Approximation of null controls for semilinear heat equations using a least-squares approach

The null distributed controllability of the semilinear heat equation $\partial_t y-\Delta y + g(y)=f \,1_{\omega}$ assuming that $g\in C^1(\mathbb{R})$ satisfies the growth condition $\limsup_{r\to \infty} g(r)/(\vert r\vert \ln^{3/2}\vert r\vert)=0$ has been obtained by Fern\'andez-Cara and Zuazua in 2000. The proof based on a non constructive fixed point theorem makes use of precise estimates of the observability constant for a linearized wave equation. Assuming that $g^\prime$ is bounded and uniformly H\"older continuous on $\mathbb{R}$ with exponent $p\in (0,1]$, we design a constructive proof yielding an explicit sequence converging strongly to a controlled solution for the semilinear equation, at least with order $1+p$ after a finite number of iterations. The method is based on a least-squares approach and coincides with a globally convergent damped Newton methods: it guarantees the convergence whatever be the initial element of the sequence. Numerical experiments in the one dimensional setting illustrate our analysis.

Japanese apophonic compounds

This paper provides a comprehensive description and analysis of Japanese apophonic compounds, such as ama-gasa (ame + kasa), ko-kage (ki + kage) or kamu-tikara (kami + tikara), in which the initial element exhibits one of three different pairs of final vowel alternations. The three pairs involved are e ∼ a, i ∼ o, and i ∼ u. To determine the controlling factors for apophony, its morphological function, its overall characteristics and its interaction with other compositional devices of Japanese (mainly rendaku) we constructed a database of 2,322 compounds. Each compound has as an element at least one of 22 “apophonic nouns” which may undergo vowel alternation when the initial element in a compound. The core results of this study are that there exists a range of morphological, lexical and phonological factors which tend to favour or disfavour apophony. The phonological factors mostly pertain to the length of either element in the compound. Further, it was also found that apophony is generally not linked, either positively (redundancy of morphological devices) or negatively (economy of morphological devices), to rendaku.

FORMATION OF ANTI-CRISIS MODEL OF RESTAURANT BUSINESS DEVELOPMENT IN UKRAINE

The current state of development and "survival" of the hotel and restaurant business in conditions of quarantine restrictions during the pandemic is characterized by uncertainty, the so-called collapse and requires new creative ideas and effective management decisions. The relevance is also aggravated by the fact that the restaurant business differs from all other types of business in specific features, the inseparability of production, provision and consumption of services, the complete and direct dependence of the profitability and profitability of the business on effective and direct communication with guests (consumers), and experienced a rather painful blow to the activity. The main strategies for the development of the restaurant business should be aimed at overcoming the business risks that arose during the pandemic. It is important to find ways to overcome the crisis in the restaurant business is relevant, as well as the restoration of their effective functioning in the already updated service market. Accordingly, the article carried out theoretical-methodological and practical analysis of the features of the functioning of restaurant businesses during the period of quarantine restrictions. The critical moments and opportunities that ensured the "survival" of the domestic restaurant business, acting as so-called "life jackets" in different periods of the COVID-19 pandemic, have been identified. The key problems and prospects of overcoming the crisis by restaurant enterprises are analyzed. Some aspects of state support for business in a pandemic have been studied. The strengthened sanitary and hygienic requirements for the functioning of restaurant business institutions during the pandemic are summarized and systematized. The importance and necessity of forming an anti-crisis policy at the enterprise is justified, the initial element of which should be the gradation of goals and expectations from the business for all stakeholders of the process. Based on the generalization and systematization of key parameters and conditions of the modern functioning of the restaurant business in Ukraine and taking into account its promising trend development, an anti-crisis model of the development of the domestic restaurant business was designed, which is segmentally divided into four blocks of technologies (economic-organizational, managerial, corporate-social and reputational) and provides for the introduction of a service management system. To ensure effective implementation of the designed anti-crisis model, a structural algorithm of its implementation mechanism is justified, which provides for a set of interconnected and systematized key tasks, which are conditionally divided by levels and content of implementation and three categories (management, service (including production), optimization).

