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For a pair of smooth transversally intersecting submanifolds in some enveloping smooth manifold, we study the algebra generated by pseudodifferential operators and (co)boundary operators corresponding to submanifolds. We establish that such an algebra has 18 types of generating elements. For operators from this algebra, we define the concept of symbol and obtain the composition formula.

Since the development of higher local class field theory, several explicit reciprocity laws have been constructed. In particular, there are formulas describing the higher-dimensional Hilbert symbol given, among others, by M. Kurihara, A. Zinoviev and S. Vostokov. K. Kato also has explicit formulas for the higher-dimensional Kummer pairing associated to certain (one-dimensional) $p$-divisible groups. In this paper we construct an explicit reciprocity law describing the Kummer pairing associated to any (one-dimensional) formal group. The formulas are a generalization to higher-dimensional local fields of Kolyvagin's reciprocity laws. The formulas obtained describe the values of the pairing in terms of multidimensional $p$-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups. In the second part of this paper, we will apply the results obtained here to give explicit formulas for the generalized Hilbert symbol and the Kummer pairing associated to a Lubin-Tate formal group. The results obtained in the second paper constitute a generalization to higher local fields, of the formulas of Artin-Hasse, K. Iwasawa and A. Wiles., The stronger reciprocity laws in this new version cover arbitrary higher local fields, as opposed to only standard higher local fields

Many studies showed that teachers and prospective teachers have difficulty solving percentage problems. This research is a qualitative descriptive study that aims to investigate the prospective teachers’ strategies in solving problems on the topic of percentages. A total of 250 students majoring in Mathematics Education and Primary Education at IAIN Syekh Nurjati and IAIN Pekalongan were purposively selected to participate in this study. The results showed that only less than half of the participants (40.1%) could give the correct answer. Qualitative data on the strategies used by prospective teachers on the percent question show that (1) teacher candidates ignore the importance of the % symbol and consider the % symbol only as a unit of measurement, (2) teacher candidates ignore the essential role of the reference quantity in the percent question, (3 ) teacher candidates are not used to solving percent problems related to determining initial values before discounts and assume that any percent problem can be solved using multiplication or division.

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].

The purpose of this study was to investigate primary school students’ estimations of number magnitudes on number lines in relation to their mathematics achievement, calculation performance, and place value understanding. The data were collected by mathematics achievement test (MAT), arithmetic performance test (APT), place value test (PVT) and computerized number line estimation tests (NLE). Computerized tests were developed by the researchers and consist of symbolic, verbal and visual (canonical and random dots) codes within 0-10 and 0-100 range designed according to the triple coding model. The study group consisted of 214 second and third grade students drawn from a city in the Central Anatolia Region. Results showed that the estimation skills of third grade students in all tests on the number lines are more linear than that of the second-grade students. The success of students in the lower and upper achievement groups determined according to the mathematics achievement test at each grade level differs in terms of APT, PVT, NLE 0-10 and 0-100. It was observed that this differentiation was more pronounced in terms of APT and PVT tests. The higher the grade level, the wider the difference in achievements between the lower and upper groups. The Verbal 0-10 and Canonical 0-10 tests, which were designed according to the triple code model, predict mathematics achievement more than other tests within 0-10 range. While Symbol 0-10 test predicts the comprehension of place value most, Canonical Dot Enumeration test is the most predictor of arithmetic performance. Looking at the tests in the range of 0-100, Symbol 0-100 predicts mathematics achievement the most, while Symbol 0-100 and Random Dot Enumeration test predict place value comprehension. Based on these results, it can be concluded that using different forms of numerical representations will be more beneficial for children's thorough understanding of mathematics.

In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.

