Regular Elements Research Articles

ON THE SINGULARITIES OF MISHCHENKO–FOMENKO SYSTEMS

To each complex semisimple Lie algebra \( \mathfrak{g} \) and regular element a ∈ \( \mathfrak{g} \)reg, one associates a Mishchenko–Fomenko subalgebra \( \mathcal{F} \)a ⊆ ℂ[\( \mathfrak{g} \)]. This subalgebra amounts to a completely integrable system on the Poisson variety \( \mathfrak{g} \), and as such has a bifurcation diagram Σa ⊆ Spec(\( \mathcal{F} \)a). We prove that Σa has codimension one in Spec(\( \mathcal{F} \)a) if a ∈ \( \mathfrak{g} \)reg is not nilpotent, and that it has codimension one or two if a ∈ \( \mathfrak{g} \)reg is nilpotent. In the nilpotent case, we show each of the possible codimensions to be achievable. Our results significantly sharpen existing estimates of the codimension of Σa.

L1-norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry

Isogeometric analysis is an efficient method to accurately represent geometry and obtain accurate solutions, and can be utilized for dynamic analysis of flexible multibody systems. In this paper, l1 norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry is presented, in which, (1) the exact shape deformation of regular NURBS element after trimming is characterized by geometric transformation, (2) the l1 norm optimization is employed to select the predominant modal shapes for accurate dynamic analysis under rapidly changed loads, and (3) motion equations are sampled by considering the acceleration of control variables influence on control variables variation to obtain stable dynamic results. Finally, the presented approach is validated with three examples. The dynamic response results show that the trimmed isogeometric analysis can be employed to achieve considerable accuracy. As the continuity between NURBS elements increases from C0 to C1, the degree of freedom is reduced by 75%, and the computational time of l1 norm based dynamic analysis is about 35% of the full order modal shapes method. Furthermore, the proposed sampling method can be utilized to reduce the 33% sampling number compared with the Latin Hypercube sampling method.

Duo Property Applied to Powers and Regular Elements

The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements. Such rings shall be called right exp-DR. We investigate the structures of group rings, right quotient rings, matrix rings and (skew) polynomial rings, through the study of right exp-DR rings. In addition, we provide a method of constructing finite non-abelian [Formula: see text]-groups for any prime [Formula: see text].

Various regularities for semigroups of transformations on a finite set determined by a zig-zag order

Consider a finite ordered set [Formula: see text] with a zig-zag order. In this paper, we consider the semigroup [Formula: see text] of all compressing-preserving transformations on [Formula: see text]. Necessary and sufficient conditions for [Formula: see text] to be regular and coregular are given. Regular and coregular elements in [Formula: see text] are completely described. For a subsemigroup [Formula: see text] of the transformation semigroup [Formula: see text], we obtain that left regular and right regular elements in [Formula: see text] are identical. A characterization of left [right] regular elements in [Formula: see text] is given. We classify all left [right] regular semigroups [Formula: see text].

On certain semigroups of transformations with an invariant set

Let [Formula: see text] be a nonempty set and let [Formula: see text] be the full transformation semigroup on [Formula: see text]. The main objective of this paper is to study the subsemigroup [Formula: see text] of [Formula: see text] defined by [Formula: see text] where [Formula: see text] is a fixed nonempty subset of [Formula: see text]. We describe regular elements in [Formula: see text], and show that [Formula: see text] is regular if and only if [Formula: see text] is finite. We characterize unit-regular elements in [Formula: see text], and prove that [Formula: see text] is unit-regular if and only if [Formula: see text] is finite. We characterize Green’s relations on [Formula: see text], and prove that [Formula: see text] on [Formula: see text] if and only if [Formula: see text] is finite. We also determine ideals of [Formula: see text] and investigate its kernel. This paper extends several results that have appeared in the literature.

Set-theoretic solutions of the Yang–Baxter equation associated to weak braces

We investigate a new algebraic structure which always gives rise to a set-theoretic solution of the Yang–Baxter equation. Specifically, a weak (left) brace is a non-empty set S endowed with two binary operations + and circ such that both (S,+) and (S, circ ) are inverse semigroups and a∘b+c=a∘b-a+a∘canda∘a-=-a+a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} a \\circ \\left( b+c\\right) = \\left( a\\circ b\\right) - a + \\left( a\\circ c\\right) \\qquad \ ext {and} \\qquad a\\circ a^- = - a + a \\end{aligned}$$\\end{document}hold, for all a,b,c in S, where -a and a^- are the inverses of a with respect to + and circ , respectively. In particular, such structures include that of skew braces and form a subclass of inverse semi-braces. Any solution r associated to an arbitrary weak brace S has a behavior close to bijectivity, namely r is a completely regular element in the full transformation semigroup on Stimes S. In addition, we provide some methods to construct weak braces.

