scholarly journals BASIS OF MULTILINEAR PART OF LEIBNIZ ALGEBRAS MANIFOLDS \overbrace{V_1}

2017 ◽  
Vol 20 (3) ◽  
pp. 76-82
Author(s):  
S.P. Mishchenko ◽  
Y.R. Pestova
Keyword(s):  
Polynomial Growth ◽  
Base Field ◽  
Leibniz Algebras ◽  
Continue Research

In the case of trivial characteristic of base field, Leibniz algebras manifolds defined by the identity x_1(x_2x_3)(x_4x_5)\equiv 0. has almost polynomial growth. In the work we continue research of this manifold, in particular, we construct bases of multilinear parts.

scholarly journals On the Structure of Graded Leibniz Algebras

2015 ◽  
Vol 22 (01) ◽  
pp. 83-96 ◽  
Author(s):  
Antonio J. Calderón Martín ◽  
José M. Sánchez Delgado
Keyword(s):  
Arbitrary Dimension ◽  
Unit Element ◽  
Homogeneous Component ◽  
Maximal Length ◽  
Base Field ◽  
Leibniz Algebras ◽  
Arbitrary Base

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form [Formula: see text] with U a subspace of 𝔏1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of 𝔏, satisfying [Ij, Ik]=0 if j ≠ k. In the case of 𝔏 being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.

Classifying the Minimal Varieties of Polynomial Growth

2014 ◽  
Vol 66 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Antonio Giambruno ◽  
Daniela La Mattina ◽  
Mikhail Zaicev
Keyword(s):  
Finite Number ◽  
Characteristic Zero ◽  
Polynomial Growth ◽  
Building Blocks ◽  
Base Field ◽  
Associative Algebras ◽  
Proper Subvariety ◽  
Variety Of Associative Algebras

AbstractLet ν be a variety of associative algebras generated by an algebra with 1 over a field of characteristic zero. This paper is devoted to the classification of the varieties ν that are minimal of polynomial growth (i.e., their sequence of codimensions grows like nk, but any proper subvariety grows like nt with t < k). These varieties are the building blocks of general varieties of polynomial growth.It turns out that for k ≤ 4 there are only a finite number of varieties of polynomial growth nk, but for each k > 4, the number of minimal varieties is at least |F|, the cardinality of the base field, and we give a recipe for their construction.

THEORETICAL PRINCIPLES OF FORECASTING THE COST OF A SOFTWARE PRODUCT

2017 ◽  
Author(s):  
Pavlo Rodionov ◽  
◽  
Anna Ploskonos ◽  
Lesya Gavrutenko ◽  
◽  
...  
Keyword(s):  
Selection Process ◽  
Individual Characteristics ◽  
Successful Implementation ◽  
Software Products ◽  
Software Product ◽  
Continue Research ◽  
Cocomo Model ◽  
Factors Of Influence ◽  
The Individual ◽  
The Cost

The paper analyzes the factors that affect the amount of effort required to create a mobile application and its cost. It is established that the main factors of influence are the design of the application, its functionality, the type of mobile platform, the availability and level of testing and support, as well as the individual characteristics of the developer. Based on the analysis of information sources, the main methods and approaches to forecasting the cost of software products are identified, which include the COCOMO model, Price-to-win method, expert evaluation, algorithmic methods and the method of analogies. It is proposed to consider the method of analogies as a tool that allows you to make predictions about the cost of resources required for the successful implementation of IT projects based on the experience of similar projects. It is proved that the advantages of this method are the simplicity of its implementation and the clarity of the results obtained, which follows from the practical orientation of this tool. Among the limitations of the method of analogy is the mandatory need for reliable data relating to similar projects, as well as the difficulty of taking into account unspecified indicators. Taking into account the mentioned limitations of the method of analogies and on the basis of the analysis of scientific sources the possible directions of its optimization are determined. Thus, among the ways to improve the effectiveness of this method are those aimed at optimizing the project selection process, the data for which are used as a basis for forecasting. Attempts to improve the method of analogies by including parameters that were previously ignored by this technique seem promising. This in turn can lead to an expansion of the scope of the method of analogies and increase the accuracy of forecasts. As prospects for further research, the need to continue research in the field of optimization of the method of analogies with the subsequent practical verification of theoretical positions on the data of real projects.

On solvable Leibniz algebras whose nilradical has characteristic sequence (m1,m2,m3)

2018 ◽  
Vol 2018 (3) ◽  
pp. 4-17
Author(s):  
K.K. Abdurasulov ◽  
Drew Horton ◽  
U.X. Mamadaliyev
Keyword(s):  
Characteristic Sequence ◽  
Leibniz Algebras

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

scholarly journals A Generalization of Strassen’s Theorem on Preordered Semirings

Order ◽  
2021 ◽  
Author(s):  
Péter Vrana
Keyword(s):  
Compact Hausdorff Space ◽  
Polynomial Growth ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Equivalent Condition ◽  
Real Numbers ◽  
Asymptotic Spectrum ◽  
Ring Of Continuous Functions ◽  
Archimedean Property ◽  
Locally Compact Hausdorff Space

AbstractGiven a commutative semiring with a compatible preorder satisfying a version of the Archimedean property, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together with a map from the semiring to the ring of continuous functions. Strassen’s theorem characterizes an asymptotic relaxation of the preorder that asymptotically compares large powers of the elements up to a subexponential factor as the pointwise partial order of the corresponding functions, realizing the asymptotic spectrum as the space of monotone semiring homomorphisms to the nonnegative real numbers. Such preordered semirings have found applications in complexity theory and information theory. We prove a generalization of this theorem to preordered semirings that satisfy a weaker polynomial growth condition. This weaker hypothesis does not ensure in itself that nonnegative real-valued monotone homomorphisms characterize the (appropriate modification of the) asymptotic preorder. We find a sufficient condition as well as an equivalent condition for this to hold. Under these conditions the asymptotic spectrum is a locally compact Hausdorff space satisfying a similar universal property as in Strassen’s work.

scholarly journals The Urban Environment Impact of Climate Change Study and Proposal of the City Micro-Environment Improvement

2021 ◽  
Vol 13 (8) ◽  
pp. 4096
Author(s):  
Jozefína Pokrývková ◽  
Ľuboš Jurík ◽  
Lenka Lackóová ◽  
Klaudia Halászová ◽  
Richard Hanzlík ◽  
...  
Keyword(s):  
Management Practices ◽  
Water Infiltration ◽  
Environment Impact ◽  
Management Procedures ◽  
Aging Infrastructure ◽  
Continue Research ◽  
Rainwater Management ◽  
The Given ◽  
The City ◽  
Very High

The water management of cities and villages faces many challenges. Aging infrastructure systems operate for many years after their theoretical lifetime (operation) with a very high need for reconstruction and repair. The solution is proper rainwater management. The investigated area is part of the cadastral area of the Nitra city. This article is based on the use of geographic information systems (GIS) as tools in proposing water retention measures that are needed to improve the microenvironment of the city. We proceeded in several steps, which consisted of area analysis, survey, surface runoff calculations in urbanized areas, proposal of a suitable solution for given location. For real possibilities of rainwater management procedures, a new site on the outskirts of the city was selected. In the given locality, it was possible to use water infiltration as a solution. The locality has suitable conditions of land ownership, pedological conditions, the slope of the area and also the interest of the inhabitants in the ecological solution. The outlined study indicates the need to continue research on the reliability of rainwater management practices.

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