scholarly journals Multipliers and unicentral Leibniz algebras

2021 ◽  
pp. 2350008
Author(s):  
Erik Mainellis
Keyword(s):  
Spectral Sequence ◽  
Cohomology Group ◽  
Leibniz Algebras ◽  
Low Dimension ◽  
Definition Of ◽  
Exact Sequences

In this paper, we prove Leibniz analogues of results found in Peggy Batten’s 1993 dissertation. We first construct a Hochschild–Serre-type spectral sequence of low dimension, which is used to characterize the multiplier in terms of the second cohomology group with coefficients in the field. The sequence is then extended by a term and a Ganea sequence is constructed for Leibniz algebras. The maps involved with these exact sequences, as well as a characterization of the multiplier, are used to establish criteria for when a central ideal is contained in a certain set seen in the definition of unicentral Leibniz algebras. These criteria are then specialized, and we obtain conditions for when the center of the cover maps onto the center of the algebra.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

scholarly journals THE VAN EST SPECTRAL SEQUENCE FOR HOPF ALGEBRAS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 33-48 ◽  
Author(s):  
E. J. BEGGS ◽  
TOMASZ BRZEZIŃSKI
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Lie Algebra ◽  
Hopf Algebras ◽  
Cohomology Group ◽  
Spectral Sequences ◽  
De Rham Cohomology ◽  
Lie Algebra Cohomology ◽  
De Rham ◽  
Definition Of

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduced. A definition of Hopf–Lie algebra cohomology is also given.

scholarly journals Experimental Evaluation of Shear Behavior of Stone Masonry Wall

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2313
Author(s):  
Maria Luisa Beconcini ◽  
Pietro Croce ◽  
Paolo Formichi ◽  
Filippo Landi ◽  
Benedetta Puccini
Keyword(s):  
Shear Behavior ◽  
Stone Masonry ◽  
Masonry Walls ◽  
Mechanical Parameters ◽  
In Situ Tests ◽  
Capacity Curves ◽  
Historical Structures ◽  
Definition Of

The evaluation of the shear behavior of masonry walls is a first fundamental step for the assessment of existing masonry structures in seismic zones. However, due to the complexity of modelling experimental behavior and the wide variety of masonry types characterizing historical structures, the definition of masonry’s mechanical behavior is still a critical issue. Since the possibility to perform in situ tests is very limited and often conflicting with the needs of preservation, the characterization of shear masonry behavior is generally based on reference values of mechanical properties provided in modern structural codes for recurrent masonry categories. In the paper, a combined test procedure for the experimental characterization of masonry mechanical parameters and the assessment of the shear behavior of masonry walls is presented together with the experimental results obtained on three stone masonry walls. The procedure consists of a combination of three different in situ tests to be performed on the investigated wall. First, a single flat jack test is executed to derive the normal compressive stress acting on the wall. Then a double flat jack test is carried out to estimate the elastic modulus. Finally, the proposed shear test is performed to derive the capacity curve and to estimate the shear modulus and the shear strength. The first results obtained in the experimental campaign carried out by the authors confirm the capability of the proposed methodology to assess the masonry mechanical parameters, reducing the uncertainty affecting the definition of capacity curves of walls and consequently the evaluation of seismic vulnerability of the investigated buildings.

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

scholarly journals Genomic Tackling of Human Satellite DNA: Breaking Barriers through Time

2021 ◽  
Vol 22 (9) ◽  
pp. 4707
Author(s):  
Mariana Lopes ◽  
Sandra Louzada ◽  
Margarida Gama-Carvalho ◽  
Raquel Chaves
Keyword(s):  
Human Genome ◽  
Satellite Dna ◽  
Repetitive Sequences ◽  
Nucleotide Composition ◽  
Genomic Component ◽  
Genomic Studies ◽  
Human Genomic ◽  
Definition Of ◽  
High Degree

(Peri)centromeric repetitive sequences and, more specifically, satellite DNA (satDNA) sequences, constitute a major human genomic component. SatDNA sequences can vary on a large number of features, including nucleotide composition, complexity, and abundance. Several satDNA families have been identified and characterized in the human genome through time, albeit at different speeds. Human satDNA families present a high degree of sub-variability, leading to the definition of various subfamilies with different organization and clustered localization. Evolution of satDNA analysis has enabled the progressive characterization of satDNA features. Despite recent advances in the sequencing of centromeric arrays, comprehensive genomic studies to assess their variability are still required to provide accurate and proportional representation of satDNA (peri)centromeric/acrocentric short arm sequences. Approaches combining multiple techniques have been successfully applied and seem to be the path to follow for generating integrated knowledge in the promising field of human satDNA biology.