Hybrids with Final Neoclassical Combining Forms in Baltic Languages

The article presents some ideas about the hybrids that are made by combining the neoclassical elements or are mixed of Lithuanian or Latvian and foreign origin combining forms. The examples of hybrids found in English are also provided. This corpus-based investigation reveals that the formation of hybrids with final neoclassical combining forms in modern Baltic languages is a sufficiently active, productive and unobtrusive process of creativity and wit. The identified structural types of hybrids are the following: 1) the hybrids with the international elements of different classical or neoclassical origin; 2) the hybrids with the initial element of non-classical origin. They are almost identical in the analysed languages, suggesting that they are often borrowed and translated rather than created, but if they are created, then this is done by obvious analogy. Some Lithuanian and Latvian hybrids have long been used and included in various dictionaries, and their frequency in the linguistic corpus is quite high. However, most examples of hybrid origin do not exist and probably do not appear in dictionaries due to their rare use, uniqueness, distinctive form or irregularity. The knowledge of hybrid formation and usage can be relevant to the learners of Lithuanian, Latvian, and English, as well as translators, terminologists, and lexicographers.

VIDÍŠ TÝM LEPŠIE, ČÍM BLIŽŠIE SA POZERÁŠ SLOVAK COMPARATIVE CORRELATIVE CC' CONSTRUCTIONS FROM A CONSTRUCTION GRAMMAR PERSPECTIVE

The Slovak Comparative Correlative (CC) construction has received little attention, although it is interesting regarding both its semantics and its form: As discussed in Horsch (2019), CCs are characterized by their complex symmetric (parallel change over time) and asymmetric (cause-effect) semantics, which are encoded in a biclausal structure in which each clause consists of a combination of fixed material and obligatory/optional slots. Typically, the first clause (C1) encodes a cause/protasis, and precedes the second clause (C2), which encodes an effect/apodosis: [čím bližšie sa pozeráš,]C1 [tým lepšie vidíš.]C2 ‘the closer you look, the better you see.’ However, there are also structures that retain the same meaning but in which C2 precedes C1 (often referred to as CC’): [Tým lepšie vidíš]C2 [čím bližšie sa pozeráš.]C1. ‘You see the better, the closer you look.’ Additionally, there is a variant in Slovak where the clause precedes the clause-initial element and comparative element: [Vidíš tým lepšie,]C2 [čím bližšie sa pozeráš.]C1. Embedded in a Usage-based Construction Grammar approach, this is the first large-scale corpus study to investigate the C2C1 order in Slovak, and how semantics influences its formal properties. It is argued that both the significantly higher amount of C1C2 order in the corpus data and the significantly higher amount of C2C1 structures in which the clause precedes the comparative element in C2 can be explained with the principle of iconicity (linguistic form is influenced by the semantics of a construction), which makes certain strings easier to process and thus leads to performance preference. From a cross-linguistic perspective, the present investigation provides evidence in support of Goldberg’s Tenet #5 (2003, p. 219), which posits that cross-linguistic generalizations can be accounted for with general cognitive constraints.

Verb Second in Norwegian: Variation and acquisition

This chapter provides an overview of the micro-variation in Norwegian when it comes to Verb Second (V2) word order, both in the various dialects and in the two standard written varieties of Norwegian. The variation is dependent on a number of factors, including clause type, type of initial element, and information structure. This overview demonstrates a rich inventory of micro-systems, raising the question of how children come to acquire such fine-grained patterns. The chapter addresses this question by providing findings from acquisition research and discusses what this considerable micro-variation and coexisting grammars tell us about the architecture of the human language faculty.

To the Historical Geography of Ossetia: The Historical Region of Khokh

The present article advocates that the oronym Khokhis K’avk’asi “the Khokh Caucasus,” catalogued by the Georgian geographer Vakhushty in the beginning of the 18th century as the name for the Side Ridge in Central Ossetia, corresponds to the historical and geographical region of Khokh, known from the toponymic, folklore and ethnographic sources of the 20th century. The oronym Khokh (“mountain”) has left a distinctive mark in the works of the Ossetian writers — natives of that region. In South Ossetia, the same oronym applies to the Main Caucasian Ridge, which has urged the author to explain this inconsistency. Besides, the Nart Epic of the Ossets also speaks of a mountainous land Akhokhayi Khokh raided by the heroes. One of the sources of the 14th century mentions the Alan province Akhokhiya. As it is evident that both toponyms refer to the region Khokh, the author deeemed necessary to explain the recurrent initial element A- in them. The author refutes the version of its Circassian origin suggesting an etymological link with Proto-Iranian prefix *ā-, one of the meanings of which is that of the preposition “on.” The general meaning of the toponym A-Khokh is thus “upland.” A typological parallel to it is the Old Persian toponym *Ākaufaka ‘Kohistan’ that consists of the same prefix *ā-, Old Persian kaufa ‘mountain,’ and a suffix. As the prefix а- fell out of free use leaving its trail only in a number of etymologically obscure toponyms of Ossetia, A-Khokh (Akhokhiya) is one of the oldest toponyms correlating to the descriptive names of the Alan province Mons in terra Alanorum and montes Alanorum mentioned in the medieval sources.

