. For its application, one needs a smartphone with Android operation system. The smartphone needs to have a capacitive screen with multi-touch input with the possibility of more than four touches at once. The size of the screen can vary, but the resolution must be 480*480 pixels. During the progress, the system calculates the indicators of banking activity approved by National bank of Ukraine. Using of the interval arithmetic gives the possibility to analyse the financial status of the bank under any conditions. The comparison of the results of arithmetical operations by using the axioms of classical and nonstandard interval analysis was carried out. The criterion of the efficiency is the value of the relative change of the final interval of the calculations that were carried out using the axioms of the nonstandard interval analysis related to the same calculations that were carried out using the axioms of the classical interval analysis. For efficiency comparison we choose standard indicators that define the financial safety of the bank. The results of the calculations show that the intervals defined according to the rules of the nonstandard interval mathematics have the size of the interval 12-90% less than the intervals calculated according to the rules of the classical interval mathematics.

Decision support system for customers during availability of trade-credit financing with different pricing situations

This study introduces a decision-making policy for a two-warehouse system with a non-instantaneous deteriorating product for credit facility with demand depending on the product price. Two different selling prices are considered in the deterioration and non-deterioration periods. Shortages are partially considered and dependent on the duration of the arrival of fresh lot. Alternative trade-credit is applied herein, and several situations are investigated in this approach. The optimization problems of the situations are solved using an interval-oriented multi-section technique via interval mathematics and its order relations. Three numerical examples are studied and solved to validate the said problem.

Minimum time overtaking problem of vehicle handling inverse dynamics based on interval mathematics

To analyze the influence of uncertain factors on minimum time overtaking, interval mathematics is used to describe the uncertainties, and the overtaking safety distance is calculated using interval analysis method. In addition, vehicle handling inverse dynamics is proposed in this paper. In this method, the driver-handling input can be obtained without the modeling of driver. The optimal control problem is first converted into a nonlinear programming problem based on Gauss pseudospectral method. Then sequential quadratic programming is applied to get the solution. The simulation results show that the overtaking behavior will be significantly different, if the drivers’ age groups or vehicles’ braking system parameters are different. Besides, the influence of different drivers’ estimate time is critical. The subjective judgments of the drivers are considered in this paper to realize the user-friendly design. This method may provide a reference for the research of unmanned vehicles and driving assistance system.