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

scholarly journals Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Matthew Yu
Keyword(s):  
Spectral Sequence ◽  
Global Symmetries ◽  
Group Symmetry ◽  
Low Dimension ◽  
The One ◽  
Group Symmetries

Abstract We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.

scholarly journals Characterization of Spent Ni-MH Batteries

2012 ◽  
Vol 730-732 ◽  
pp. 569-574
Author(s):  
Marta Cabral ◽  
Fernanda Margarido ◽  
Carlos A. Nogueira
Keyword(s):  
Quantitative Analysis ◽  
Electrode Materials ◽  
Phase Identification ◽  
Recycling Process ◽  
X Ray ◽  
Leaching Experiments ◽  
Plastic Components ◽  
Definition Of ◽  
Physical And Chemical

Spent Ni-MH batteries are not considered too dangerous for the environment, but they have a considerable economical value due to the chemical composition of electrodes which are highly concentrated in metals. The present work aimed at the physical and chemical characterisation of spent cylindrical and thin prismatic Ni-MH batteries, contributing for a better definition of the recycling process of these spent products. The electrode materials correspond to more than 50% of the batteries weight and contain essentially nickel and rare earths (RE), and other secondary elements (Co, Mn, Al). The remaining components are the steel parts from the external case and supporting grids (near 30%) containing Fe and Ni, and the plastic components (<10%). Elemental quantitative analysis showed that the electrodes are highly concentrated in metals. Phase identification by X-ray powder diffraction combined with chemical analysis and leaching experiments allowed advancing the electrode materials composition. The cathode is essentially constituted by 6% metallic Ni, 66% Ni(OH)2, 4.3% Co(OH)2 and the anode consists mainly in 62% RENi5 and 17% of substitutes and/or additives such as Co, Mn and Al.

scholarly journals Surface and Underground Geomechanical Characterization of an Area Affected by Instability Phenomena in Zaruma Mining Zone (Ecuador)

2021 ◽  
Vol 13 (6) ◽  
pp. 3272
Author(s):  
Paúl Carrión-Mero ◽  
Maribel Aguilar-Aguilar ◽  
Fernando Morante-Carballo ◽  
María José Domínguez-Cuesta ◽  
Cristhian Sánchez-Padilla ◽  
...  
Keyword(s):  
Mass Movement ◽  
Mining Activity ◽  
Mining District ◽  
Mean Values ◽  
Surface Areas ◽  
Definition Of ◽  
Action Measures ◽  
Geomechanical Characterization ◽  
The City

In the last decade, in the mining district of Zaruma-Portovelo, there has been significant land subsidence related to uncontrolled mining activity. The purpose of this work was to carry out a surface and underground geomechanical characterization of a mining sector north of the city of Zaruma that allows the definition of potentially unstable areas susceptible to the mass movement. The methodology used consists of the following stages: (i) compilation of previous studies; (ii) surface and underground characterization of rocky material to establish its susceptibility to mass movement; (iii) interpretation of results; and (iv) proposal of action measures. Among the most relevant results, it stands out that 26.1% of the 23 stations characterized on the surface present conditions that vary from potentially unstable to unstable. In underground galleries, the studied mean values of the 17 stations indicate that the rock has a medium to good quality, representing a medium susceptibility to gallery destabilization. The results obtained for the surface areas (depths up to 50 m, where altered materials predominate) and the underground areas (depths > 50 m, where the alterations are specific) can be used to identify the areas with a more significant potential for instability. For both cases, it has been possible to define specific monitoring, control, and planning actions for sensitive areas.

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