Constructive Description Research Articles

Solving Inverse Magnetometry Problems Using Fuzzy Logic

Integration interpretation of geophysical anomalies is a procedure for extracting geological and geophysical information about the object under study from observed physical fields. Interpretations are closely related to solutions of systems of linear algebraic equations (SLAE), therefore the possibility of the most complete and constructive description of all solutions of SLAE is of particular importance. It will allow you to take into account all additional information about the object and obtain the highest quality interpretation. The paper presents the authors’ results on the constructive description of SLAE solutions and its application to the construction of gravimetric interpretations.

Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement.

Political Judgment and Ingenium: Rethinking the Sensus Communis Through Arendt and Vico

ABSTRACT This paper elaborates on the role played in (political) judgment by ingenium – the human faculty operating connections between different world-objects through analogy and imagination. Using Arendt and Vico, the paper argues that the concept of ingenium offers important clues as to how we should understand the judgment of the singular, a key aspect of political thought. Between rational-discursive approaches – reducing singularity to its subsumption into general categories – and radically contextualist accounts, the notion of ingenium allows to conceptualize a political judgment both able to account for singular objects and events, and capable of operating context-transcending reflection. The argument proceeds in three steps. First, I show with Arendt how singular judgment relies on sensus communis, capturing singularity beyond rational categories. Second, I discuss the difficulty of accommodating sensus communis in post-Kantian terms, where it becomes tied solely to affective reactions, making judgment of the singular exclusively evaluative, while its identification is restricted to categorial cognition. Lastly, through Vico, I discuss how ingenium reframes the sensus communis. By operating through analogy and exemplarity ingenium enables a sensus communis that establishes not only evaluative connections, but also contributes to the constructive identification and description of worldly objects and events in their singularity.

A Classification of Elements of Function Space F(R,R)

In this paper, we present a constructive description of the function space of all real-valued functions on R(F(R,R)) by presenting a partition of it into 28 distinct blocks and a closed-form formula for the representative function of each of them. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between the well-known representatives of four of the blocks: the Cantor function, the Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored.

Constructive Description of a Class of Periodic Functions on the Real Line

Constructive Description of a Class of Periodic Functions on the Real Line

The orbit spaces $G_{n,2}/T^n$ and the Chow quotients $G_{n,2}//(\pmb{\mathbb{C}}^{\ast})^n$ of the Grassmann manifolds $G_{n,2}$

The complex Grassmann manifolds $G_{n,k}$ appear as one of the fundamental objects in developing an interaction between algebraic geometry and algebraic topology. The case $k=2$ is of special interest on its own as the manifolds $G_{n,2}$ have several remarkable properties which distinguish them from the $G_{n,k}$ for $k>2$. In our paper we obtain results which, essentially using the specifics of the Grassmann manifolds $G_{n,2}$, develop connections between algebraic geometry and equivariant topology. They are related to well-known problems of the canonical action of the algebraic torus $(\mathbb{C}^{\ast})^n$ on $G_{n,2}$ and the induced action of the compact torus $T^n\subset(\mathbb{C}^{\ast})^n$. Kapranov proved that the Deligne-Mumford-Grothendieck-Knudsen compactification $\overline{\mathcal{M}}(0,n)$ of the space of $n$-pointed rational stable curves can be realized as the Chow quotient $G_{n,2}//(\mathbb{C}^{\ast})^{n}$. In recent papers of the authors a constructive description of the orbit space $G_{n,2}/T^n$ was obtained. In deducing this result the notions of the complex of admissible polytopes and the universal space of parameters $\mathcal{F}_{n}$ for the $T^n$-action on $G_{n,2}$ were of essential use. Using the techniques of wonderful compactification, in this paper an explicit construction of the space $\mathcal{F}_{n}$ is presented. In combination with Keel's description of $\overline{\mathcal{M}}(0,n)$, this construction enabled one to obtain an explicit diffeomorphism between $\mathcal{F}_{n}$ and $\overline{\mathcal{M}}(0,n)$. In this way, we give a description of $G_{n,2}//(\mathbb{C}^{\ast})^{n}$ as the space $\mathcal{F}_{n}$ with a structure described in terms of admissible polytopes $P_\sigma$ and spaces $F_\sigma$. Bibliography: 32 titles.

