Invariant Components Research Articles

Character varieties and knot symmetries

Those are notes of the mini-course given in the school Winter Braids VII, held in Caen from February 27th to March 2nd 2017. They overview the variety of representations and characters of a three-manifold in SL 2 ℂ, putting emphasis on explicit computations. The notes also discuss the canonical component of a hyperbolic knot, and a recent joint work with Luisa Paoluzzi, on the invariant components of the variety of characters for knot symmetries.

Narrative typologies of the English-American Narrative School

The article deals with the becoming and development history of the English and American researchers narrative typologies of ХХ centuries, that remain actual in modern narratology. Under "narrative typologies of ХХ century" scientists understand typology classifications of novels narration, that do possible consideration and classification of its invariant components, narrative structures and their expressions methods. Their principles were formed by the representatives of English-American scientific school (were worked out by H. James and P. Lubbock, and specified by N. Friedman, W. Booth) and got the name "The inductive typology of narration" in science. Dynamic development of narrative theories resulted in the subsequent of internal text communication and selection in her two prospects, that were declared yet by ancient philosophy: diegesis (discursive aspect of narration) and mimesis (his visual aspect, show). So, American scientific Norman Friedman continued P. Lubbocks tradition in consideration of novel narrations forms, gave attention on a "Points of view" concept, offered the carefully worked out system of its varieties. Under other visual angle the problem of Narrative forms and Narrator was examined by the American philologist W. Booth, asserting that any the narrations - it one of rhetoric forms, by means of that an author protects the "interests secret or obvious, predetermining the reaction of reader on the work". Investigating on the examples of well-known novels the category of presence / absence of teller in history, that is told and his external / internal position in relation to it, representatives of English-American scientific school formulated the detailed typology of novel narrative forms in the aspect of "point of view" and tellers "voice", that became their main achievement in narratology. This typology is fruitfully used in the modern scientific studios of narrative and its forms, spreading from linguistics and literary criticism to psycholinguistics, pragmatic, sociolinguistics, gender researches.

Содержание обучения письменной речи студентов направления подготовки «Журналистика»

The development of written speech skills of students of non-linguistic programmes should be focused on the future professional activity of graduates. We consider three approaches to foreign language teaching for professional communication: foreign language for specific purposes, integrated subject-language teaching and teaching profile disciplines in a foreign language. We conclude that integrated subject-language teaching creates the most optimal conditions to study a foreign language and profile subject content. The analysis of works on the subject content selection of teaching students of non-linguistic programmes in the framework of integrated sub-ject-language teaching allowed to distinguish the content of teaching written speech to students of “Journalism” programme, which includes invariant and variable components. The invariant part of content of written speech teaching is characteristic for most of the humanitarian programmes and includes skills development for writing personal letter, essay, structural abstract, report, and filling out questionnaire. The variable part reflecting the specifics of the journalist’s professional activities will include the development of the following skills: a) informational genres: writing chronicle of events, informational correspondence, writing notes, an information report, informational interview, coverage, necrology, blitz survey; b) analytical genres: compile analytical report, analytical survey, conduct analytical correspondence, prepare analytical interview, write material in the conversation genre, comments, reviews, articles, journalistic investigation, outlooks, material in the media review genre, forecast, analytical press release.

A Comparability Analysis of Anxiety Scale For International Students’ Classifications: Invariance Across Gender, Status, and Students’ Current Degree

