Multiloop Multirate Continuous‐Discrete Drone Stabilization System: An Equivalent Single‐Rate Model

The article discusses the UAV lateral motion stabilization system, as a MIMO multiloop multirate continuous-discrete system, specified in the form of an input–output model in the domain of discrete Laplace transform or in the form of a structural diagram. Approaches to the construction of equivalent T and NT single-rate models for MIMO multiloop multirate continuous-discrete systems are considered. Here, T is the largest common divisor of the sampling periods of the system, N is a natural number that is the smallest common multiple of the numbers characterizing the sampling periods of the system. The resulting impulse representations of the outputs of equivalent models are in the form of rational functions. The basis for the construction of these models is a matrix of sampling densities—a structural invariant of sampling chains. An example of the construction of the indicated matrix and an equivalent single-rate model are given. Obtaining equivalent single-rate models for MIMO multiloop multirate systems allows us to extend the methods of research and synthesis of MIMO continuous and continuous-discrete systems to a common theoretical base—the theory of polynomials and rational functions, which are typical elements of the description of these classes of systems.

Topological Indices of Some New Graph Operations and Their Possible Applications

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

PERSON AND SUPREME FORCES: INVARIANT ELEMENTS IN SCENES OF BOLDINO WORKS

In “The Tales of Belkin”, “Little Tragedies” and some other works of Pushkin (including those of the sculptural myth) there is a common scene associated with direct clash between a character and uncontrollable forces (in particular, of superhuman nature). Such a force impends over a character during a long time and, suddenly, actualizes physically. As a result, a character fights against the fatal forces or loses his/her will - falls without unconscious (the most frequent reaction), begs for mercy or runs away. Insistent repeatability of the situation revels here a structural invariant. It can be combined with the presence of a hidden powerful observer as well as with a plot complex based on a treaty concluded in the past.

Phase Transition as an Emergent Phenomenon Analysed by Violation of Structural Invariant (M, BM)

When modeling complex systems, we usually encounter the following difficulties: partiality, large amounts of data and uncertainty of conclusions. The most common approach used for modeling is the physical approach, sometimes reinforced by statistical procedures. If we assume emergences in the complex system, a physical approach is not appropriate at all. Instead, we build here the approach of structural invariants. In this paper, we show that another plane can be built above the plane of physical description, which is responsible for violation of structural invariants. Main attention is concentrated (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with Ramsey graph theory. In addition, the article introduces a calculus that describes the emergent phenomena using two quantities - the power of the emergent phenomenon and the complexity of the structure of the considered complex system. We show the application of the method for modeling phase transition in chemistry.

The Forensic Symptoms Inventory—Youth Version—Revised: Development and Age Invariance Testing of a Broad-Spectrum Questionnaire for Forensic Assessment

Covering both individual and neuropsychological factors, the Forensic Symptom Inventory—Youth Version—Revised (FSI-YV-R) is the first broad spectrum questionnaire for adolescents in forensic care, measuring several deficits, such as executive dysfunctions, anger, and inadequate coping to enhance treatment goals and evaluate interventions. In this study, both the factor structure and the measurement and structural invariance of the FSI-YV-R were investigated. The sample consisted of 159 forensic juvenile outpatients (79.9% males and 20.1% females) aged 12 to 19 with a mean age of 16.07 ( SD = 1.57). Multi-Group Confirmatory Factor Analyses identified a second-order model (measuring executive functioning) and proved measurement and structural invariant across age groups (younger adolescents, 12–15 years and older adolescents, 16–18 years). Contrary to the expectations none of the FSI-YV-R subscales differentiated between younger adolescents (N = 74) and older adolescents (N = 85). These results and implications for both theory and practice are discussed.

Detection of Emergent Situations in Complex Systems by Structural Invariant (MB, M)

The paper introduces complete description of the detection method that uses structural invariant Matroid and its Bases (MB, M). There are recapitulated essential concepts from the used knowledge field as “complex system, emergent situations (A, B, C)”, Ramsey theorem and principal computation variables “power” and “complexity” of emergence phenomenon. The method is explained in details and the demonstration of its application is done by the detection of emergent situation – violation of Short Water Cycle in an ecosystem.