An experimental and theoretical study of the structural, optical, electrical, and dielectric properties of PrAsO4

This study reports the synthesis (by the co-precipitation method) and characterization of the PrAsO 4 polycrystals. The crystal structure has been determined using the Rietveld method. Two validation methods were used to confirm the structural model: the bond valence sum (BVS) and the charge distribution (CHARDI). A constructive description of the structure was made, starting with the connection modes of the coordination polyhedron. The electronic structure of the compound, determined by the DFT method, shows a direct band gap semiconductor material with a calculated energy of 2.21 eV. This compares favorably with the experimental band gap energy value of about 2.52 eV. The microstructural study showed grain and crystalline sizes of about 500 and 17 nm, respectively. TGA analysis was used to study the thermal stability of the compound, which showed a plateau in the 550 − 650 °C range due to the oxidation of Pr 3+ to Pr 4+ . This oxidation was confirmed by the emission spectra of Pr 3+ obtained from the photoluminescence study. The electrical study in the 440–600 °C temperature range shows that the PrAsO 4 is a bad ionic conductor with a value of about 10 −8 Scm −1 . The dielectric study showed a value of 1400 for the dielectric constant ε, and the dipolar polarization dominated the polarization phenomenon. About 10 −6 s was obtained for the relaxation time (τ r ) • The crystal structure of PrAsO4 was determined Rietveld refinement and confirmed by two validation models (BVS) and CHARDI. • The electronic structure was determined by DFT method which shows a direct band gap with energy of 2.21 eV. • The experimental band gap energy is of about 2.52 eV. • The thermal analysis shows the oxidation of Pr3 + to P4 + in the 550–650 °C temperature range. • The electrical measurement shows that PrAsO4 has a conductivity of about 10 −8 Scm −1

Constructive Description of Hölder Classes on Compact Subsets of ℝ3

Constructive Description of Hölder Classes on Compact Subsets of ℝ3

ЗМІ як чинник багаторівневої системи управління соціально-психологічною адаптацією внутрішньо переміщених осіб

Досліджено роль засобів масової інформації щодо соціально-психологічної адаптації внутрішньо переміщених осіб. Визначено сутнісні характеристики соціально-психологічної адаптації внутрішньо переміщених осіб. Встановлено тип інформаційних впливів на внутрішньо переміщених осіб. Проаналізовано характеристики негативного та позитивного впливу медіа на висвітлення проблем внутрішньо переміщених осіб. Розглянуто умови інформаційно-психологічної безпеки внутрішньо переміщених осіб. Зроблено висновок про необхідність непрямого регулювання висвітлення засобами масової інформації тематики внутрішньо переміщених осіб із боку органів державної влади, органів місцевого самоврядування, громадських організацій та об’єднань журналістів.

On the Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree

On the Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree

Constructive Description of Hölder Classes on Some Multidimensional Compact Sets

In this paper, a constructive description of Holder classes of functions on certain compact sets in $${{\mathbb{R}}^{m}}$$ (m $$ \geqslant $$ 3) is given in terms of the rate of approximation by harmonic functions in shrinking neighborhoods of these compact sets. The compact sets under consideration are a higher-dimensional generalization of compact subsets of curves in $${{\mathbb{R}}^{3}}$$ whose arc is commensurable with chord. The neighborhood size is directly connected with the rate of approximation: it shrinks when the approximation is getting more accurate. In addition to being harmonic in the neighborhood of the compact, the approximating functions are subject to the condition that looks similar to the Holder condition, but is weaker. Namely, the difference in values at two points is estimated in terms of the size of the neighborhood, if the distance between these points is commensurate with the size of the neighborhood (and thus estimated in terms of the distance between the points).

