Varieties of unitary algebras with small growth of codimensions

Author(s):  
M. A. de Oliveira ◽  
A. C. Vieira

In the last years, the sequence of codimensions of PI-algebras has been studied by several authors and the classification of unitary algebras, up to equivalence, with at most cubic codimension growth was given by Giambruno, La Mattina and Petrogradsky in 2007. In this paper, we establish a new approach by studying the possibilities of specific proper codimensions of a unitary algebra with growth [Formula: see text] in order to present a complete list of varieties generated by unitary algebras with polynomial growth [Formula: see text]. Also, we classify, up to PI-equivalence, the unitary algebras with growth [Formula: see text] whose leading coefficient of the polynomial describing the codimension sequence achieves the largest and the smallest possible value.

Author(s):  
Oleksandr Ostrohliad

Purpose. The aim of the work is to consider the novelties of the legislative work, which provide for the concept and classification of criminal offenses in accordance with the current edition of the Criminal Code of Ukraine and the draft of the new Code developed by the working group and put up for public discussion. Point out the gaps in the current legislation and the need to revise individual rules of the project in this aspect. The methodology. The methodology includes a comprehensive analysis and generalization of the available scientific and theoretical material and the formulation of appropriate conclusions and recommendations. During the research, the following methods of scientific knowledge were used: terminological, logical-semantic, system-structural, logical-normative, comparative-historical. Results In the course of the study, it was determined that despite the fact that the amendments to the Criminal Code of Ukraine came into force in July of this year, their perfection, in terms of legal technology, raises many objections. On the basis of a comparative study, it was determined that the Draft Criminal Code of Ukraine needs further revision taking into account the opinions of experts in the process of public discussion. Originality. In the course of the study, it was established that the classification of criminal offenses proposed in the new edition of the Criminal Code of Ukraine does not stand up to criticism, since other elements of the classification appear in subsequent articles, which are not covered by the existing one. The draft Code, using a qualitatively new approach to this issue, retains the elements of the previous classification and has no practical significance in law enforcement. Practical significance. The results of the study can be used in law-making activities to improve the norms of the current Criminal Code, to classify criminal offenses, as well as to further improve the draft Criminal Code of Ukraine.


2021 ◽  
Vol 11 (4) ◽  
pp. 1855
Author(s):  
Franco Guzzetti ◽  
Karen Lara Ngozi Anyabolu ◽  
Francesca Biolo ◽  
Lara D’Ambrosio

In the construction field, the Building Information Modeling (BIM) methodology is becoming increasingly predominant and the standardization of its use is now an essential operation. This method has become widespread in recent years, thanks to the advantages provided in the framework of project management and interoperability. Hoping for its complete dissemination, it is unthinkable to use it only for new construction interventions. Many are experiencing what happens with the so-called Heritage Building Information Modeling (HBIM); that is, how BIM interfaces with Architectural Heritage or simply with historical buildings. This article aims to deal with the principles and working methodologies behind BIM/HBIM and modeling. The aim is to outline the themes on which to base a new approach to the instrument. In this way, it can be adapted to the needs and characteristics of each type of building. Going into the detail of standards, the text also contains a first study regarding the classification of moldable elements. This proposal is based on current regulations and it can provide flexible, expandable, and unambiguous language. Therefore, the content of the article focuses on a revision of the thinking underlying the process, also providing a more practical track on communication and interoperability.


2010 ◽  
Vol 03 (01) ◽  
pp. 155-184
Author(s):  
L. L. STACHÓ

Weighted grids are linearly independent sets {gw : w ∈ W} of signed tripotents in Jordan* triples indexed by figures W in real vector spaces such that {gugvgw} ∈ ℂgu-v+w (= 0 if u - v + w ∉ W). They arise naturally as systems of weight vectors of certain abelian families of Jordan* derivations. Based on Neher's grid theory, a classification of association free non-nil weighted grids is given. As a first step beyond the setting of classical grids, the complete list of complex weighted grids of pairwise associated signed tripotents indexed by ℤ2 is established.


1985 ◽  
Vol 29 (2) ◽  
pp. 213 ◽  
Author(s):  
Rene T. A. Lysloff ◽  
Jim Matson
Keyword(s):  

2021 ◽  
Author(s):  
Kulinich O.V. ◽  
Orel Yu. ◽  
Bykovets K.Yu.

The article examines the approaches to the classification of social enterprises by different classification features, such as: objectives and direction of using profit, priority sources of funding, the degree of integration of social programs and business processes, the degree of financial capacity, ways to create social enterprises, specifics of entrepreneurial activity organization, organizational and legal form, areas of activity, size, location, etc. A new approach to classification according to the criterion of innovative potential of enterprises is proposed.


1997 ◽  
Vol 1 (1) ◽  
pp. 111-133 ◽  
Author(s):  
Aimo Seppänen

Ever since the days of Jespersen, voices have been raised which argue that relative that is not a pronoun like who and which, but a conjunction/complementizer, as shown in particular by the ban on the sequence preposition + that, which is claimed to be best described by treating that as a conjunction. Taking up the question of the proper analysis of that as it appears in the word's relationship to prepositions, the present paper argues that in actual fact the descriptions built by Jespersen and various generative grammarians on the view of that as a conjunction/complementizer are not at all adequate to deal with some crucial facts of the word's syntax. Noting then some further facts which even the traditional ban is unable to deal with, the paper develops a new approach to the question which is derived from an examination of Finnish relatives and which handles all the English facts noted in terms of a general principle about the internal order of elements within the fronted relative phrase. The principle invoked is completely neutral as regards the word-class status of that, but some of the facts explored strongly argue for the classification of the word as a pronoun.


1983 ◽  
Vol 73 (3) ◽  
pp. 135-149 ◽  
Author(s):  
F. Debon ◽  
P. Le Fort

ABSTRACTA classification is proposed, based mainly on major element analytical data plotted in a coherent set of three simple chemical-mineralogical diagrams. The procedure follows two complementary steps at two different levels. The first is concerned with the individual sample: the sample is given a name (e.g. granite, adamellite, granodiorite) and its chemical and mineralogical characteristics are determined. The second one is more important: it aims at defining the type of magmatic association (or series) to which the studied sample or group of samples belongs. Three main types of association are distinguished: cafemic (from source-material mainly or completely mantle-derived), aluminous (mainly or completely derived by anatexis of continental crust), and alumino-cafemic (intermediate between the other two types). Subtypes are then distinguished among the cafemic and alumino-cafemic associations: calc-alkaline (or granodioritic), subalkaline (or monzonitic), alkaline (and peralkaline), tholeiitic (or gabbroic-trondhjemitic), etc. In the same way, numerous subtypes and variants are also distinguished among the aluminous associations using a set of complementary criteria such as quartz content, colour index, alkali ratio, quartz–alkalies relationships and alumina index.Although involving a new approach using partly new criteria, this classification is consistent with most of the divisions used in previous typologies. The method may also be used in the classification of the volcanic equivalents of common plutonic rocks.


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