Regular Elements Research Articles

Regular elements in bases of Hecke algebras

Let G˜=GL(n,F¯q) where q is a power of a prime. Let F be the standard Frobenius map of G˜. Let B˜ denote the Borel subgroup of G˜ of upper triangular matrices in G˜ and let T˜ denote the maximal split torus of G˜ contained in B˜. Let W denote the Weyl group of the B˜,N˜ pair where N˜=NG˜(T˜). Let w∈W and let w˙ denote an element in the pre-image of the natural surjection map from NG˜(T˜) to W. The double coset B˜w˙B˜ contains only regular elements if and only if w is a Coxeter element of minimal length. In the following we consider an element w∈W that is not of minimal length and thus B˜wB˜ contains nonregular elements. We explicitly describe certain cosets that are subsets of B˜wB˜ and contain only regular elements. These cosets are chosen for their importance in the construction of a basis of a Hecke algebra associated with G=G˜F.

Field programmable gate array implementation of variable‐bins high efficiency video coding CABAC decoder with path delay optimisation

Context-based adaptive binary arithmetic coding (CABAC) is a single operation mode for entropy coding in the last video coding standard high-efficiency video coding. For high-resolution applications, the throughput of one bin/cycle is not sufficient and it is a very challenging task to implement pipeline and/or parallel CABAC decoding architecture by simply adding more stages. Indeed, the tight data dependencies make it difficult to parallelise and cause it to be a throughput bottleneck for video decoding. Consequently, in order to improve the CABAC decoder throughput, parallel and pipeline architectures are used in authors’ design. In this work, an algorithm-architecture adequation is proposed to implement a CABAC decoder on a field programmable gate array. Mainly, a new classification of 32 syntax elements is given to speed up the authors’ solution. Furthermore, the context selection and modelling of regular syntax elements are studied, designed and implemented. Finally, a novel technique of memories rearrangement to reduce the critical path delay required to process each binary symbol is proposed. As a result, the implementation can process 2.2 bins/cycle when operated at 123.49 MHz and exhibits an improved high-throughput of 271.678 Mbins/s. The hardware architecture is coded using hardware description language and synthesised using ISE Xilinx tools targeting the Virtex4 platform.

Modified general relativity

In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric tensors can be constructed in terms of the Lie derivative along $ \bm{X} $ of the metric and a product of the unit vectors; and a linear sum of divergenceless symmetric tensors. A modified Einstein equation of general relativity is then obtained by using the principle of least action, the decomposition and a fundamental postulate of general relativity. The decomposition introduces a new symmetric tensor $ \varPhi_{\alpha\beta} $ which describes the energy-momentum of the gravitational field. It completes Einstein's equation and addresses the energy localization problem. Variation of the action with respect to $ X^{\mu} $ restricts $u_{\mu}$ to a particular value, which defines the possible Lorentzian metrics. $ \Phi $, the trace of $ \varPhi_{\alpha\beta} $, describes dark energy. The cosmological constant is dynamically replaced by $ \Phi $. A cyclic universe that developed after the Big Bang is described. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch. Assuming dark matter does not exist, a solution to the modified Einstein equation introduces two additional terms into the Newtonian radial force equation, from which the baryonic Tully-Fisher relation is obtained.

Interactions of p53 with poly(ADP-ribose) and DNA induce distinct changes in protein structure as revealed by ATR-FTIR spectroscopy.

