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We consider the general framework of perturbative quantum field theory for the pure Yang–Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs. Next, we prove that the Wick expansion property can be preserved for all cases in order n = 2 . However, gauge invariance is broken for chronological products of Wick submonomials. [ABSTRACT FROM AUTHOR]

Introduction. Today, the system of secondary vocational education (SVE) is faced by a multi-factorial problem: the training of qualified specialists, taking into account approved federal unified standards; the fulfillment of potential employers’ requirements, which often do not coincide with these standards; and the determination of rapid responses to continuous changes in labour market conditions, i. e. the requirement for a qualitative human resources upgrade in regional production clusters and holding companies, as well as numerous small enterprises.The aim of the research was to develop a methodology for analysing vocational-educational problematics. The methodology was designed for the differentiation, specification and justification of relevant specialised competencies, which complement universal and general professional competencies documented in educational standards.Methodology and research methods. As a research methodology, a causal approach was used, specifically implemented in the form of a multi-dimensional matrix informing a stage-by-stage analysis, which links the need for qualified personnel (experts, who have necessary competencies) with the pedagogical conditions for their preparation (formation of necessary competencies in students).Results and scientific novelty. We present a recommendation for the organisational and content-based improvement of specialist education in terms of key SVE tasks and factors. This education should be conducted by means of systematic identification and assessment of multi-dimensional regional and sectoral needs for trained personnel, projections of results of monitoring on educational programmes and development of means for the acquisition of the relevant skills. The structure and algorithm of multi-dimensional matrix analysis, providing a stageby-stage presentation of problems found in industrial enterprises concerning specified SVE graduate competencies, are described and visually presented. This also enables to effectively build and timely adjust the learning process of really demanded, competitive experts capable to realise innovative projects, to master and create new equipment, i. e. to keep the successful operation and development of production and economics of a region and a country in general. The logic-semantic model of formation of transprofessional competencies, which integrates technological, informational, legislative and communicative-interprofessional components, is designed. The model consists of eight coordinate axes (“Structure of package tasks”, “Significant factors”, “Components”, “Theoretical bases”, “Implementation”, “Criteria of formation of competencies”, “Result”, “Strategic partners”) and reflects internal interrelations between all the elements of process of vocational education.Practical significance. The materials of the research and its results complement the theory and practice of vocational education, on the one hand, by new tools for development of federal and other standards, on the other hand, by methodological means of rational choice and justification through the introduction of the specific profile of variable professional competencies into SVE programmes. The authors proposed the methodological and graphic solutions of the problems and the recommendations, which can be used in the organisations of vocational education.

It is known that the elimination of anomalies in all orders of perturbation theory is an open problem. The constraints given by usual invariance properties and the Wess–Zumino identities are not enough to eliminate the anomalies in the general case of a Yang–Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of perturbation theory. So, anti-BRST transform gives nothing new, and we have to find other ideas to restrict and eventually eliminate the anomalies for a general Yang–Mills theory.

We consider gauge models in the causal approach and study one-loop contributions to the chronological products and the anomalies they produce. We prove that in order greater than 4 there are no one-loop anomalies. Next we analyze one-loop anomalies in the second- and third-order of the perturbation theory. We prove that the even parity contributions (with respect to parity) do not produce anomalies; for the odd parity contributions we reobtain the well-known result. [ABSTRACT FROM AUTHOR]

Highlights: [•] Most research on complement realisation has been concerned with verbs. [•] The article investigates the neglected area of adjectival valency. [•] The data consist of 181 polyvalent adjectives occurring in 956 patterns. [•] Predictability and the aspectual- and the causal approaches to complement realisation are assessed. [•] The findings support the view that valency belongs to the idiosyncratic aspects of language. [ABSTRACT FROM AUTHOR]