Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

This paper provides a brief overview of modern applications of nonbinary logic models, where the design of heterogeneous computing systems with small computing units based on three-valued logic produces a mathematically better and more effective solution compared to binary models. For application, it is necessary to implement circuits composed of chipsets, the operation of which is based on three-valued logic. To be able to implement such schemes, a fundamentally important theoretical problem must be solved: the problem of completeness of classes of functions of three-valued logic. From a practical point of view, the completeness of the class of such functions ensures that circuits with the desired operations can be produced from an arbitrary (finite) set of chipsets. In this paper, the closure operator on the set of functions of three-valued logic that strengthens the usual substitution operator is considered. It is shown that it is possible to recover the sublattice of closed classes in the general case of closure of functions with respect to the classical superposition operator. The problem of the lattice of closed classes for the class of functions T2 preserving two is considered. The closure operators R1 for the functions that differ only by dummy variables are considered equivalent. This operator is withiin the scope of interest of this paper. A lattice is constructed for closed subclasses in T2={f|f(2,…,2)=2}, a class of functions preserving two.

Impact of stock health on fish prices: Evaluation and implications for food accessibility

The continuous rise of the world’s population has made food security a major point of the global agenda, with fisheries providing a key source of nutrition, especially in developing countries. Ensuring their health is key to maintain the availability of the resource, but its effect over accessibility is yet unclear. In this paper, we discuss the relevance of stock health for ensuring the price accessibility of the resource. A Least Square Dummy Variable panel model is proposed for bluefin tuna prices, with a biological explanatory component, and dummy variables reflecting changes in fishing trends. Both have proven to be significant to explain annual price variations, with improvements in stock health achieving price reductions.

Cluster Analysis of Financial Strategies of Companies

Measuring the value of companies and assessing their risk often relies on econometric methods that consider companies as a set of objects under study, homogeneous in the sense of their use of financial strategies. This paper shows that cluster analysis methods can divide companies into classes according to financial strategies that they employ. This indicates that homogeneity can be considered within these classes, while between-class companies should rather be perceived as heterogeneous. The clustering of companies has to be performed on quite a dense set of strategies, which requires a combination of formal and heuristic methods. To divide companies into classes, we used financial coefficients characterizing strategies for the 2030 largest non-financial companies within the time period from 2006 to 2018. As a result, a stable division into seven clusters/strategies was obtained. We revealed that some strategies were more characteristic for the companies of high-tech economy, while others were typical for the companies in basic industries. The dynamics of clusters is characterized by an increase in the share of risky strategies. A good meaningful interpretation of the resulting clustering confirms its consistency. The identified clusters can be used as dummy variables in econometric studies of companies to improve the quality of the results.

Daily abnormal returns and price effects in the “passion investments” market

This paper explores price effects in the “passion investments” market after days with abnormal returns. To do this, daily prices for stamps and diamonds over the periods 1999–2021 and 1989–2021 are analyzed. The following hypothesis is tested: One-day abnormal returns create stable patterns in price behavior on the next day. Statistic tests (t-test, ANOVA, Mann–Whitney U test, modified cumulative abnormal returns approach, regression analysis with dummy variables) confirm the presence of price patterns related to extreme returns: price fluctuations on the day after extreme returns are higher than returns on “normal” days. On the days after positive abnormal returns, the momentum effect is detected. Contrarian effect is typical for the days after negative abnormal returns. A trading strategy based on detected price effects showed the presence of exploitable profit opportunities. Results of this paper provide additional pieces of evidence in favor of inconsistencies between the efficient market hypothesis and practice and can be used by traders to generate extra profits in the “passion investments” market. Acknowledgment The authors gratefully acknowledge financial support from the Ministry of Education and Science of Ukraine (0121U100473).

Cross-species bamboo grading based on flexural properties

This experiment studied five species of bamboo culms [e.g. B. vulgaris (ampel), D. asper (betung), G. apus (tali), G. atroviolacea (hitam), and G. pseudoarundinaceae (andong)], then analyzed the possibility to develop cross-species bamboo structural grading (both strength and capacity grading) models by mean of dummy variable regression. Since the regression analysis resulted the significantly different coefficient values of the dummy variables, any coincided trendline did not found, but some parallel ones were obtained. The non-coincided but parallel trendlines indicated that a linear equation can estimate the average value of the grade determining property (GDP) of cross-species bamboo structural grading, while the constants must be added to consider the species influence. Meanwhile the non-parallel trendlines indicated that the different linear equation must be applied for every bamboo species. The crossspecies bamboo structural grading could not reliably justify in this study. Species have a strong influence on bamboo grading. Therefore, the authors suggest considering the species identification in the bamboo structural grading.

A Method of Joining Piecewise Functions to Produce Continuous Functions of Difficult Data

This article describes a method of modelling data that involves splitting the curve into two (or more) and creating separate piecewise functions for each part; these functions are then concatenated via a linking function to create one overall continuous function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two (or more) subfunctions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

A Method of Joining Piecewise Functions to Produce Continuous Functions of Difficult Data

This article describes a method of modelling data that involves splitting the curve into two (or more) and creating separate piecewise functions for each part; these functions are then concatenated via a linking function to create one overall continuous function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two (or more) subfunctions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

Mathematical relations for constructing an algorithm for estimating signal parameters under conditions of constraints

Статья посвящена разработке математических соотношений для построения алгоритма оценивания параметров сигналов в условиях ограничений. При работе транспортной системы возникают довольно сложные проблемы, которые связаны с необходимостью проведения оценки принятых параметров с требованиями соблюдения имеющихся ограничений. Ограничения могут представлять собой как равенства, так и неравенства. Поскольку ограничения-неравенства могут быть сведены путём добавления фиктивных переменных к условиям, а также их можно проверить по шагам, переводя в состав равенства, в статье разработан алгоритм, позволяющий иметь ограничения-равенства. Данная задача относится к классу статистических проблем оптимизации. Для ее решения использованы стандартные функции из подкаталога "optimization" вычислительной среды MatLAB. Построение такого алгоритма даст возможность не только уменьшить складские расходы, но и сократить основное производственное время. The article is devoted to the development of mathematical relationships for constructing an algorithm for estimating signal parameters under constraints. During the operation of the transport system, rather complex problems arise, which are associated with the need to assess the adopted parameters with the requirements of compliance with the existing restrictions. Constraints can be either equality or inequality. Since the inequality constraint can be reduced by adding dummy variables to the equality conditions, and they can also be checked step by step, transforming them into equality, we will develop an algorithm that allows us to have equality constraints. This task belongs to the class of statistical optimization problems. To solve it, standard functions from the "optimization" subdirectory of the MatLAB computing environment will be used. The construction of such an algorithm will make it possible not only to reduce storage costs, but also to reduce the main production time.