Due to multiple domains and in part intrinsically disordered regions, structural analyses of p53 remain a challenging task, particularly in complex with DNA and other macromolecules. Here, we applied a novel attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopic approach to investigate changes in secondary structure of full-length p53 induced by non-covalent interactions with DNA and poly(ADP-ribose) (PAR). To validate our approach, we confirmed a positive regulatory function of p53’s C-terminal domain (CTD) with regard to sequence-specific DNA binding and verified that the CTD mediates p53–PAR interaction. Further, we demonstrate that DNA and PAR interactions result in distinct structural changes of p53, indicating specific binding mechanisms via different domains. A time-dependent analysis of the interplay of DNA and PAR binding to p53 revealed that PAR represents p53’s preferred binding partner, which efficiently controls p53–DNA interaction. Moreover, we provide infrared spectroscopic data on PAR pointing to the absence of regular secondary structural elements. Finally, temperature-induced melting experiments via CD spectroscopy show that DNA binding stabilizes the structure of p53, while PAR binding can shift the irreversible formation of insoluble p53 aggregates to higher temperatures. In conclusion, this study provides detailed insights into the dynamic interplay of p53 binding to DNA and PAR at a formerly inaccessible molecular level.

On the undrained and drained hydraulic fracture splits

SummaryThe simulation of hydraulic fracturing (HF) involves the solution of a hydro‐mechanically coupled system. This article presents a new iterative sequential coupling algorithm, the undrained HF split, that improves the simulation of HFs in impermeable media. A poromechanics analogy is used to derive a stable split for the hydro‐mechanically coupled system in which the mechanical subproblem is solved first. The proposed undrained HF split is applied to the simulation of cohesive HFs in an impermeable elastic medium. The cubic law is used as the constitutive model for simulating fluid flow in fractures. A minimum hydraulic aperture is assumed in the cohesive tip zone, where the mechanical aperture smoothly vanishes. While general in its nature, the undrained HF splitting scheme is employed within the context of a two‐dimensional eXtended finite element model for the fractured solid, and a regular finite element model for fluid in the fracture. The undrained HF split is successfully used to simulate self‐similar plane strain HFs as well as the propagation of HFs from a wellbore under anisotropic stress conditions. Fracture trajectories and local alteration of stress field are investigated. The solution of the undrained HF split converges to the same solution as the fully coupled model, whereas the commonly used P→W sequential algorithm, referred to in this article as the drained HF split, generates spurious oscillations and fails to converge in many problems. The undrained HF split is shown to be stable and robust in applications where the drained HF split is unstable.

Bases of Leavitt path algebras with only strongly regular elements

Recent articles consider invertible and locally invertible algebras (respectively, those having a basis consisting solely of invertible or solely of strongly regular elements). Previous contributions to the subject include the study of when Leavitt path algebras are invertible. This article investigates the local invertibility property in Leavitt path algebras. A complete classification of strongly regular monomials in Leavitt path algebras is given. Additionally, it is show that all directly finite and (von Neumann) regular Leavitt path algebras are locally invertible. It is also shown that a Leavitt path algebra has a basis consisting solely of strongly regular monomials if and only if it is commutative.

Diagonal reduction of matrices over commutative semihereditary Bezout rings

It is proven that every commutative semihereditary Bezout ring in which any regular element is Gelfand (adequate), is an elementary divisor ring.

On clean and regular elements of noncommutative ring extensions

Let R be an associative ring with identity and α be an endomorphism of R. In this article, we are interested to study the some of relations between a ring R and that of D. A. Jordan’s construction of the ring A(R,α) as well as the skew Laurent polynomial ring . The main propose of this article is to characterize the unit elements, the idempotent elements, von Neumann regular elements, π-regular elements, von Neumann local elements and also the clean elements of the skew Laurent polynomial ring as well as Jordan’s construction of the ring A(R,α). Applying these characterizations, one can easily get some nice radical-theoretic properties of the mentioned classes of rings.

The AMORE paradigm for finite element analysis

The objective in this paper is to largely review, but also give new insight into, the recent development of a novel paradigm for finite element analysis. The approach enables much easier meshing than usually performed for finite element analysis and then the computationally efficient solution of the finite element model. The important aspects of the paradigm are the automatic meshing on any given geometry (typically given by use of a CAD program or a computerized scan) with the use of overlapping and regular finite elements – hence the acronym AMORE for Automatic Meshing with Overlapping and Regular Elements. We summarize the basic steps used in the paradigm, give the basic equations to formulate the overlapping elements, discuss specific attributes, give some applications and conjecture on the further development and use of the solution scheme. Our discussion is based on previously published work with a focus on simplifying the formulation of the overlapping elements, providing novel insight, and suggesting a notation. The paradigm has so far only been applied in the linear analyses of solids, however embodies significant potential for general and wide use in computer-aided engineering.