PurposeWhen the augmentative and alternative communication (ACC) model (Lloyd et al., 1990) was proposed, these components of symbols were not considered, nor were they contemplated when superordinate (Lloyd and Fuller, 1986) and subordinate levels (Fuller et al., 1992) of AAC symbol taxonomy were developed. The purpose of this paper is to revisit the ACC model and propose a new symbol classification system called multidimensional quaternary symbol continuum (MQSC)Design/methodology/approachThe field of AAC is evolving at a rapid rate in terms of its clinical, social, research and theoretical underpinnings. Advances in assessment and intervention methods, technology and social issues are all responsible to some degree for the significant changes that have occurred in the field of AAC over the last 30 years. For example, the number of aided symbol collections has increased almost exponentially over the past couple of decades. The proliferation of such a large variety of symbol collections represents a wide range of design attributes, physical attributes and linguistic characteristics for aided symbols and design attributes and linguistic characteristics for unaided symbols.FindingsTherefore, it may be time to revisit the AAC model and more specifically, one of its transmission processes referred to as the means to represent.Originality/valueThe focus of this theoretical paper then, is on the current classification of symbols, issues with respect to the current classification of symbols in terms of ambiguity of terminology and the evolution of symbols, and a proposal for a new means of classifying the means to represent.Peer reviewThe peer review history for this article is available at: https://publons.com/publon10.1108/JET-04-2021-0024

By using a Wick symbol transform, a characterization theorem is proven for the white noise operators in terms of a new spaces of (p, q)-entire functions with certain growth rates determined by Young functions and a suitable (p, q)-exponential map. Next, we investigate the main aim of this paper which is to give unitary equivalent representations of the (p, q)-square oscillator white noise algebra in the basis of noncommutative white noise theory.

In the article, the semantic structure of language units representing the hierarchy of a character is analyzed in detail using data from the scientific literature. Besides, this work clarify the issue of the structure of the meanings of lexical-semantic means (lexical-semantic indicators of graduality) representing gradation as well. KEY WORDS: lexical layer, character, hierarchy, language units, semantic structure.

Wittgenstein’s “machines-as-symbols” are considered with respect to their historical sources and their symbolic and logical nature. Among these sources and precursors, along with Leonardo’s drawings of machines, there are illustrated “machine books” (theatra machinarum), a kind of book published in the period from the 16th to the 18th centuries which consist of pictures and descriptions of a variety of mechanical devices. Most probably, these books were one of Wittgenstein’s inspirations for his view of machines as components of language-games (not just for his earlier philosophy of depicting symbols in TLP). The picture of homo volans in Vrančić’s (Verantius) machine book (1615/16) possessed by Wittgenstein is taken as an example. In particular, homo volans is shown to contain patterns of logical laws and rules and to be abstractly interpretable as a logical symbol. A machine (or its picture), taken as a symbol, is shown (a) to be a precondition of a meaningful “overview” of a mechanical work (including logical formalisms) that exceeds the limits of decidability ; (b) to possess causal features if causality is understood teleologically and in a deeper sense of a “binding” life.

SUMMARY Prior research shows that ghost ticking, or documenting audit work not actually performed, is a persistent threat to audit quality. We examine whether requiring self-references in audit workpapers (i.e., “I” performed the test) can effectively curtail ghost ticking, compared to other workpaper language that can be used in practice. We also design and test an alternative to tick marks (symbol-based notation commonly used in workpapers to describe the results of audit procedures), in which auditors select the same description of the procedure performed, but from a prepopulated drop-down list. Consistent with our hypotheses, we find that using both self-references and descriptions (as opposed to tick marks) jointly reduces ghost ticking, compared to when only one (or neither) of these are used. Overall, we demonstrate how two simple and easily implementable changes to language and tick marks can significantly curtail ghost ticking and therefore reduce its threat to audit quality. JEL Classifications: M40; M42.

The Tamil word is basic ally from the grammar of the Tamil word. The grammar system that divides world life into 'Thinai' is a very important system in Tamil. Language changes are taking place in a scientifically functioning society. The cultivation and productivity of the foundation of society have an impact on the superstructure of the society, the art, literature and culture. The religious god thought is in the life classification of the Tamil grammar which is the basis for the creation of words. The tholkappiyam period of the resurrection of the collective life is a symbol of the non-religious protodravidian ism and directly links the doctrine of God to the people. The authors of the well developed landslide society, who wrote to tholkappiyam, have also incorporated the theory of God, based on the various religious and social contexts. The Veera Choliam with buddhist background and Neminatha with Jainism link the god sandals in the higher dina. The nannul also inscribes the sanskrit influence of the deity and the naraka of the sanskrit influence, and the sanskrit influential theory of the proto Dravidian grammar of the grammar, the devar and the narakar a number of religious theories.

