Search results for "Abstract algebra"
showing 10 items of 452 documents
Hidden supersymmetries in supersymmetric quantum mechanics
2001
We discuss the appearance of additional, hidden supersymmetries for simple 0+1 $Ad(G)$-invariant supersymmetric models and analyse some geometrical mechanisms that lead to them. It is shown that their existence depends crucially on the availability of odd order invariant skewsymmetric tensors on the (generic) compact Lie algebra $\cal G$, and hence on the cohomology properties of the Lie algebra considered.
Contractions of Filippov algebras
2010
We introduce in this paper the contractions $\mathfrak{G}_c$ of $n$-Lie (or Filippov) algebras $\mathfrak{G}$ and show that they have a semidirect structure as their $n=2$ Lie algebra counterparts. As an example, we compute the non-trivial contractions of the simple $A_{n+1}$ Filippov algebras. By using the \.In\"on\"u-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the $\mathfrak{G}=A_{n+1}$ simple case) the Lie algebras Lie$\,\mathfrak{G}_c$ (the Lie algebra of inner endomorphisms of $\mathfrak{G}_c$) with certain contractions $(\mathrm{Lie}\,\mathfrak{G})_{IW}$ and $(\mathrm{Lie}\,\mathfrak{G})_{W-W}$ of the Lie algebra Lie$\,\mathfrak{G}$ as…
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…
Bòvedas tabicadas: experimental and numerical analysis
2008
A class of thin vaults, the so-called “bovedas tabicadas”, which represent one of the most common Spanish traditional building techniques at the end of XIX century are studied here, treating the relevant analysis problem through a numerical, as well as an experimental, approach. At first the problem is studied by searching for the behaviour of the material effecting suitable experiments. Once the constitutive behaviour of the materials and the structural elements are experimentally characterized, a semi inverse method for the identification of the optimum mechanical parameters to assign to an equivalent homogeneous ideal material through analysis reproducing the executed experimental tests …
Technique of Statistical Validation of Rival Models for Fatigue Crack Growth Process and Its Identification
2011
The development of suitable models of stochastic crack growth process is important for the reliability analysis of fatigued structures as well as the scheduling of inspection and repair/replacement maintenance. Based on modifications of the solution of the deterministic differential equation for the crack growth rate, where a stochastic nature of this rate is expressed by a random disturbance embedded in the solution of the differential equation, the simple stochastic models are presented for practical applications. Each of these models represents a stochastic version of the solution of the Paris-Erdogan law equation. The models take into account the random disturbance parameters while main…
An efficient method for clustered multi-metric learning
2019
Abstract Distance metric learning, which aims at finding a distance metric that separates examples of one class from examples of the other classes, is the key to the success of many machine learning tasks. Although there has been an increasing interest in this field, learning a global distance metric is insufficient to obtain satisfactory results when dealing with heterogeneously distributed data. A simple solution to tackle this kind of data is based on kernel embedding methods. However, it quickly becomes computationally intractable as the number of examples increases. In this paper, we propose an efficient method that learns multiple local distance metrics instead of a single global one.…
On the solution growth of single crystals of solid solutions
1986
Abstract Homogeneous solid solution crystals are needed for studying the behaviour of systems with a glass state or incommensurate phases. A simple solution growth procedure is described. It is based on a temperature difference growth method with thermally enforced convection and the use of equilibrated solid and liquid solutions. First results of its application to the [(CH3)4N]2ZnCl 4−xBrx and the Rb1−x(NH4)xH2PO4 systems are presented.
A Nonconventional Approach toward Multihydroxy Functional Polystyrenes Relying on a Simple Grignard Reagent
2020
Capitalizing on the inertness of styrene toward Grignard reagents, 4-vinylphenylmagnesium bromide was utilized for the rapid and convenient preparation of the protected monomer 2,2-dimethyl-4-(4-vi...
Ascorbic acid decomposition into oxalate ions: a simple synthetic route towards oxalato-bridged heterometallic 3d-4f clusters.
2015
Two types of oxalato-bridged heterometallic 3d–4f dodeca- and hexanuclear compounds have been obtained by connecting six bi- and, respectively, trinuclear moieties through oxalato bridges arising from the slow decomposition of the L-ascorbic acid.
Control zeros and nonminimum phase LTI mimo systems
1999
Abstract The paper presents a new, general, inverse-model/output-zeroing approach to zeros of LTI discrete-time multivariable, possibly nonsquare systems. It is shown on simple examples that the existing definitions of multivariable zeros fail to detect certain important zeros which contribute to zeroing the system output. As a result, a concept of ‘control zeros’ is introduced, followed by a general redefinition of minimum/nonminimum phase systems, both new contributions being based on the notion of (generalized) inverse systems. Output-zeroing/inverse-model/minimum-variance control-related justifications of the new approach are presented.