This study aimed to investigate the structure of the latent factor of an anxiety symptoms scale (Pudrovska et al., 2001) and the stability of invariance across groups of international students’ classifications (gender, students’ current degree, and students’ status). In the large, non-clinical sample (619), Saudi students as international students in the USA completed the anxiety symptom scale. Confirmatory factor analysis (CFA) was used to test the factor structure of the scale, and a multiple-group confirmatory factor analysis (MGCFA) model was used to test stability of invariance across groups of students’ classifications. The findings of theCFA indicated support for the original one-factor model. Additional analyses of the MGCFA method support for the measurement (configural, metric and strong) invariant and practical invariant components of this model. There was an invariant across gender. The instrument appeared to measure the same constructs in both groups (male and female). However, there was partially invariant across groups of students’ current degree. The instrument appeared to measure the same constructs in both groups (undergraduate students and graduate students), except for Item 3. Moreover, there was partially invariant across groups of students’ status. The instrument appeared to measure the same constructs in both groups (single and married), except for Item 3 and 4.Given that this study is the first investigation for the structure of anxiety symptoms scale (Pudrovska et al., 2001), it will be important for future studies to replicate the findings.

Uncertainties in the South African wind load design formulation

This paper presents an investigation of the uncertainties inherent in the South African formulation of design wind loads on structures, as stipulated by SANS 10160-3:2011. The investigation follows from the identification of anomalous values in the existing South African probabilistic wind load models during a reliability assessment of SANS 10160. The primary wind load components which have the greatest effect on the total wind load uncertainty are identified as the time variant free-field wind pressure, followed by the time invariant pressure coefficients and terrain roughness factors. A rational and transparent reliability framework for the quantification of the uncertainties inherent in the formulation of these components is then presented. Probabilistic models of these components were developed following independent investigations of each component. The results from these investigations show that the existing probabilistic wind load models underestimate the uncertainty of the wind load components, particularly when considering the time invariant components.

ICS for multivariate outlier detection with application to quality control

In high reliability standards fields such as automotive, avionics or aerospace, the detection of anomalies is crucial. An efficient methodology for automatically detecting multivariate outliers is introduced. It takes advantage of the remarkable properties of the Invariant Coordinate Selection (ICS) method which leads to an affine invariant coordinate system in which the Euclidian distance corresponds to a Mahalanobis Distance (MD) in the original coordinates. The limitations of MD are highlighted using theoretical arguments in a context where the dimension of the data is large. Owing to the resulting dimension reduction, ICS is expected to improve the power of outlier detection rules such as MD-based criteria. The paper includes practical guidelines for using ICS in the context of a small proportion of outliers. The use of the regular covariance matrix and the so called matrix of fourth moments as the scatter pair is recommended. This choice combines the simplicity of implementation together with the possibility to derive theoretical results. The selection of relevant invariant components through parallel analysis and normality tests is addressed. A simulation study confirms the good properties of the proposal and provides a comparison with Principal Component Analysis and MD. The performance of the proposal is also evaluated on two real data sets using a user-friendly R package accompanying the paper.

Thermal Casimir and Casimir–Polder interactions in N parallel 2D Dirac materials

The Casimir and Casimir–Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir–Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due to the graphene Dirac-like energy spectrum. The spatial dispersion and temperature dependence in the optical response are also found to be important for enhancing the interactions especially at smaller separations. Analytical expressions for low and high temperature limits and their comparison with corresponding expressions for an infinitely conducting planar stack are further used to expand our understanding of Casimir and Casimir–Polder energies in Dirac materials. Our results may be useful to experimentalists as new ways to probe thermal effects at the nanoscale in such universal interactions.