In this paper, we define the localization operator associated with the Riemann–Liouville operator, and show that it is not only bounded, but it is also in the Schatten–von Neumann class. We also give a trace formula when the symbol function is nonnegative.

We introduce new tools for analytic microlocal analysis on Kahler manifolds. As an application, we prove that the space of Berezin–Toeplitz operators with analytic contravariant symbol is an algebra. We also give a short proof of the Bergman kernel asymptotics up to an exponentially small error.

Data from plurilingual Belize shows that not everyone recognizes stability as an essential feature of aspoken language. Belizeans consider the use of Kriol as a symbol of belonging but foreground its readiness for variation across communities in space and time. Their use of liquid languages is a different form of cultural construction than the one our textbooks show. It questions a good part of linguistics and reveals its possibly Eurocentric point of view. Data from plurilingual Belize shows that not everyone recognizes stability as an essential feature of aspoken language. Belizeans consider the use of Kriol as a symbol of belonging but foreground its readiness for variation across communities in space and time. Their use of liquid languages is a different form of cultural construction than the one our textbooks show. It questions a good part of linguistics and reveals its possibly Eurocentric point of view.

Starting from a complete family for the unit sphere S n in the complex n-space C n (whose elements are coherent states attached to the Barut–Girardello space), we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation of the asymptotic behaviour of functions in the complete family. Furthermore, in an analogous manner (slightly weaker) we obtain the asymptotic expansion of the covariant symbol of a pseudo-differential operator on L 2 ( S n ).

Let Λ be a 𝑛-dimensional lattice, and 𝑐1, . . . , 𝑐𝑛−1 be any 𝑛 − 1 vectors in 𝑛-dimensional real Euclidean space. We show that there exists a basis 𝛼1, . . . ,𝛼𝑛 of Λ such that $$|𝛼𝑖 − 𝑁𝑐𝑖| = 𝑂(log^2 𝑁), (1 2, where the constant implied by the 𝑂 symbol depends only on Λ and 𝑐1, . . . , 𝑐𝑛−1.

We study the Galois symbol map associated to the multiplicative group and an abelian variety which has good ordinary reduction over a $p$-adic field. As a byproduct, one can calculate the "class group" in the view of the class field theory for curves over a $p$-adic field.

The main purpose of this article is using the elementary methods and the properties of the character sums of the polynomials to study the calculating problem of one kind sixth power mean of the two-term exponential sums weighted by Legendre's symbol modulo $ p $, an odd prime, and give an interesting calculating formula for it.

Mathematics is a symbol of rationality and the highest intellectual achievements of human civilization. Mathematics has always been seen as abstract and formal knowledge. However, in the last few decades, the idea has emerged that mathematics is a knowledge that develops in human cultural activities. The concept of mathematics in culture is widely known as ethnomathematics. This paper aims to briefly describe the history, criticism, and challenges of ethnomathematics, the thoughts of ethnomathematics experts, and their influence in learning mathematics today. The development of ethnomathematics gave rise to a field of study covering aspects of anthropology and the history of mathematics, non-formal mathematics practice, traditional mathematics, and multicultural learning. Various research results indicate that ethnomathematics contributes to improving school mathematics. Although culture has an important role in learning mathematics, to integrate it requires comprehensive efforts to overcome various obstacles. Teachers need to improve competencies related to understanding local culture to maximize the transformation of ethnomathematics learning in the classroom.

This article is based on the study, which tries to unpack strategies of reduction of abstraction in learning abstract algebra from learners’ perspective. Ethnography was used to collect the required information. The study found the strategies of reduction of abstraction in abstract algebra are: making sense and meaning through previous experiences and existing knowledge an analogical creation of mental image, using first person language in course of doing mathematics by students as teachers do in the classroom for logical arguments, focusing on “symbol” or some mathematical entity to manage abstraction for their idiosyncratic understandings of abstract mathematical structure rather than the reflective thinking, using students own idiosyncratic figures to reduce the degrees of complexity of mathematical concepts. This study can lead teachers of abstract algebra to a new awareness of their teaching strategies and their practices.

