Possibility of increasing the switching resource of liquid-metal self-regulating fuses with fusion insert

THE PURPOSE. Assessment of the state of the art in the development of current limiters based on liquid metal self-healing fuses and an increase in the switching life of self-healing fuses with a composite fuse-link.METHODS. When solving the problem, the method of literature analysis was used, as well as the method for calculating dependencies for different materials of the fuse-link, the implemented method of scientific computer mathematics.RESULTS. Literary sources contain information about the designs of liquid-metal self-healing fuses and their research, allowing conclusions to be drawn about their viability and the possibility of obtaining a practical yield. A common disadvantage of the of liquid-metal self-healing fuses design is a limited switching resource due to an increase in the diameter of the fuse-link under the action of arc erosion. A significant effect of increasing the switching resource and the stability of the protective characteristic is possessed by the design of a of liquid-metal self-healing fuses with a composite fusible link. However, in such designs, the switching capacity is reduced. It is shown that the main criterion for the operability of the liquid-metal self-healing fuses with a composite fusible link is the value of the ratio between the value of the shunting resistance and the resistance of the electric ARC. The performance of the liquid-metal self-healing fuses with a composite fusible link is ensured at values of this value below critical.CONCLUSION. The proposed mathematical expression may turn out to be useful in the development of liquid-metal self-healing fuses with a composite fusible link design, for example, when choosing an electrode material, liquid metal, etc. This will significantly increase the switching resource of the liquid-metal self-healing fuses with a composite fusible link. The condition must be taken into account in the parametric synthesis of the current limiter based on the liquid-metal self-healing fuses with a composite fusible link.

A Multimodal Retrieval and Ranking Method for Scientific Documents Based on HFS and XLNet

Aiming at the defects of traditional full-text retrieval models in dealing with mathematical expressions, which are special objects different from ordinary texts, a multimodal retrieval and ranking method for scientific documents based on hesitant fuzzy sets (HFS) and XLNet is proposed. This method integrates multimodal information, such as mathematical expression images and context text, as keywords to realize the retrieval of scientific documents. In the image modal, the images of mathematical expressions are recognized, and the hesitancy fuzzy set theory is introduced to calculate the hesitancy fuzzy similarity between mathematical query expressions and the mathematical expressions in candidate scientific documents. Meanwhile, in the text mode, XLNet is used to generate word vectors of the mathematical expression context to obtain the similarity between the query text and the mathematical expression context of the candidate scientific documents. Finally, the multimodal evaluation is integrated, and the hesitation fuzzy set is constructed at the document level to obtain the final scores of the scientific documents and corresponding ranked output. The experimental results show that the recall and precision of this method are 0.774 and 0.663 on the NTCIR dataset, respectively, and the average normalized discounted cumulative gain (NDCG) value of the top-10 ranking results is 0.880 on the Chinese scientific document (CSD) dataset.

Low-cost arabinose induced genetic circuit for protein production: Modeling.

A low-cost reagent-producing genetic circuit was designed during this work. Its functioning is based on a positive feedback loop induced by a small amount of arabinose, allowing users to obtain reactants in a safe, constant, and controlled manner. The design-only approach to the project allows us to work in different kinds of computational models, thus, an ODE-based model was thoroughly developed and a cellular automata-based one was experimented with. Working on the ODE model, equilibrium states and system stability were studied. Circuit properties were also focused on one of which was a high concentration of interest protein produced by low inductor inputs. As a result, a mathematical expression capable of describing the quantity of produced reagent was obtained. In addition, the cellular automata model offers a new perspective, given its differences from the ODE model e.g. this type of model is a stochastic analysis and describes each cell individually instead of describing the whole cellular population.

