Search results for " Homology"
showing 10 items of 633 documents
M-bornologies on L-valued Sets
2017
We develop an approach to the concept of bornology in the framework of many-valued mathematical structures. It is based on the introduced concept of an M-bornology on an L-valued set (X, E), or an LM-bornology for short; here L is an iccl-monoid, M is a completely distributive lattice and \(E: X\times X \rightarrow L\) is an L-valued equality on the set X. We develop the basics of the theory of LM-bornological spaces and initiate the study of the category of LM-bornological spaces and appropriately defined bounded “mappings” of such spaces.
The perturbation classes problem for closed operators
2017
We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.
A new incremental method of computing the limit load in deformation plasticity models
2015
The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter $\zeta\in[0,\zeta_{lim})$, where $\zeta_{lim}$ is generally unknown. In the new method, the incremental procedure is operated in terms of an inverse mapping and the respective parameter $\alpha$ is changing in the interval $(0,+\infty)$. Theoretically, in each step of this algorithm, we obtain a guaranteed lower bound of $\zeta_{lim}$. Reduction of the problem to a finite element subspace associated with a mesh $\mathcal T_h$ generates computable bound $\zeta_{lim,h…
Blow-up of the non-equivariant 2+1 dimensional wave map
2014
It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.
CHEVALLEY COHOMOLOGY FOR KONTSEVICH'S GRAPHS
2005
We introduce the Chevalley cohomology for the graded Lie algebra of polyvector fields on $R^d$. This cohomology occurs naturally in the problem of construction and classification of fomalities on the sapce $ R^d$. Considering only graphs formalities, we define the Chevalley cohomology directly on spaces of graphs. We obtain some simple expressions for the Chevalley coboundary operator and we give examples and applications.
SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS
2001
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using two-sided semi-ideals, one using commutators, and one based on Schwartz spaces on the groupoid.
Cohomology and associated deformations for not necessarily co-associative bialgebras
1992
In this Letter, a cohomology and an associated theory of deformations for (not necessarily co-associative) bialgebras are studied. The cohomology was introduced in a previous paper (Lett. Math. Phys.25, 75–84 (1992)). This theory has several advantages, especially in calculating cohomology spaces and in its adaptability to deformations of quasi-co-associative (qca) bialgebras and even quasi-triangular qca bialgebras.
Cloning of Two Putative Ecdysteroid Receptor Isoforms from Tenebrio Molitor and their Developmental Expression in the Epidermis during Metamorphosis
1997
Using the Drosophila EcR-B1 cDNA as a probe, we have cloned the putative ecdysteroid receptor from the mealworm Tenebrio molitor. We have isolated two cDNAs with different 5' termini that contain a complete open reading frame. These two cDNAs encode two proteins with distinct N-terminal regions corresponding to two isoforms. The coleopteran receptor is obviously related to the ecdysteroid receptor of other insects, but shares only 89% and 61% amino acid identities with the DNA-binding and ligand-binding domains of the Drosophila receptor, respectively. Its expression pattern has been examined in the epidermis during the last larval instar and pupal stage of T. molitor, in correlation with t…
Glial expression of Swiss cheese (SWS), the Drosophila orthologue of neuropathy target esterase (NTE), is required for neuronal ensheathment and func…
2016
ABSTRACT Mutations in Drosophila Swiss cheese (SWS) or its vertebrate orthologue neuropathy target esterase (NTE), respectively, cause progressive neuronal degeneration in Drosophila and mice and a complex syndrome in humans that includes mental retardation, spastic paraplegia and blindness. SWS and NTE are widely expressed in neurons but can also be found in glia; however, their function in glia has, until now, remained unknown. We have used a knockdown approach to specifically address SWS function in glia and to probe for resulting neuronal dysfunctions. This revealed that loss of SWS in pseudocartridge glia causes the formation of multi-layered glial whorls in the lamina cortex, the firs…
Evolutionary conservation of the structural, pharmacological, and genomic characteristics of the melanocortin receptor subtypes
2005
We have cloned melanocortin receptors (MCRs) from several species of fish. The MC4R and MC5R subtypes arose early in vertebrate evolution and their primary structure is remarkably conserved. Expression and pharmacological characterization of the MCRs in fish has revealed that they bind and respond to melanocortin peptides with high potency. Detailed characterization of the binding properties of the different subtypes suggests that MCRs in early vertebrates had preference for adrenocorticotropic hormone (ACTH) peptides, while the high sensitivity for the shorter proopiomelanocortin (POMC) products, such as the alpha-, beta-, and gamma-melanocyte-stimulating hormone (MSH), has appeared later,…