This article contains a survey of a new algebro-geometric approach for working with iterated algebraic loop groups associated with iterated Laurent series over arbitrary commutative rings and its applications to the study of the higher-dimensional Contou-Carrère symbol. In addition to the survey, the article also contains new results related to this symbol. The higher-dimensional Contou-Carrère symbol arises naturally when one considers deformation of a flag of algebraic subvarieties of an algebraic variety. The non-triviality of the problem is due to the fact that, in the case 1$?> , for the group of invertible elements of the algebra of -iterated Laurent series over a ring, no representation is known in the form of an ind-flat scheme over this ring. Therefore, essentially new algebro-geometric constructions, notions, and methods are required. As an application of the new methods used, a description of continuous homomorphisms between algebras of iterated Laurent series over a ring is given, and an invertibility criterion for such endomorphisms is found. It is shown that the higher- dimensional Contou-Carrère symbol, restricted to algebras over the field of rational numbers, is given by a natural explicit formula, and this symbol extends uniquely to all rings. An explicit formula is also given for the higher-dimensional Contou-Carrère symbol in the case of all rings. The connection with higher-dimensional class field theory is described. As a new result, it is shown that the higher-dimensional Contou-Carrère symbol has a universal property. Namely, if one fixes a torsion-free ring and considers a flat group scheme over this ring such that any two points of the scheme are contained in an affine open subset, then after restricting to algebras over the fixed ring, all morphisms from the -iterated algebraic loop group of the Milnor -group of degree to the above group scheme factor through the higher-dimensional Contou-Carrère symbol. Bibliography: 67 titles.

Many children with autism spectrum disorder (ASD) demonstrate poor comprehension of language at the sentence level in both the spoken modality and the graphic symbol modality. This study explored whether children with ASD are able to follow directives when presented with a graphic symbol sentence that includes an animated symbol for a verb. A total of five participants with moderate-to-severe ASD were presented with 10 graphic symbol sentences and asked to perform the directive using the provided figurines/objects. Results demonstrated that children with ASD can correctly carry out full-sentence directives to varying degrees when the directives represented graphically include an animated verb. Several observations were noted pertaining to participants’ performance and autism severity. The results of this study may have important implications for using animation as a tool to facilitate symbol syntax comprehension.

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of $$T \times W$$ T × W models, and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

In local class field theory, the Schmid-Witt symbol encodes interesting data about the ramification theory of $p$-extensi-ons of $K$ and can, for example, be used to compute the higher ramification groups of such extensions. In 1936, Schmid discovered an explicit formula for the Schmid-Witt symbol of Artin-Schreier extensions of local fields. Later, his formula was generalized to Artin-Schreier-Witt extensions, but still over a local field. In this paper we generalize Schmid's formula to compute the Artin-Schreier-Witt-Parshin symbol for Artin-Schreier-Witt extensions of two-dimensional local fields of positive characteristic.

The main purpose of this article is using the properties of the Legendre's symbol and the classical Gauss sums to study the calculating problem of the fourth power mean of a certain two-term exponential sums, and give an interesting calculating formula for it.

Aided communicators often have an opportunity to express themselves with speech-generating devices (SGDs) that produce symbol by symbol (SBS) and/or pre-stored (PS) utterances. Studies on the usage of PS utterances report that these utterances affect conversations positively, but it appears that aided communicators and professionals may have divergent views on their benefits. The aim of this study is to analyse how school-aged aided communicators, their mothers, peers, and speech and language therapists (SLTs) co-construct the social actions of PS utterances during their everyday interactions. The theoretical framework of this study is conversation analysis. This approach to analysing the data enhances our understanding of the linguistic and temporal resources of PS utterances and how they are used to reinforce various rich social actions that promote the progress of aided conversations to resemble natural spoken conversations. The results of this study will help SLTs and teachers in their planning content for SGDs as well as in teaching, and guiding aided communicators and their partners to utilize PS utterances in combination with SBS utterances during their conversations.