Development of refined one-dimensional finite element models using a nodal kinematics optimization method

This paper presents refined one-dimensional (1D) finite element models develop by an effective nodal kinematics optimization method. The refined models belong to Best Theory Diagrams, which are built by using the Carrera Unified Formulation (CUF), Axiomatic/Asymptotic method and a Genetic Algorithm (GA). The influence of different chromosome types on the refined models and GA performance have been investigated. It is shown that the proposed method can improve the accuracy of regular 1D-CUF finite element models. Furthermore, the results suggest that it is possible to built refined models for compound loads from the ones optimized for individual loads.

Effectiveness and the Ways of Using Pedagogical Innovative Technologies in Teaching Process

Innovation is the process of making new changes in various fields of activity, as well as in the field of education and industry. The result of such changes is news. Any innovation is inevitable, which is formed in the logic of changes and development in society. The essence of innovation is to the tools and methods to achieve new results, obtain them, to overcome traditional or regular elements of traditional activities. The transition of enterprises and organizations of the national economy (including the education) has further strengthened these all conflicts, but the most painful situation is the need to restore the minds of these employees.

Capillary suction predictions in granular materials subjected to 1D compression and triaxial loading with emphasis on projectile penetration

The role of partial saturation in penetration resistance of projectiles in granular materials is not clear due to experimental constraints imposed by high cost and special considerations in equipment design. In this work, granular material near the tip and far-field of the projectile is numerically simulated based on 1D compression and triaxial stress paths, respectively, using the finite discrete element method. The crushing of grains in 1D compression simulations is implemented by pre-inserting cohesive interface elements in regular finite element mesh. The capillary suction is numerically predicted by extracting the deformed granular assembly microstructure at different loading steps as an input to the pore morphology method. The results demonstrate the development of high capillary suction in 1D compression loading due to the significant crushing of grains. The evolution of capillary suction is negligible during triaxial loading compared to the 1D compression loading. This suggests that future simulations related to projectile penetration in partially saturated granular materials should account for coupled hydromechanical effects near the tip whereas the far-field can be approximated as a dry material. Finally, the capillary suction corresponding to extreme comminution near the projectile tip is estimated from a 3D assembly of spherical grains with a mean grain size of 1 µm.

Overgroups of regular unipotent elements in reductive groups

Abstract We study reductive subgroups H of a reductive linear algebraic group G – possibly nonconnected – such that H contains a regular unipotent element of G. We show that under suitable hypotheses, such subgroups are G-irreducible in the sense of Serre. This generalises results of Malle, Testerman and Zalesski. We obtain analogous results for Lie algebras and for finite groups of Lie type. Our proofs are short, conceptual and uniform.

Quantification of mineral and toxic elements in milk of dairy cows by ICP-MS

Milk is an important component of mammalian metabolism which included micro and macronutrients. The objective of this study was to survey the concentrations of minerals and toxic elements in cow milk samples by inductively coupled plasma-mass (ICP-MS). In this study, it was analyzed the content of sodium, magnesium, potassium, calcium, titanium, chromium, manganese, iron, cobalt, nickel, copper, zinc, selenium, arsenic, cadmium, thallium, lead in cow milk samples (n=25) collected from Kahramanmaraş province of Turkey. The highest levels recorded for potassium, calcium and sodium with average concentrations of 1587.36, 1157.98, 643.34 mg L-1, respectively. The results revealed that there was no toxic element contamination in cow milk samples. Regular element analysis of cow's milk, which is the most widely used milk in dairy industry, is important for health.

Support varieties over skew complete intersections via derived braided Hochschild cohomology

In this article we investigate homological aspects of a skew complete intersection R, i.e. a skew polynomial ring modulo an ideal generated by a sequence of regular normal elements. We compute the derived braided Hochschild cohomology of R relative to the skew polynomial ring and show its action on ExtR(M,N) is noetherian for finitely generated R-modules M and N respecting the braiding of R. When the parameters defining the skew polynomial ring are roots of unity we use this action to define a support theory. In this setting applications include a proof of the Generalized Auslander-Reiten Conjecture and that R possesses symmetric complexity.

