Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

ASSESSMENT METHODS

The article is devoted to the research analysis of the current patterns of development of evaluation activities. Three systemic approaches used in modern evaluation activities are considered. Their analysis and criticism is carried out. Conclusions are drawn about their effective symbiosis. Definitions of cost and price are given. An approximate method of market analysis on the example of movable property is disclosed. Each of the stages is revealed. In conclusion, it was concluded that modern valuation methods require improvement, since any valuation method gives only an approximate cost. The main problem of all evaluation methods is also formulated: irrationality of the market: sellers and buyers

AN APPROXIMATE METHOD TO PRESENT THE BUCKLING STRENGTH OF A GRILLAGE IN A PROBABILISTIC FORM

An approximate method for calculation in probabilistic terms of the buckling strength of a grillage under unidirectional in-plane compression is proposed. The geometric properties of longitudinals and transverses and the mechanical properties (yield stress and modulus of elasticity) of the material they are built from are treated as random parameters that may change over ship’s service life. The cumulative distribution function of the grillage’s critical buckling strength is calculated by using an analytical formula for multitude sets of input parameters while all of them having the same level of certainty. The assumption is that the critical buckling strength has the same (or very similar) level of certainty as that of the input parameters. The accuracy of the proposed approximate method is relatively high (the maximal error is around 2%). It is recommended for use when specialized computer programs for application of Monte Carlo simulation method are not available. The method does not require a complicated specialized computer program and can be run on EXCEL computer program.

Development and verification of meshless diffuse approximate method for simulation of compressible flow between parallel plates

A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.

Determining the rank of a number in the residue number system

In this article, the formulation and proof of the theorem on the difference in the ranks of the numbers represented in the Residue Number System is carried out. A method is proposed that allows to reduce the amount of necessary calculations and increases the speed of calculating the rank of a number relative to the method for calculating the rank of a number based on the approximate method. To find the rank of a number in the method for calculating the rank of a number based on the approximate method, it is necessary to calculate n operations with numbers exceeding the modulus value; in the proposed method, it is necessary to calculate n·(n−1)/2 operations not exceeding the value of the module.