The unwinding that Cook (J. Symbol. Log. 69(3), 767–774 2004) proposed is a simple but powerful method of generating new paradoxes from known ones. This paper extends Cook’s unwinding to a larger class of paradoxes and studies further the basic properties of the unwinding. The unwinding we study is a procedure, by which when inputting a Boolean modal net together with a definable digraph, we get a set of sentences in which we have a ‘counterpart’ for each sentence of the Boolean modal net and each point of the digraph. What is more, whenever a sentence of the Boolean modal net says another sentence is necessary, then the counterpart of the first sentence at a point correspondingly says the counterparts of the second one at all accessible points of that point are all true. The output of the procedure is called ‘the unwinding of a Boolean modal net on a definable digraph’. We prove that the unwinding procedure preserves paradoxicality: a Boolean modal net is paradoxical on a definable digraph, iff the unwinding of it on this digraph is also paradoxical. Besides, the dependence digraph for the unwinding of a Boolean modal net on a definable digraph is proved to be isomorphic to the unwinding of the dependence digraph for the Boolean modal net on the previous definable digraph. So the unwinding of a Boolean modal net on a digraph is self-referential, iff the Boolean modal net is self-referential and the digraph is cyclic. Thus, on the one hand, the unwinding of any Boolean modal net on an acyclic digraph is non-self-referential. In particular, the unwinding of any Boolean modal net on $\langle {\mathbb N}

As a symbol of identity, pride, and support the development of Bahasa Indonesian, the study of the local language is required. One of them is Mandailing language, a local language with the majority of speakers in the area of Mandailing Natal Regency, Indonesia. This research deals with (1) what is the homonymy form in Mandailing language? (2) how is homonymy relation in Mandailing language. The objectives of this research are: (1) to explain homonymy forms in Mandailing language; (2) to describe homonymy relations in the Mandailing language. The research method used is descriptive qualitative. The data is oral data through key informants. Based on the analysis and discussion of data, it is known that (1) homonymy form in Mandailing language includes single form (free morpheme) and complex form (complex morpheme), (2) homonymy relations in Mandailing language include relations in two meanings and relations in three meanings.

The goal of this study was to develop an excretion system module in Biology subjects to stimulate the understanding of the concepts of high school students. The research method refers to the steps of research and Development. The research begins by analyzing the need of the excretory system material to be used as a learning resource for students. The trial module was limited to 20 high school students in Kepahiang District who had received excretion system material. The result showed that the ability to understand the concepts of students varied greatly, the ability to understand the concepts of students was mostly in the good category (35%), and sufficient (65%). The ability of students in aspect of understanding an idea, translating relationship that exist in a symbol, illustration, map, diagram, table, graph, has been well developed (translation). The ability to develop and obtain information that is not explicitly listed from the referenced source has been well developed (interpretation), and the ability to predict or give an idea of something based on trends that apper in the data that has not been well developed (extrapolation). In summary, the excretory system learning module is capable of stimulating the ability to understand the concept of students in terms of classical values.

It is observed that in the wake of developments in digital technologies, the role of shareholders in the learning-teaching process changed and a transition from the classical face-to-face communication into online learning communication occurred. This transition also led to a change the knowledge and behaviours expected from indivudals. In this context, they are expected to acquire several skills considered as the skills of the 21 st century, among which are critical and analytical thinking. Recent studies suggest that programming teaching is influential on these skills. However, programming teaching refers to a process which is structuraly difficult and complex. Thus, we need novel methods and techniques regarding programming teaching. Considering that particulalrly online learning environments have begun to be a crucial part of the learning-teaching process recently, it is believed that assisting onlne learning environments with learning videos in which audiovisual symbol systems are used together may play a crucial role in developing the programming skill that is abstract and unclear intuitively. From this point of view, this study aims to propose a framework related to desgning video-assisted online learning environments for programming teaching. To achieve this goal, the design-based research has been conducted. The research has been conducted through the participation of 48 (F: 27, M: 21) registered undergraduate students and of 4 instructors (F: 1, M: 3) of the Department of Computer Education and Instructional Technology based in the Faculty of Education at a state university located in the east of Turkey. Observation forms, reflective student diaries, the focus group interview, interview, and graded scoring key were used as data collection tools. As a result of the research, a framework has been proposed in the context of "content", "visual design", "interaction" and "practicability" related to the design of video-assisted online learning environments for "cognitive", "affective", "methodological" and "environmental" problems. Suggestions were presented within the framework of the results obtained from the study and the experiences of the researcher.