Genderproblematics inwestern class analysis: the dynamics oftheoretical approaches

The article represents an analytical review of the axiomatics of sociological approaches to class analysis, taking into account gender diferentiation since the 1940s till nowadays. Te problems of primary units selection of the class analysis, conceptual grounds for determining the class position of women and the features of their social status, conditioned by this position, ways of normalizing gender inequality in conventional approaches and criticizing their legitimacy have been considered in the research. It has been found that within the framework of the structural and functional approach of T. Parsons, the class status of the individual is ascetic, the main mechanism for its acquisition and transmission is kinship, while gender inequality is regarded as condition for maintaining the stability of the social system. Te changing structure of employment and women’s emancipation has led to the revision of the conventional approach foundations by problem consideration of families as the primary units of class analysis. Subsequently, the dominant approach of J. Goldthorpe eliminates the gender inequality aspect, linking the class position of the household with the position of the partner who plays a leading role in its economic provision. E.O. Wright’s approach, representing an infuential neo-Marxist alternative model of class analysis, presupposes the existence of an individual actor as the initial element of class analysis. At the same time, the author emphasizes the existence of exploitation relations in the family, as well as the high degree of risk and uncertainty of the social status of a signifcant number of women. Awareness of the role of individualization in social dynamics, changes in the structure of the global economy and the consequences of de-industrialization in the 1990s changed the original axiomatics of class analysis. Te focus of attention has shifed from the disputes about the criteria of class diferentiation to the analysis of real diferences in people’s way of life, generated by social inequality. Modern studies of social inequality take into account the intersection of gender, class, racial and other characteristics of individuals and communities.

The Phenomenon and the Semantics of Sound in Modern Music as the Subject of Development in Music Education (Based on Works by Alexander Bakshi)

The nature of the sound is unique and inimitable in the works of modern composers, crystallizing in the complex search for musical expression. The article attempts to trace the formation of a new phenomenon in Russian music – “Theater of sound”, which is possible for comprehending in terms of value of a separate sound in the organization of compositions by the Moscow composer A. Bakshi where each of them realized by an initial element of creation of the work coloristic is calculated. The weight of the acoustic point at the intersection of sense-forming factors of different plan, allows us to consider each sound in a musical work semantically significant unit, because it instantly reflects the change in content, sensitive to the situation, is endowed with great energy impact. The article reveals some features of the sound organization and its fundamental role in vanguard compositions, which creates conditions for the search and development of new meanings. The method of analysis of instrumental works is based on the movement from particular manifestations to generalizations concerning the whole work and its stage life. The creative process of writing this author is unique in that it begins with the search and formation of a single sound, giving a special energy stress with its timbre, character. The composer extracts the maximum of possibilities from it, using rhythmic variability, timbre, tessitura, various methods of sound production. Individualization not only enhances the expressive properties, but also increases the semantic and functional load of more significant constructions. As a result, there are new ways of organizing the musical fabric, based on associations, the game of meanings, ambivalence. Coloristic work, sound transformations complicate the code of meaning generation, which characterizes the change in the type of communication. In connection with the “visual turn”, new types of codes are developed that contribute to the volumetric perception of the work in the polysemantic whole. The understanding of the essence of the considered processes in the musical-theoretical aspect is a necessary condition for the inclusion of creativity of modern composers in the content of musical education.

Pre-verbal position in BP: a reinterpretation of the "avoid pronoun principle"

The aim of this paper is to analyze the changes occurring in Brazilian Portuguese, regarding the possibility of null subjects, and suggest the kinds of constraints that explain its present distribution. In this paper, we will propose that the null subject parameter is defi ned at the interfaces. At the level of Logical Form, a constraint like Chomsky’s (1981) Avoid Pronoun will be atwork for languages that are prototypical null subject languages, like Spanish and Chinese. For languages like BP, a system with a particular distribution of null subjects, the constraint will be more specifi c: Avoid non-referential pronouns. We will also propose that at the other interface, the Phonetic Form, languages have fi lters regarding their rhythm. To account for the preference for certain forms, a constraint of the form: Avoid V1 will be proposed. This constraint hasnothing to do with an XP constituent in Spec of C, like in V2 languages, but with a phonetic requirement. This means that the initial element can be a head or an XP.