A generalization of co-maximal graph of commutative rings

Let [Formula: see text] be a commutative ring with [Formula: see text]. Let [Formula: see text] be a graph with vertices as elements of [Formula: see text], where two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] for some non-zero idempotent [Formula: see text] in [Formula: see text]. In this paper, we establish a relation between completeness of the graph [Formula: see text] and regularity of the ring [Formula: see text]. For a finite commutative ring [Formula: see text] with [Formula: see text], we show that the chromatic number of [Formula: see text] is equal to the number of regular elements in [Formula: see text]. Moreover, we characterize some graph theoretic properties of [Formula: see text] and finally we characterize Eulerian property of the graph [Formula: see text].

Asymptotic associate primes

We investigate three cases regarding asymptotic associate primes. First, assume (A,m) is an excellent Cohen–Macaulay (CM) non-regular local ring, and M=Syz1A(L) for some maximal CM A-module L which is free on the punctured spectrum. Let I be a normal ideal. In this case, we examine when m∉Ass(M/InM) for all n≫0. We give sufficient evidence to show that this occurs rarely. Next, assume that (A,m) is excellent Gorenstein non-regular isolated singularity, and M is a CM A-module with projdimA(M)=∞ and dim⁡(M)=dim⁡(A)−1. Let I be a normal ideal with analytic spread l(I)<dim⁡(A). In this case, we investigate when m∉AssTor1A(M,A/In) for all n≫0. We give sufficient evidence to show that this also occurs rarely. Finally, suppose A is a local complete intersection ring. For finitely generated A-modules M and N, we show that if ToriA(M,N)≠0 for some i>dim⁡(A), then there exists a non-empty finite subset A of Spec(A) such that for every p∈A, at least one of the following holds true: (i) p∈Ass(Tor2iA(M,N)) for all i≫0; (ii) p∈Ass(Tor2i+1A(M,N)) for all i≫0. We also analyze the asymptotic behavior of ToriA(M,A/In) for i,n≫0 in the case when I is principal or I has a principal reduction generated by a regular element.

-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS

Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p&gt;0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman, $x$ is contained in a connected subgroup of $G$ of type $A_{1}$. In this paper we prove that with two exceptions, $X$ itself is contained in such a subgroup (the exceptions arise when $(G,p)=(E_{6},13)$ or $(E_{7},19)$). This extends earlier work of Seitz and Testerman, who established the containment under some additional conditions on $p$ and the embedding of $X$ in $G$. We discuss applications of our main result to the study of the subgroup structure of finite groups of Lie type.

XML-TEI Stand-off Markup: One Step Beyond

Stand-off markup is widely considered as a possible solution for overcoming the limitation of inline XML markup, primarily dealing with multiple overlapping hierarchies. Considering previous contributions on the subject and implementations of stand-off markup, we propose a new TEI-based model for encoding, that still uses the regular TEI elements, but in a stand-off manner. Our light notation moves the bulk of markup into a separate element, grouping layers of related textual features encoded via existing TEI elements (eg. or ) into individual elements; furthermore, our proposed notation provides a schema for referencing the transcription using the xml:id attribute. This approach is illustrated through a variety of examples. Our proof-of-concept transformation package works directly on the stand-off markup, without the necessity of reducing it back to inline TEI for parsing, querying and visualizing.