There has been debate between those who maintain that indexical expressions are not essential and those who maintain that such indexicals cannot be dispensed with without an important loss of content. This version of the essentialist view holds that thoughts must also have indexical elements. Indexical thoughts appear to be in tension with the computational theory of mind (CTM). In this case we have the following inconsistent triad:\ud \ud (i) De se thoughts are essential.\ud (ii) De se thoughts are indexical, they have a (Kaplanian) character.\ud (iii) Computations can only take the syntactic type into account, they cannot take tokens into account.\ud If (iii) is correct, then it seems we cannot make sense of a thought which uses a character such that its referent could vary from tokening to tokening. I argue that (iii) need not cause a problem, while maintaining the CTM. I claim that computations need not be sensitive to the features of a tokened symbol in the way that character demands. This job may be performed by a non‐modular part of the mind. Resolving the triad in this way provides a reason to accept that indexicals in thought are possible.

Purpose: To investigate the effects of symbol format and verb argument structure on the naming, identification, and sentence generation in people with aphasia (PWA).Methods: A 2 × 2 randomized, mix...

This essay locates the moment at which commonplace marks were ‘translated’ from printed classical texts into English vernacular drama in a manuscript of Gascoigne and Kinwelmersh's Jocasta, dated 1568. Based on a survey of the use of printed commonplace marks in classical drama between 1500 and 1568, it demonstrates that this typographical symbol was strongly associated with Greek tragedy, particularly Sophocles and Euripides, and hardly at all with Seneca. In light of this, it argues that the commonplace marks in the Jocasta manuscript should be read as a deliberate visual gesture towards Euripides. In this period, commonplace marks evoked printed Greek rather than Latin tragedy, and early modern readers might bring such associations to the English dramatic texts in which these marks also appeared, including the First Quarto of Hamlet (1603).

The main purpose of this paper is using the analytic methods and the properties of the Legendre's symbol and quadratic residue mod p to study the computational problem of the fourth power mean of a sum analogous to Kloosterman sum, and give a sharp asymptotic formula for it.

Background. In modem linguistics, the questions of the linguistic portrait of the person, the establishment of its structural and functional components are actualized. The study of eminent linguistic persons is very important, and George Y. Shevelov is one of them - as an eminent linguist, historian of literature, and critic. The scientific task to establish the linguistic corpus structure of George Y. Shevelov’s discursive practices is highly motivated.Purpose. The purpose of die article is to establish and implement an experimental and research model of text corpus of George Shevelov’s linguistic person with the determination of the main corpus components, patterns of free linguistic text navigation.Methods. The method of discursive analysis, body content analysis are used.Results. Text corpus contains all the Ukrainian-language published texts by George Y. Shevelov, it was created on the free NoSketch Engine corpus manager and is available on the server of the Department of General and Applied Linguistics and Slavic Philology in Vasyl’ Stus Donetsk National University at corpora.donnu.edu.ua. The quantitative parameters of the created corpus are as follows: 104 documents contain 1 346 424 tokens, and 1 037 949 are words in 66 039 sentences. The total lexicon includes 138 187 different word forms and punctuation marks, 157 original tags, and 32 172 lemmas. Conclusions and Prospects. The created corpus of George Y. Shevelov is research type, full-text and dynamic, has extralinguistic and linguistic markings. Among the important features: a) building a concordance based on simple search, search in lemmas, search for a phrase, wordfonn, symbol or a certain pattern created using die regular expression; b) frequency analysis for word forms, lemmas, and tags. The prospect of the research is the creation of a comprehensive George Y. Shevelov' s Texts Corpus, which will cover documents in Ukrainian and English and will be a reliable basis for studying the features of the outstanding scientist’s speech.Article received 26.07.2019

