Features of software development using arrays in an object-oriented environment

The features of software development using static and dynamic arrays in the C ++ Builder object-oriented environment are considered. The syntax of various options for creating static and dynamic arrays in the C ++ Builder language is considered in detail. Examples of working with static and dynamic arrays in C ++ Builder developed by the authors and the corresponding algorithms are presented in the form of block diagrams, program codes and program interfaces. Examples of program development are given using one-dimensional and multidimensional arrays. Examples of memory allocation are given for dynamic arrays. The choice of the required method for solving the problem is substantiated, taking into account the available input data and taking into account the expected results, as well as the peculiarities of their obtaining and processing. The external specification and the main features of the solution of the assigned tasks are considered. The development of algorithms and programs for solving problems using arrays in the C ++ Builder environment is the basis for solving engineering and technical problems using software on a computer. The proposed approaches can be used in practice, since the algorithms outlined in the work will serve as a complex example in solving the set engineering and technical problems.

Processing and visualization of the results of parametric numerical calculations

In modern problems of mathematical modeling in computational gas dynamics, it is increasingly necessary to implement parametric studies. In these cases, the key factors of the problem under consideration vary with the chosen step within the given ranges. Calculations of this kind can be effectively carried out by constructing a generalized computational experiment. A generalized computational experiment is a computational technology that combines the solution of mathematical modeling problems, parallel technologies, and visual analytics technologies. The results of a generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the number of key factors. Processing and visual presentation of such arrays requires solving a number of separate tasks. The processing and visual presentation of the results are carried out for target functionals represented as a function of many variables. The report presents an examples of solving specific processing and visualization problems based on the implemented generalized computational experiment for 3D cone in supersonic flow.

Example of internal function for Sponge scheme built on the basis of the generalized AES design methodology

The purpose of this article is to construct an internal function underlying the “Sponge” scheme for constructing cryptographic hash functions. An internal function in the “Sponge” scheme is a fixed-length transformation or permutation that operates on a fixed number of bits that make up the internal state of the function. There are various constructive approaches to functiondesign. The most common approach is to use a permutation based on a symmetric block encryption algorithm with constants as the key. This article builds an internal function using the generalized AES design methodology. This methodology makes it easy to design block ciphers to encrypt large blocks of plaintext with small components, representing the processed data as multidimensional arrays. The internal function is a block cipher that processes 2048 bits, represented as a 9-dimensional array of 512 4-bit elements with size 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Each round of encryption consists of three transformations (S-blocks, linear transformation, and permutation), similar to the three round transformations of AES SubBytes, MixColumns, and ShiftRows. The constructed function can be used as an internal function in the modified “Sponge” schemefor constructing cryptographic hash functions.

Multidimensional Arrays, Indices and Kronecker Products

Much of the algebra that is associated with the Kronecker product of matrices has been rendered in the conventional notation of matrix algebra, which conceals the essential structures of the objects of the analysis. This makes it difficult to establish even the most salient of the results. The problems can be greatly alleviated by adopting an orderly index notation that reveals these structures. This claim is demonstrated by considering a problem that several authors have already addressed without producing a widely accepted solution.

Canonical tensor scaling

In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion required for generalizations of the recommender system problem beyond a matrix of user-product ratings to multidimensional arrays involving coordinates based both on user attributes (e.g., age, gender, geographical location, etc.) and product/item attributes (e.g., price, size, weight, etc.).

Searching for clusters in population data

The article continues the series of publications developing new statistically motivated approach to data clustering. Proposed method is applied for searching clusters of increased or decreased frequencies of some events in sets of neighboring cells in two dimensional tessellations of plane. Such cells may correspond to administrative regions, counties etc. The case of simple frequency tables (histograms) with rectangular cells was considered earlier. The observed distribution of event frequencies in cells can be compared either with expected one (for instance uniform) or with distribution corresponding to the previous moment of time. The groups of neighboring cells with the same direction of changes are unified in clusters which are checked to be statistically significant with account on multiple comparisons. Each group of cells is characterized with two parameters – its size (the number of cells) and the intensity of changing. If the size of group or (and) its intensity are too pronounced then such group is considered to be statistically significant cluster. There are no a priori suggestions concerning the number, size or shape of potentially existing clusters. Method can be used for clustering any multidimensional arrays of p-values which are independent and uniformly distributed according null hypothesis, while alternative is that there are sets of neighboring cells where p-values are close to 0 or to 1.