Методика формирования численного проекционно-сеточного алгоритма на основе «трехмерного регулярного элемента» для расчета 3D-моделей магнитного поля в цилиндрической системе координат для синхронных магнитоэлектрических машин в составе высокотехнологических электротехнических комплексов

Методика формирования численного проекционно-сеточного алгоритма на основе «трехмерного регулярного элемента» для расчета 3D-моделей магнитного поля в цилиндрической системе координат для синхронных магнитоэлектрических машин в составе высокотехнологических электротехнических комплексов

ПРОСТОРОВО-ЧАСОВИЙ АНАЛІЗ ФОРМУВАННЯ СТРУКТУРИ СУЧАСНИХ САДОВО-ПАРКОВИХ ЛАНДШАФТІВ ПРАВОБЕРЕЖНОЇ УКРАЇНИ

The spatial and temporal analysis of the formation of the structure of garden-park landscapes of the Right-Bank Ukraine on the example of the National Dendrology Park “Sofiyivka” of the National Academy of Sciences of Ukraine, Alexandria Dendrological Park the National Academy of Sciences of Ukraine, Sinitsky Park of Cherkassy region, Nemirovsky Park, Sokiletsky and Pechersk parks of Vinnitsa region were done in the article. The emphasis was placed on the spatial location of Right-Bank Ukraine, the peculiarities of natural conditions and the diversity of natural landscapes, which determined the attractiveness of the territory for its development by different peoples and ethnic groups. The boundary of the situation led to the interaction and overlay of Western European and Eastern European cultures, the material expression of which are garden-park landscapes. Garden-park landscapes are a special group of anthropogenic landscapes, which are composed of natural and technical blocks. The features of the technical block are determined not only by the natural conditions of the territory but also by the culture of the organization and creation of the garden-park landscapes that is characteristic of the corresponding historical period. It was noted that in the landscape structure of the old garden-park landscapes, there are a river, floodplain, sloping and watershed types of areas that are typical for the research area. Formation, functioning and development of gardens and parks are associated with the peculiarities of the socio-economic and historical development of the territory. The river-floodplain type of terrain is represented by tracts of rivers, ponds, islands, levelling surfaces, occupied by meadow vegetation. Mostly, the tracts of this type of terrain are complicated by such landscape-technical systems as bridges and dams. On average, the river-floodplain type of terrain accounts for 10 to 20% of the area of the garden park landscape. The sloping type of terrain includes a variety of simple and complex tracts with steep slopes of 50 to steep sloping walls. Busy, mostly, parked plantations and ray fields. Landscape-technical systems are represented by different types of stairs. This type of terrain accounts for the largest share of a garden-park landscape – from 60% to 90%. This fact is connected with the specifics of the organization of garden-park landscapes within the territory of Right-Bank Ukraine. Watershed type of terrain is represented by tracts of weakly wavy surfaces. It includes a park building, which is represented by various buildings. Regardless of the landscape style of planning the territory, within the limits of the water-type type of terrain, there are regular elements of the organization of the territory – they are alleys, parterals, bosqueets, etc. Up to 20% of the area of the landscape garden landscape belongs to the tract of the watershed type of terrain. It was concluded that most of the garden-parf landscapes of Right-bank Ukraine are now in poor condition. In order to preserve and improve the modern structure of garden-park landscapes, the following measures should be taken: to significantly expand their areas and improve the functioning of the infrastructure elements; to regulate the boundaries of garden-park landscapes and to pay more attention to their paragenetic and paradigmatic interconnections with the surrounding territories: to clearly outline the role and significance of existing and future garden-park landscapes in the structure of regional ecosystems.

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The purpose of this paper is to study some results of homological algebra in the category A-Alg (resp. Alg-A) of left (resp. right) A-algebra in the noncommutative case. In this paper A is a subring of B. So the main results of this paper are, if B is a noetherian duo-ring, S a central saturated multiplicatively closed subset of A, SR the set of regular elements of S, a finitely presented right A-algebra and a (B-A)-bialgebra, then is isomorphic to , also is isomorphic to , for any integer n.