On the relation between torsion submodule and Fitting ideals

Let [Formula: see text] be a commutative ring and let [Formula: see text] be a submodule of [Formula: see text] which consists of columns of a matrix [Formula: see text] with [Formula: see text] for all [Formula: see text], [Formula: see text], where [Formula: see text] is an index set. For every [Formula: see text], let I[Formula: see text] be the ideal generated by subdeterminants of size [Formula: see text] of the matrix [Formula: see text]. Let [Formula: see text]. In this paper, we obtain a constructive description of T([Formula: see text]) and we show that when [Formula: see text] is a local ring, [Formula: see text]/T([Formula: see text]) is free of rank [Formula: see text] if and only if I[Formula: see text] is a principal regular ideal, for some [Formula: see text]. This improves a lemma of Lipman which asserts that, if I([Formula: see text]) is the [Formula: see text]th Fitting ideal of [Formula: see text] then I([Formula: see text]) is a regular principal ideal if and only if [Formula: see text] is finitely generated free and [Formula: see text]/T([Formula: see text]) is free of rank [Formula: see text]

A Comprehensive Program of activities to develop sustainable core skills in novice scientists

This paper is aimed at studying scientific communication as an integral part of a scientists activity. The authors of this article analysed the development of informational technologies, which gave rise to a new paradigm of scientific communication Research 2.0. In the present study the analysis of research papers, describing models of scientific communication is done. The findings allow to define the structure and content of a comprehensive program of activities, connected to scientific communication in compliance with the Scientific Communication Life Cycle Model. In order to implement the program, aimed at developing core skills through scientific communication of scientists, a target audience, comprising postgraduate students and young researchers in Mathematics and Teaching Methods was engaged. A five-stage program of activities, which was developed, prompted scientific activity of young researchers and gave them an opportunity to learn about means of presenting research results, elements of management, mechanisms for applying the findings. A constructive description of each module of the program is done, actions and a strategy are described, communication between participants and tutors through the platform Higher School Mathematics Teacher is arranged in this research. In order to assess the efficiency of implementing the program, Researcher Development Framework (RDF) is used. The study also presents the results of the activity of young researchers, who were engaged in the program. Following the change in the phase of the development of researchers characteristic features and in compliance with RDF, a conclusion is made about a positive impact of the program on the development of career skills of young scientists, their interaction skills, awareness of professional behavior procedure.

Computer geometric modeling of quasi-rotation surfaces

The paper presents an analytic description of quasi-rotation correspondence. The formulas for calculation of values characterizing geometric objects are provided on the basis of constructive description of the quasi-rotation correspondence. The values characterizing circles generated through quasi-rotation of the initial point are calculated. A system of parametric equations describing a generic quasi-rotation surface is provided. Every type of curvilinear second-degree axis – circular, elliptic, parabolic, and hyperbolic – is considered. An algorithm for surface modeling through computer algebra systems has been developed on the basis of the analytic description and tested by means of Maple software. The algorithm allows one to acquire plots of separate sheets of the surface as well as all four sheets simultaneously. The capability to acquire 3D models of quasi-rotation surfaces given the desired shape and mutual location of the axis and the generatrix is demonstrated. The developed algorithm is applicable to any flat generating curve belonging to the axis plane and defined by a single-parameter system of equations. The resultant 3D model polygon count is user-defined and only limited by computer’s processing capability assuring high surface quality. The images of several four-sheet quasi-rotation surfaces are provided. The developed algorithm allows one to design surfaces of pre-defined properties.

Constructive description of Hölder classes on some multidimensional compact sets

We give a constructive description of Hölder classes of functions on certain compacts in Rm (m > 3) in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of these compacts. The considered compacts are a generalization to the higher dimensions of compacts that are subsets of a chord-arc curve in R3. The size of the neighborhood is directly related to the rate of approximation it shrinks when the approximation becomes more accurate. In addition to being harmonic in the neighborhood of the compact the approximation functions have a property that looks similar to Hölder condition. It consists in the fact that the difference in values at two points is estimated in terms of the size of the neighborhood, if the distance between these points is commensurate with the size of the neighborhood (and therefore it is estimated in terms of the distance between the points).