EDUCATIONAL COMPETENCE: THE ESSENCE AND PEDAGOGICAL MODEL OF FORMATION IN THE CONTEXT OF LIFELONG EDUCATION

Introduction . Dynamic changes in the modern world, rapid development of innovative technologies, increasing amount of information have updated the requirement of implementation of the concept “lifelong education” which has to replace the classical “final” education that had existed over the centuries. However, full implementation in practice of a new educational paradigm is interfered by the lack of evidence-based means and ways of support for gradual development of the personality potential upon transition from one education level to another. The aim of this article is to present the essence and structure of educational competence as an invariant of lifelong education which enables to provide continuity between the process of knowledge and improvement of practical skills at all its stages. Methodology and research methods . The methodological framework of the research involves the theory of contextual education, and competency-based approach that establishes the conceptual principle for pedagogical models at different levels of the educational system. As the main research methods were used: analysis, synthesis, generalization; modeling and designing pedagogical objects. Results and scientific novelty . The invariant structure of the theoretical construct “educational competence” is described and proved; this structure is considered as a basic unit of lifelong education and, under the unitary approach, provides consistent personal, cultural and professional development of a student at school, higher education institution and centers for additional education. Cognitive, social and reflexive components of educational competence integrated in the continuous educational process serve as an efficient tool for successful competence development required by Federal State Educational Standards. The application of these invariant components, as a whole, enables the individual to “switch” from academic activity to practice-focused, educational-professional preparation and professional activity. The competencecontext model of learning and education was designed in order to master the technique of educational competence application by students in general schools as one of the stages of the lifelong learning system. Practical significance . The presented materials can be used by researchers engaged in the development and realization of lifelong education technologies as well as education administrators and teachers interested in quality and efficiency improvement of their professional activity.

A clonotype-independent pre-TCR complex and its downstream signals can support transformation of thymic T cells.

Abstract The kinase ataxia telangiectasia mutated (ATM) communicates between molecules that sense DNA damage in the form of double stranded breaks (DSB) and effector mechanisms that maintain genomic integrity. Persistent DSBs can lead to transformation and ATM-deficiency is associated with increased lymphoid malignancies in both humans and mice. ATM-deficient mice exclusively develop thymic T cell lymphomas with high penetrance. We explored the requirement for specific components of the TCR and its signaling pathway for the induction of these thymic lymphomas. We generated multiple strains of ATM-deficient mice in which mature T cell are absent by deletion of CD3ɛ, an invariant component of the pre-TCR complex; by deletion of RAG or TCRβ, in which recombining TCR variable components are deleted; or by deletion of LAT, an important component of pre-TCR and TCR signaling. These strains all showed a similar and severe developmental arrest at thymic DN3. Despite this arrest, mice deficient in RAG or TCRβ, exclusively developed thymic T cell lymphomas. In contrast, mice deficient in CD3ɛ or LAT, developed no or few T cell tumors, respectively, but developed B cell lymphomas. These findings suggest the importance of a clonotype-independent TCR complex and its downstream signals in transformation of T cells. Experiments are in progress to ask if survival of ATMKO T cell lymphomas after transformation is similarly dependent on CD3ɛ and LAT signaling.

РОЛЬ ПЕДАГОГІЧНОГО СИСТЕМНОГО ПІДХОДУ В ОФОРМЛЕННІ ПОНЯТТЯ “МЕТОДИЧНА СИСТЕМА НАВЧАННЯ МОВИ”

The article presents the analysis of scientific researches on the problem of pedagogical system approach as the basis for the development of systemic phenomena. Pedagogical system approach is considered from the standpoint of modern scientific tendencies. Methodical system of language teaching is considered as a kind of pedagogical systems. The role of the general scientific systemic principle of isomorphism in the possibility of identifying the invariant component of the methodical system of language learning is established. Key words: pedagogicalsystemapproach, pedagogicalsystem, didacticsystem, methodicalsystemoflanguageteaching.

The Implicit Commitment of Arithmetical Theories and Its Semantic Core

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear (proof-theoretic) reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories.

The magnetic nature of umbra–penumbra boundary in sunspots

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aim. Here, we aim at studying the magnetic nature of umbra–penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Methods. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra–penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. Results. We statistically prove that the umbra–penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849–1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. Conclusions. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra–penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.