Regular, unit-regular, and idempotent elements of semigroups of transformations that preserve a partition

Let X be a nonempty set and \({{\mathcal {T}}}_X\) the full transformation semigroup on X. For a partition \({{\mathcal {P}}}\) of X, we study semigroups \(T(X, {{\mathcal {P}}}) = \{f\in {{\mathcal {T}}}_X\mid (\forall X_i\in {{\mathcal {P}}}) (\exists X_j \in {{\mathcal {P}}})\;X_i f \subseteq X_j\}\), \(\Sigma (X, {{\mathcal {P}}}) = \{f\in T(X, {{\mathcal {P}}})\mid (\forall X_i \in {{\mathcal {P}}})\; Xf \cap X_i \ne \emptyset \}\), and \(\Gamma (X, {{\mathcal {P}}}) = \{f\in {{\mathcal {T}}}_X\mid (\forall X_i\in {{\mathcal {P}}})(\exists X_j\in {{\mathcal {P}}})\; X_i f = X_j\}\) under composition. We give necessary and sufficient conditions for \(\Gamma (X,{{\mathcal {P}}})\) to be the semigroup of all closed selfmaps on X endowed with the topology having \({{\mathcal {P}}}\) as a basis. For finite X, we characterize unit-regular elements of \(T(X, {{\mathcal {P}}})\) and \(\Sigma (X, {{\mathcal {P}}})\). We discuss set inclusions between \(\Gamma (X, {{\mathcal {P}}})\) and certain semigroups of selfmaps that preserve \({{\mathcal {P}}}\). We characterize idempotents and regular elements of \(\Gamma (X, {{\mathcal {P}}})\). For finite X, we also prove that all regular elements of \(\Gamma (X, {{\mathcal {P}}})\) are unit-regular. We finally count the number of elements, idempotents, and regular elements of \(\Gamma (X, {{\mathcal {P}}})\) for finite X.

The lattice and semigroup structure of multipermutations

We study the algebraic properties of binary relations whose underlying digraph is smooth, that is, has no source or sink. Such objects have been studied as surjective hyper-operations (shops) on the corresponding vertex set, and as binary relations that are defined everywhere and whose inverse is also defined everywhere. In the latter formulation, they have been called multipermutations. We study the lattice structure of sets (monoids) of multipermutations over an [Formula: see text]-element domain. Through a Galois connection, these monoids form the algebraic counterparts to sets of relations closed under definability in positive first-order logic without equality. We show one side of this Galois connection, and give a simple dichotomy theorem for the evaluation problem of positive first-order logic without equality on the class of structures whose preserving multipermutations form a monoid closed under inverse. These problems turn out either to be in [Formula: see text] or to be [Formula: see text]-complete. We go on to study the monoid of all multipermutations on an [Formula: see text]-element domain, under usual composition of relations. We characterize its Green relations, regular elements and show that it does not admit a generating set that is polynomial on [Formula: see text].

Performance of Multicriteria Evaluation and Heuristic Methods in the Delineation of Green Infrastructure in Areas with Fragmented Landscapes

The EU Commission has established Green infrastructure as one of the tools to preserve biodiversity and grant the provision of ecosystem services that reduce impacts on natural values like those produced by climate change. Therefore, a European green infrastructure strategy has been created that commit member states to incorporate green infrastructure to their territorial planning. Yet, methodologies to delimit green infrastructure so as to facilitate its inclusion in territorial plans are still scarce. The available methods are mainly based in multicriteria evaluation and focus on zoning general green infrastructure areas taking into account the provision potential of just a few ecosystem services. Considering the provision of a wide range of ecosystem services to delimit green infrastructure elements is key to grant their multifunctionality and increase their efficiency mitigating climate change impacts in natural values and human population. However, the lack of data or the high cost to accurately map ecosystem services provision potential, leads most of the time to infer it from land cover data. This creates problems when using these maps to delimit green infrastructure in areas with fragmented landscapes; since identified green infrastructure areas may be irregular and scattered. There are heuristic methods like simulated annealing that have been used to identify ecosystem services hot spots which consider the regularity and size of the identified patches. These methods can be used to delimit green infrastructure in fragmented landscapes finding a balance between the regularity of the areas and their potential to provide multiple ecosystem services. In the current work, a comparison has been made between the performance of simulated annealing and current multicriteria evaluation methods to delimit green infrastructure multifunctional buffer zones in an area of north-western Spain with a very fragmented landscape. Results have shown that simulated annealing delimits more regular multifunctional buffer areas but with a less average potential for providing multiple ecosystem services. The conclusions of the paper indicate that simulated annealing is good produces more regular multifunctional areas but with a lower ESs provision potential. It was observed that in the case of ESs that were mapped considering factors at landscape scale, their provision potential did not vary too much between the multifunctional buffer areas delimited with each of the methods. This indicates that delineation methods may produce more regular GI elements if ESs provision potential is mapped considering the influence of biophysical factors at a wider landscape scale.

