scholarly journals On the relative homology of q-Runge pairs

2000 ◽  
Vol 38 (1) ◽  
pp. 45-52
Author(s):  
Mihnea Colţoiu
Keyword(s):  
Relative Homology

Relative Homology

1994 ◽  
pp. 347-359
Author(s):  
M. Auslander ◽  
Ø. Solberg
Keyword(s):  
Relative Homology

Relative and Tate homology with respect to semidualizing modules

2014 ◽  
Vol 13 (08) ◽  
pp. 1450058 ◽  
Author(s):  
Zhenxing Di ◽  
Xiaoxiang Zhang ◽  
Zhongkui Liu ◽  
Jianlong Chen
Keyword(s):  
Exact Sequence ◽  
London Math ◽  
Projective Dimension ◽  
Relative Cohomology ◽  
Relative Homology ◽  
Semidualizing Module ◽  
Coherent Ring ◽  
Semidualizing Modules ◽  
Tate Homology ◽  
Dualizing Module

We introduce and investigate in this paper a kind of Tate homology of modules over a commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing module. We show firstly that the class of modules admitting a Tate ℱC-resolution is equal to the class of modules of finite 𝒢(ℱC)-projective dimension. Then an Avramov–Martsinkovsky type exact sequence is constructed to connect such Tate homology functors and relative homology functors. Finally, motivated by the idea of Sather–Wagstaff et al. [Comparison of relative cohomology theories with respect to semidualizing modules, Math. Z. 264 (2010) 571–600], we establish a balance result for such Tate homology over a Cohen–Macaulay ring with a dualizing module by using a good conclusion provided in [E. E. Enochs, S. E. Estrada and A. C. Iacob, Balance with unbounded complexes, Bull. London Math. Soc. 44 (2012) 439–442].

scholarly journals Inequalities of holographic entanglement of purification from bit threads

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Dong-Hui Du ◽  
Fu-Wen Shu ◽  
Kai-Xin Zhu
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Gravity ◽  
Entanglement Entropy ◽  
Geometric Analysis ◽  
Quantum Information Theory ◽  
Relative Homology ◽  
Holographic Entanglement Entropy ◽  
New Inequalities

Abstract There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology.

scholarly journals On Proper and Exact Relative Homological Dimensions

2020 ◽  
Vol 27 (03) ◽  
pp. 621-642
Author(s):  
Driss Bennis ◽  
J.R. García Rozas ◽  
Lixin Mao ◽  
Luis Oyonarte
Keyword(s):  
Homological Dimension ◽  
Dimension Theory ◽  
Relative Homology ◽  
Homological Dimensions ◽  
Derived Functors ◽  
Exact Sequences ◽  
Relative Homological Dimension

In Enochs’ relative homological dimension theory occur the (co)resolvent and (co)proper dimensions, which are defined by proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some authors have been interested in relative homological dimensions defined by just exact sequences. In this paper, we contribute to the investigation of these relative homological dimensions. First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs. Then relative global dimensions are studied, which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories. At the end of this paper, relative derived functors are studied and generalizations of some known results of balance for relative homology are established.

The second relative homology of Leibniz algebras

2020 ◽  
Vol 224 (1) ◽  
pp. 206-217
Author(s):  
Seyedeh Narges Hosseini ◽  
Behrouz Edalatzadeh ◽  
Ali Reza Salemkar
Keyword(s):  
Leibniz Algebras ◽  
Relative Homology

Human Platelet Glycoprotein VI: Identification of Residues Involved in the Binding to Collagen.

Blood ◽  
2004 ◽  
Vol 104 (11) ◽  
pp. 1550-1550
Author(s):  
Martine Jandrot-Perrus ◽  
Christelle Lecut ◽  
Veronique Arocas ◽  
Hans Ulrichts ◽  
Jean-Luc Villeval ◽  
...  
Keyword(s):  
Site Directed Mutagenesis ◽  
Platelet Glycoprotein ◽  
Directed Mutagenesis ◽  
Time Sharing ◽  
Binding Assays ◽  
Glycoprotein Vi ◽  
Linear Peptide ◽  
Relative Homology ◽  
Collagen Receptor ◽  
Competition Assays

Abstract Glycoprotein VI (GPVI), an essential platelet collagen receptor, belongs to the immunoglobulin (Ig) superfamily and presents two Ig-like loops in its extracellular domain (EC1, EC2). Little is known about the structures involved in GPVI binding to collagen and to its specific ligands, convulxin and collagen related peptides (CRP). Our aim was to characterize these sites using different approaches: competition assays, monoclonal antibodies (MoAb) directed against the GPVI extracellular par, phage display, molecular modelling and site-directed mutagenesis. In binding assays using soluble or cell-expressed human GPVI, we observed that: (i) collagen, CRP and convulxin, competed with one another for the binding to GPVI; (ii) GPVI interaction with either ligand is inhibited by at least two MoAb directed to different independent epitopes, and (iii) MoAb displayed selective inhibitory properties on GPVI interaction with each ligand. These observations indicate that the binding sites on GPVI for the diverse ligands seem to be distinct, exhibiting specific features but at the same time sharing common elements. MoAb 9O12 is a potent inhibitor of GPVI binding to collagen. Its epitope was mapped by screening a 15 mer linear peptide library. This allowed the identification of a motif of 7 residues of which 5 are conserved and that presented a relative homology with the GPVI 30–40 sequence. In a computer model, these residues appeared in close vicinity on a surface loop exposed at the surface of the molecule and accessible to ligands. Site-directed mutagenesis revealed that Val34 and Leu36 are critical for GPVI interaction with collagen and CRP. This study allowed the identification of residues within a loop on GPVI EC1 that might be part of a collagen/CRP-binding site.

Single-space axioms for homology theory

1959 ◽  
Vol 55 (1) ◽  
pp. 10-22 ◽  
Author(s):  
G. M. Kelly
Keyword(s):  
Homology Theory ◽  
Homology Groups ◽  
Relative Homology ◽  
The Absolute

Eilenberg and Steenrod(1) give a set of axioms for the homology theory of pairs of spaces and their maps, and prove that these axioms are categorical on triangulable pairs.Here we give a set of axioms for the homology theory of single spaces and their maps, that is, for absolute rather than relative homology. This axiomatization is shown to be essentially equivalent to that of Eilenberg and Steenrod, the relative homology groups being suitably denned in terms of the absolute groups.

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