Faster emergence and introduction of the new technologies in the modern world requires changes in the field of engineering education. Large volumes of knowledge must be transferred in a shorter time. In this paper, an alternative view on structuring the process of studying electrical devices is presented, using electrical machines and frequency converters as the examples. It is proposed to use the set of logical blocks, graphically described by a pentagram — a well-known symbol and a geometric figure — for the organization and transfer of the knowledge. It is assumed that this method of knowledge transfer will be more efficient in terms of the time required. A pentagram is a set of related logical, locks that describes a set of physical processes, effects, their connections with each other and, probably, even the philosophy of building the electrical devices.

Universal graphic automaton Atm(G, G′ ) is the universally attracting object in the category of automata, for which the set of states is equipped with the structure of a graph G and the set of output symbols is equipped with the structure of a graph G′ preserved by transition and output functions of the automata. The input symbol semigroup of the automaton is S(G, G′ ) = End G×Hom(G, G′ ). It can be considered as a derivative algebraic system of the mathematical object Atm(G, G′ ) which contains useful information about the initial automaton. It is common knowledge that properties of the semigroup are interconnected with properties of the algebraic structure of the automaton. Hence, we can study universal graphic automata by researching their input symbol semigroups. For these semigroups it is interesting to study the problem of definability of universal graphic automata by their input symbol semigroups — under which conditions are the input symbol semigroups of universal graphic automata isomorphic. This is the subject we investigate in the present paper. The main result of our study states that the input symbol semigroups of universal graphic automata over reflexive graphs determine the initial automata up to isomorphism and duality of graphs if the state graphs of the automata contain an edge that does not belong to any cycle.

This chapter considers why individual language users and researchers may find it difficult to identify patterns. A pattern is essentially repetition. A symbol may occur once only: but when it occurs twice or more it becomes a minimal pattern. The identification of pattern in a corpus implies a connection between theory, method and technique. To summarise: observing pattern in concordance lines essentially involves grouping those lines together. Expanding the concordance lines allows ambiguities to be resolved. In short, obtaining a manageable sample of concordance lines for a very frequent word can make it difficult to observe patterns reliably. The dominant pattern is indeed an anticipatory it and an evaluative adjective. For example, expanding the lines where view is followed by that shows that there are two distinct patterns – view + appositive clause and view + relative clause: The chapter has made some assumptions about the notion of 'frequency'; some of these will be made explicit.

The article presents the material and the results of the study of a political cartoon in the Arabic and French languages. The relevance of this work is due to the description of the precedence in a polycode text in a comparative aspect due to the lack of a sufficient number of scientific papers affecting this issue. The authors offer an overview of the main stages of the study of texts with iconic and verbal components and different types of the component links; and history of the appearance of the terms that nominate this type of text. The text in our research is characterized by the use of semiotic codes, for example, colour and kinesics; it is accompanied by paragraphemic means, which are font variations that go beyond the use of punctuation marks in the standard language, and topographic means, representing various flat layouts of text. The implementation of the described type of text becomes a political discourse, the study of which also relates to the actual research topics of modern linguistics. It should be noted that a political cartoon is always a reflection of the opinion of society or an individual’s reaction to a significant public event, and it is its universal feature, which makes it possible to compare the means and categories of a creolized text of political cartoon in different linguistic cultures/in different languages. The object of the analysis is the creolized text of a political cartoon; the subject of the research is the category of precedence and its features aimed at the realization of the author’s intention in the political cartoon in Arabic and French. An important systemic characteristic of a creolized text is the category of precedence, which in this article corresponds to the category of intertextuality. The authors give examples to examine the use of precedent information at the level of the text and the image and their interconnection. The thorough analysis of the cartoons demonstrates the possibility of decoding a precedent sign in accordance with the type of speech culture of a native speaker. Precedence in a political cartoon can be expressed by a textual or graphic representation of universal human precedent phenomena, civilizational precedent phenomena, onyms and events of a supraregional nature. The formal expression of precedence can also be a symbol. In the conclusion, the article proposes a summary of the results of the study.