Integrative-modular technology of general chemistry teaching

The paper deals with integrative and modular technology of teaching General Chemistry to medical students that was developed and implemented at Chemistry Department of Siberian State Medical University. To design educational programs, the paradigm of training was exchanged to the paradigm of productive exercises with greater independence of students who become designers of their own knowledge, professional and universal competences. The content block of this discipline consists of two components: invariant and variant. Invariant component includes elective course on the chemistry of biologically active compounds. The paper describes the use of combination of academic and innovative methods and technologies of training. An approximate algorithm is offered for the course module, which focuses on the adsorption equilibrium and processes. It includes theoretical training, provided by textbooks, lecture text and teaching aids. Students assess the quality of academic work on their own with the help of tests and in the implementation of practical tasks in laboratory studies.

Inherently Stable Weighted Least-Squares Estimation of Common Acoustical Poles With the Application in Feedback Path Modeling Utilizing a Kautz Filter

In adaptive feedback cancellation, the feedback path must be modeled precisely using as few adaptive parameters as possible to reduce computational complexity and enable rapid convergence. To reduce the number of adaptive parameters, the feedback path is usually modeled with a transfer function composed of an invariant component and a variable component using all-pole, all-zero, and pole-zero filters. These filters may be inefficient, requiring a large number of parameters for their specification, particularly in reverberant environments. In this letter, we present a weighted least-squares algorithm to precisely estimate the common poles of feedback paths, and we then model the invariant basis functions employing a Kautz filter. The Kautz filter is defined by a set of the fixed poles and a corresponding set of tap output weights. The fixed poles are associated with prominent peaks that are common to the measured feedback path frequency responses. The algorithm guarantees unconditionally the stability of the estimated poles of the inferred model. The experimental results using measured acoustic feedback paths from a two-microphone, behind-the-ear hearing aid show that the proposed method provides an accurate model of the feedback paths for a variety of acoustic environments that were not employed in estimating the common poles.

Developing a useful and integrative STEM disciplinary language

STEM disciplinary language is a necessary component for STEM success. It can be developed through experiences and attention to the development of STEM activities that are rich in language and can be acquired through practical experiences and systematic practice. Secondary students participated in an informal STEM summer camp where they learned to use Google Sketchup ® and a 3-D printer to design their own objects. They interacted with peers and collaborated on issues as they arose, to solve problems. They took the Aural/Spatial Interactions and Invariant Components of Vocabulary for STEM instrument pre and posttest, and the results were analyzed qualitatively. Students progressed through styles of communication that were precipitated by terminological inexactitude, cognitive negotiation and then analogous/metaphoric, clarifying, and technical discourses to build mutual understanding and success.

Dynamics of transcendental H\xe9non maps

The dynamics of transcendental functions in the complex plane has received a significant amount of attention. In particular much is known about the description of Fatou components. Besides the types of periodic Fatou components that can occur for polynomials, there also exist so-called Baker domains, periodic components where all orbits converge to infinity, as well as wandering domains. In trying to find analogues of these one dimensional results, it is not clear which higher dimensional transcendental maps to consider. In this paper we find inspiration from the extensive work on the dynamics of complex Hénon maps. We introduce the family of transcendental Hénon maps, and study their dynamics, emphasizing the description of Fatou components. We prove that the classification of the recurrent invariant Fatou components is similar to that of polynomial Hénon maps, and we give examples of Baker domains and wandering domains.

Life prospects of the unemployed: invariant and variable components in the prism of the last decade (2009-2018)

The article discusses the results of a comparison of the content and structure of life prospects of the unemployed men and women surveyed in 2009 and 2018. The study showed the specificity of the relationship of the socio-cultural context of a person’s life and his/her life prospects. The invariant and variable components of the life prospects of the unemployed are revealed. Over the past ten years, a pessimistic and contradictory view of the future, a temporary orientation to a negative past and a fatalistic present, a weak eventful and targeted saturation of the future, lack of long-term planning, the existence of a conflict of time settings are invariant, which, in many respects, is a reflection of the difficulty of experiencing the absence of work. Along with the stable characteristics, transformations of the content of life planning in a situation of lack of work are revealed. The assessment of the life prospects of the unemployed, who tend to see the future as swift and useful, turned out to be varied.