Assessing the sustainability development of an organization

Introduction. The article presents a review of scholarly literature and the author's assessment of the potential for sustainable development of a medical organization. The purpose of the article is to describe the author's methodology for assessing the potential for sustainable development, and to evaluate the effectiveness of its application in a medical organization. Materials and Methods. The study used the following research methods: comparative analysis, T.L. Saati, and the author’s methodology for assessing the potential for sustainable development of a medical organization. Results. In the process of analyzing the methodology for self-assessment of the maturity on the way to achieving the sustainable development of the ISO 9004 standard organization, the author revealed a number of problems. They include low sensitivity to individual assessment of processes, the lack of a mathematical expression of the level of development for certain areas of activity, and the absence of an integral indicator sensitive to minimal changes. The author describes in detail process of developing her methodology for assessing the potential for sustainable development of an organization and illustrates the application of this methodology within a medical organization for evaluating sustainable development in statics and dynamics. Conclusions. Finally, conclusions are drawn about the ways of applying the author's assessment methodology by the head of the medical organization.

Methodology for calculating the criteria of economic efficiency of investments in nuclear icebreakers

An economic and analytical model for evaluating the criteria of efficiency (profitability) of investments in the projects of innovative nuclear icebreakers of the Northern Sea Route is suggested. The model is based on the new analytical representation of the methodology for forecasting the investment project efficiency that is widely used in international practice. The mathematical expression for the net discounted income provides convenient formulas for calculating several investment efficiency criteria for nuclear icebreakers: internal rate of return, minimum annual revenues from icebreaker convoys, discounted payback period, and the volume of delivered cargo. The paper gives estimates of the criteria for the efficiency of investments in “Leader” class icebreakers that depend on the discount rate of cash flows, capital, and operating costs. It is shown that at high capital costs, typical for construction of “Leader” class nuclear icebreakers, the minimum required revenue of an icebreaker, representing a financial burden for ships transporting cargo along the NSR, rapidly increases with the growth of discount rate and the reduction of investment payback period. This means that the profitability of such icebreakers is only possible at low discount rates of 2–3% per year, which is an extremely low-interest credit. Even with low interest and impressive technical characteristics of the icebreaker (high speed of navigation, large number of ships in the caravan and their maximum capacity) the payback period would exceed 25 years.

CONSTRUCTION OF MATHEMATICAL MODELS USING THE METHODS OF CORRELATION AND REGRESSION ANALYSIS

The article discusses the construction of a mathematical model using the methods of correlation and regression analysis in determining the functional relationship between the quantities. When conducting an experiment, it is often necessary to establish the interdependence between two or more quantities in order to obtain an empirical formula. In some cases, this is a simple task, because these connections are almost obvious or known in advance. As a rule, to establish the relationship between different indicators, factors and characteristics is not a trivial task. There is a need to use some hypothesis in the form of functional dependence. In other words, it is necessary to replace this functional dependence with a fairly simple mathematical expression. Such a mathematical expression can be a linear equation or a polynomial. In order to use such experimental data to determine such a mathematical or functional relationship between variables, the methods of correlation and regression analysis are used. Correlation analysis provides an answer to the statistical hypothesis of the absence or presence of a relationship between variables with some predetermined confidence probability. Determination of the functional dependence between different values on their experimental values is carried out using regression analysis. It is based on the well-known method of least squares. Proposing one or another regression equation, the researcher determines both the very existence of the relationship between variables and its mathematical form. Regression analysis considers the relationship between the dependent quantity and non-dependent variables. This relationship is represented using a mathematical model, that is, an equation that connects the dependent and independent variables. Processing of experimental data using correlation and regression analysis allows us to build a statistical mathematical model in the form of a regression equation. Thus, the methods of correlation and regression analysis are closely related.

VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System

Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.

SET-UP DUE TO RANDOM WAVES: INFLUENCE OF THE DIRECTIONAL SPECTRUM

The correct estimation of set-up is very important to evaluate coastal hazard and to design coastal structures. In this paper, we derived a mathematical expression for wave set-up in the context of random waves. The solution to this expression assumes straight, parallel depth contours and constant average flow parameters in the longshore direction. We then investigated the effect of different types of sea state taking account of different frequency spectrum and spreading function assumed in the expression on estimates of wave set-up. We found the set-up was highly influenced by the frequency spectrum used. Finally, we applied this expression to estimate set-up values at locations in Italy and in the United States using buoy data provided by ISPRA (Istituto Superiore per la Protezione e la Ricerca Ambientale) and NDBC (National Data Buoy Centre).

Mathematical framework for describing multipartite entanglement in terms of rows or columns of coefficient matrices

In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.