Reflecting Algebraically Compact Functors

A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. Functors with this property are said to be algebraically compact. This is a very strong property used in programming semantics which allows one to interpret recursive datatypes involving mixed-variance functors, such as function space. The construction of compact algebras is usually done in categories with a zero object where some form of a limit-colimit coincidence exists. In this paper we consider a more abstract approach and show how one can construct compact algebras in categories which have neither a zero object, nor a (standard) limit-colimit coincidence by reflecting the compact algebras from categories which have both. In doing so, we provide a constructive description of a large class of algebraically compact functors (satisfying a compositionality principle) and show our methods compare quite favorably to other approaches from the literature.

Solvable Lie Algebras of Vector Fields and a Lie's Conjecture

We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional analytical solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.

The use of learning dashboards to support complex in-class pedagogical scenarios in medical training: how do they influence students\u2019 cognitive engagement?

This study aims to contribute to empirical and interdisciplinary knowledge on how visual learning analytics tools can support students’ cognitive engagement in complex in-class scenarios. Taking a holistic approach, instructional design, learning analytics, and students’ perceptions were examined together. The teaching of systematic viewing and image interpretation in radiology education was used to exemplify a complex in-class scenario, and a specific learning dashboard was designed as a support tool. The design was based on both educational and visualization theories and aligned with a pedagogical scenario integrating individual and class-wide activities. The quantity and quality of the cognitive engagement of a group of 26 students were explored. A mixed method approach was used, including computer log file analyses of individual work, analysis of video recordings of in-class small group discussions, and a focus group discussion with the students involved. The in-class scenario with the learning dashboard resulted in a good balance between individual tasks and group discussions and a high degree of active cognitive engagement. Constructive and interactive forms of cognitive engagement were, however, less evident. In addition, the products of these constructive (description of findings) and interactive (type of dialogue) cognitive engagements were of mediocre quality and therefore not optimal for knowledge transfer. The study also showed that the way the students and teacher understood their respective tasks and used the available interaction techniques of the learning dashboard highly influenced the students’ cognitive engagement. Finally, several ideas emerged that could help to overcome the deficits found in the training of participants and to improve the tasks set and the learning dashboard itself.

Problems of proactive management of socio-cyberphysical systems: current state and prospects of solution

Goal. The purpose of the study is to consider existing and promising approaches to solving the prob-lems of complex modeling and proactive management of socio-cyberphysical systems (SCPS). Materials and methods. To achieve this goal, the authors of the article used the methods of modern system analysis, integrated modeling and management decisions in complex organizational and technical objects, which include SCPS. Results. The article analyzes the main aspects of the investigated problem under study related to its con-structive description, the formation of the necessary data, information and knowledge for this, their constant updating based on the use of cyberphysical systems (CPS), as well as intelligent multimodal interfaces. In addition, the article describes the problem of the proactive management of SCPS at the set-theoretical level. Scientific novelty. The article proposes a new scientific approach based on the applied theory of proactive control of the structural dynamics of SCFS developed by the authors. It consists in the fact that, on the basis of it, as shown by preliminary studies, the following possibilities work out. Firstly, to directly relate those common goals, the achievement of which the functioning of a specific SCPS at a specific stage of its life cycle, with its strategic and tactical goals. Secondly, reasonably determine and choose the appropriate sequences of tasks and performed operations (actions) related to controlled structural dynamics (controlled by self-organization of SCPS). And, thirdly, to consciously find compromise multi-criteria solutions for the allocation of limited resources of SCPS allocated to control the structural dynamics of these systems in the conditions of possible crisis, emergency and emergency situations.

Structural and constructive analysis of San Juan de Dios basilica dome, in Granada (Spain).

The St. Juan de Dios Basilica, in Granada was built between 1734 and 1757, by design of architect Jose de Bada y Navajas. It is considered one of great Spanish Baroque works. In this paper, it is presented the architectural analysis and constructive description of basilica, focused on the dome over transept, built according to the faux dome model, which was spread by Fray Lorenzo de San Nicolas. By a measurement on-site campaign, with measuring tape and laser metre, dome geometric modelling is presented for first time. It is also presented the application of different methodologies of structural analysis to timbrel domes: Rankine-Schwedler membrane analysis; analysis of stability by application of limit analysis, and seismic analysis based on the discrete element method (DEM). Application of different methodologies allows compare the obtained results. Finally, it is presents suggestions for constructive conservation measures.