Anisotropic Continuum Stored Energy Functional Solved by Lie Group and Differential Geometry

An anisotropic continuum stored energy (CSE), which is essentially composed of invariant component groups (ICGs), is postulated to be balanced with its stress work done, constructing a partial differential equation (PDE). The anisotropic CSE PDE is generally solved by the Lie group and the ICGs through curvatures of elasticity tensor are particularly grouped by differential geometry, representing three general deformations: preferred translational deformations, preferred rotational deformations, and preferred powers of ellipsoidal deformations. The anisotropic CSE constitutive models have been curve-fitted for uniaxial tension tests of rabbit abdominal skins and porcine liver tissues, and biaxial tension and triaxial shear tests of human ventricular myocardial tissues. With the newly defined second invariant component, the anisotropic CSE constitutive models capture the transverse effects in uniaxial tension deformations and the shear coupling effects in triaxial shear deformations.

Distance training of geography teachers in the context of educational reform

In the system of continuous geographical education, upgrading teachers’ professional skills plays an important role. Acquaintance with modern tendencies of educational technology and constant normative-legislative and methodical changes form a permanent basis for training and self-improvement of teachers. Since 2016 V.N. Karazin Kharkiv National University, in addition to specialists training, has been offering teachers’ qualifications improvement in the form of part-time classes, at the courses for teachers of general educational establishments of different types and forms of ownership in Kharkiv region in the study field «Geography. Geography of Ukraine». The purpose of the article is to analyze the organization of distance learning of geography teachers within the framework of teacher training courses. The main material. The program of training courses for geography teachers involves consideration of educational problems, features of teaching geography on various programs and courses, specialized training, courses for gifted children. High efficiency of the training is assured by the implementation of both invariant and variant components. The thematic plan is designed for 210 hours (7 credits). According to the curriculum, distance learning relates to the professional unit. During the on-site classes, teachers obtain basic knowledge, which is furthered with the distance course «Geography for Teachers», designed for 120 academic hours. The course «Geography for Teachers» is based on the Moodle platform designed to support distance learning. It contains such structural elements as glossary, tasks, resources, tests, a forum, a chat and consists of 12 information packs. Digital online classes take place within 4 weeks, which includes independent online study. This stage for teachers finishes with preparing and presenting the paper (implementation of the practical task) and taking the test. During this period, course participants can get a personal tutorial in the chat or the forum. It is important to maintain feedback from teachers because they work during the learning process due to the lack of time. Each of them has the opportunity to work with the distance course and get a tutorial in their free time. The distance course «Geography for Teachers» has been repeatedly tested by groups of teachers who were upgrading their qualification and has been improved with every comment or suggestion. The course has got the certificate of recognition as an educational and methodical work. Conclusions. To sum up, the usage of the distance course «Geography for Teachers» as a form of continuous geographical education certainly has a number of benefits: mobility, modernity of information, accessibility and informality. This improves the perception and work of geography teachers in self-education and upgrading their professional competencies. It also provides the opportunity to use new, up-to-date information in the form of lectures, presentations, manuals, statistical yearbooks and other information resources that are necessary for a teacher in his or her work.

Iteration of the Translated Tangent

The iteration of the map $$z \mapsto \lambda + \tan z$$ on the complex plane is investigated for each complex number $$\lambda $$ . It is shown that its Fatou set always contains a completely invariant component and the Julia set is either totally disconnected or connected. A necessary and sufficient condition for totally disconnected Julia set is proved. When the Julia set is connected, it is seen that the Fatou set can consist of additional components, which can be completely invariant attracting domain, a Siegel disk, a two periodic attracting domain or parabolic domain. Examples of each case are given. Further, a necessary and sufficient condition is provided for the Julia set to be a Jordan curve passing through infinity. It is proved that the set of parameters corresponding to Jordan curve Julia sets is connected, whereas the set of those corresponding to totally disconnected Julia sets is disconnected.