EVALUATING THE WORKING EFFICIENCY OF A STATIC COOLING SYSTEM UNDER MODERNIZATION OF A POWER INSTALLATION BY DYNEL REPLACEMENT

Problem. Every year the transport engineering industry creates new and improves old transport means, the volume of which exceeds millions of units annually, this includes cars, boats, tanks, etc. In most cases, modernization is not cost-effective due to the introduction of a large number of changes in the design. A separate unit is a ground transportation vehicle, which was produced in large quantities more than 40 years ago, it is obsolete technically and requires modernization. One of the possible options for modernization is the replacement of the obsolete diesel by a more modern, more powerful one. In the case of this machine, a variant with a diesel engine upgrade of the 5TDF type is proposed. Goal. Determine the methodology for assessing the working capacity of the regular cooling system of a ground-based transport vehicle with a V-46-6 diesel engine during modernization by replacing the internal combustion engine with domestic-produced diesel. Methodology. The analysis of design features of the cooling systems for the regular and new diesel, the speed of the heat carriers, their types, etc., was used to estimate the amount of heat by the standard cooling system with a standard diesel engine and simulate the operation of the standard heat exchangers together with a new diesel engine of the type 5TDF with the subsequent estimation of an opportunity of maintenance of working capacity of the given diesel engine by comparison of the brought up heat by a diesel engine and the greatest possible quantity of heat taken away exchangers. Result. The performance of the power plant was evaluated during the modernization of the ground transport vehicle with the V-46-6 diesel engine by replacing the diesel with a new one, type 5TDF with the preservation of the regular elements of the cooling system. It is determined that the regular cooling system allows to ensure the operation of a power plant of a ground transport vehicle with a diesel engine of the type 5TDF at the operating mode of operation. Origina­lity. Due to the fact that earlier similar studies were carried out in the stand conditions this technique will allow us to simulate the operation of the cooling system before installing a new diesel engine on the upgraded facility. Practical value. The method allows to evaluate the efficiency of the regular cooling system of the modernized transport vehicle with the new engine of the power plant.

Correction of aggregation level of basic regular blood elements in patients with hypertension and dyslipidemia receiving rosuvastatin and non-medicinal treatment

Correction of aggregation level of basic regular blood elements in patients with hypertension and dyslipidemia receiving rosuvastatin and non-medicinal treatment

IMPROVED RELIABILITY OF OPERATION OF GAS SUPPLY SYSTEMS ON THE BASIS OF SERVICE OPTIMIZATION

General principles of the spare parts amount selection when operating gas supply systems for renewable and non-renewable elements have been developed. Nomenclature is considered as a list of numbers and names of reserve instruments and equipment, which is compiled in accordance with a certain grouping and sequencing according to the producing plants technical documentation and which includes mechanical details, assemblies, and aggregates. The assessment criteria of the spare parts set sufficiency have been chosen based on the condition of the sufficient system operation reliability which is based on the estimates of the failure emergence probability during the period of regular element removals. The demand for spare parts and materials is of random nature and it is considered as a stable process which is described by the Poisson’s distribution. The calculation principle comes down to determining the possibility of the fact that all the service channels and waiting spaces in the mechanism will be filled in accordance with the queuing theory. The technique for spare parts amount selection when operating gas supply systems has been developed eventually.

Fast tetrahedral mesh generation and segmentation of an atlas-based heart model using a periodic uniform grid

Abstract A fast procedure for generation of regular tetrahedral finite element mesh for objects with complex shape cavities is proposed. The procedure like LBIE-Mesher can generate tetrahedral meshes for the volume interior to a polygonal surface, or for an interval volume between two surfaces having a complex shape and defined in STL-format. This procedure consists of several stages: generation of a regular tetrahedral mesh that fills the volume of the required object; generation of clipping for the uniform grid parts by a boundary surface; shifting vertices of the boundary layer to align onto the surface.We present a sequential and parallel implementation of the algorithm and compare their performance with existing generators of tetrahedral grids such as TetGen, NETGEN, and CGAL. The current version of the algorithm using the mobile GPU is about 5 times faster than NETGEN. The source code of the developed software is available on GitHub.