Research on tomography algorithm of furnace flame temperature field based on acoustic method in thermal power station

An improved Tikhonov regularization algorithm MCTR based on Markov radial basis function is proposed to obtain the feedback of closed-loop control for pulverized coal injection process in thermal power plant, so as to solve the ill posed problem in temperature field reconstruction in furnace. The algorithm constructs a new regularization matrix to replace the standard Tikhonov regularization element matrix, so as to achieve the correction effect of the new algorithm. MCTR algorithm determines the boundary singular value of small singular value defined in this paper by determining the proportion between the standard deviation component corresponding to small singular value and the sum of standard deviation components corresponding to all singular values after singular value decomposition of coefficient matrix. After determining the boundary, a new regularization matrix is constructed according to the eigenvector corresponding to small singular value. Compared with the MTR algorithm using the identity matrix as the regularization matrix, MCTR algorithm only selectively modifies the parameters corresponding to small singular values after determining the regularization parameters, which improves the stability of the parameter solution and the reconstruction accuracy of the temperature field, and is helpful to the automatic control of thermal power plants and the efficiency of coal combustion.

The Collaborative Folktale Project of a Family: The Synoptic Critical Edition of a 19th-Century Hungarian Folktale and Riddle Collection

AbstractIn 1862, a volume of tales was published under the title Eredeti népmesék (‘Original Folktales’) by László Arany, the then 18-year-old son of János Arany, the national poet of the period. Eredeti népmesék has been classified by folkloristics as the first canonical folktale collection in Hungary. Besides scholarly recognition, it has also become one of the most popular folktale collections of the past one and a half century, as selected tales from this collection have been continuously republished in schoolbooks and anthologies and have become a regular element in children's literature. After the Second World War, in the basement of the main building of the Hungarian Academy of Sciences in Budapest, a huge pile of manuscripts had been found in very poor condition, consisting of, among others, various 19th-century folklore collections. In the 1960s, it was discovered that a part of these manuscripts was identical to the texts published in Eredeti népmesék. The vast majority of the manuscript tales had been recorded by the family members of János Arany, namely, his young daughter (Julianna Arany) and his wife (Julianna Ercsey), in the period between 1850 and 1862, presumably for family use. A comparison of the manuscript texts with their published versions revealed that in the editing process, László Arany significantly reworked the texts of the manuscript tales, implementing significant stylistic modifications. This article reports on the research project underlying the synoptic critical edition of the manuscript and published tales of the Arany family (2018). In the first part, the author presents the manuscript and published tales and their place in the history of Hungarian folkloristics, followed by an introduction of the members of the Arany family with an emphasis on their socio-cultural background, and concluding with a discussion of the roles they played in this collaborative folktale project as collectors, editors, copy editors, and theoreticians. The second part is a summary of the textological concept and techniques applied in the course of the development of the synoptic critical edition.

Linear eigenvalue analysis of laminated thin plates including the strain gradient effect by means of conforming and nonconforming rectangular finite elements

The paper presents a finite element method to investigate the critical buckling loads and the natural frequencies of laminated Kirchhoff plates including the nonlocal strain gradient effect, which could have considerably consequences at the nanoscale. With respect to the existing literature, the proposed numerical methodology is developed to deal with general stacking sequences of orthotropic layers with arbitrary orientations and various boundary conditions. The resulting membrane-bending coupling is emphasized in the formulation, which requires to study the whole set of partial differential equations. The membrane and bending degrees of freedom are all approximated by means of Hermite interpolating functions with higher-order continuity requirements. To this aim, regular rectangular finite elements based on conforming (C) and nonconforming (NC) approaches are used. A wide validation procedure is carried out to prove the effectiveness of the proposed formulation. A set of new results is presented for general mechanical configurations with arbitrary restraints.

Overgroups of regular unipotent elements in simple algebraic groups

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly when their connected component is a torus. This extends the earlier result of Testerman and Zalesski treating connected reductive subgroups.

Pre-adolescents narrate classroom experience

Abstract This study applies sociocultural narrative theory and method to integrate children’s perspectives into research on classroom climate. Sociocultural narrative theory explains how individuals use expressive genres to make sense of environments, how they fit, and what they would like to change. This study incorporates such theory and method into a qualitative research design, applying quantitative analysis techniques to understand trends in student attention and expression. The main goal of this study is to examine whether and how students enact and express socioemotional and spatiotemporal (climate) sensitivities with their use of regular narrative elements. This study employs plot and character analyses to understand 22 sixth graders’ narrations of best and worst classroom experiences. These analyses reveal diverse patterns of focus on classroom events. Differences in the young narrators’ attention highlight areas for ongoing inquiry, with implications for mixed methods studies of classroom climate and related developmental research.