Search results for "singular"
showing 10 items of 589 documents
The Bruce–Roberts Number of A Function on A Hypersurface with Isolated Singularity
2020
AbstractLet $(X,0)$ be an isolated hypersurface singularity defined by $\phi \colon ({\mathbb{C}}^n,0)\to ({\mathbb{C}},0)$ and $f\colon ({\mathbb{C}}^n,0)\to{\mathbb{C}}$ such that the Bruce–Roberts number $\mu _{BR}(f,X)$ is finite. We first prove that $\mu _{BR}(f,X)=\mu (f)+\mu (\phi ,f)+\mu (X,0)-\tau (X,0)$, where $\mu $ and $\tau $ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen–Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which the hypersurface $(X,0)$ was assumed to be weighted homogeneous.
Input-to-state stability for discrete-time nonlinear switched singular systems
2016
Discrete-time nonlinear switched singular systems (SSSs) are investigated.The input-to-state stability (ISS) problems for discrete-time nonlinear SSSs are concerned.The ISS criteria are obtained via average dwell time approach and iterative algorithm of discrete-time systems.The switching rules are optimized and designed. This paper investigates the input-to-state stability (ISS) problems for a class of discrete-time nonlinear switched singular systems (SSSs). Two novel ISS criteria are proposed based on average dwell time (ADT) approach and iterative algorithm of discrete-time systems (IADS). In particular, the following two cases are considered for the underlying systems: the first case i…
Invariant varieties of discontinuous vector fields
2004
We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
2014
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance…
Analysis of singular bilinear systems using Walsh functions
1991
The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…
Large negative magnetoresistance effects in Co2Cr0.6Fe0.4Al
2003
Abstract Materials, which display large changes in resistivity in response to an applied magnetic field (magnetoresistance) are currently of great interest due to their potential for applications in magnetic sensors, magnetic random access memories, and spintronics. Guided by striking features in the electronic structure of several magnetic compounds, we prepared the Heusler compound Co2Cr0.6Fe0.4Al. Based on our band structure calculations, we have chosen this composition in order to obtain a half-metallic ferromagnet with a van Hove singularity in the vicinity of the Fermi energy in the majority spin channel and a gap in the minority spin channel. We find a magnetoresistive effect of 30% …
A singular case of near-haploid stemline karyotype in a renal oncocytoma.
1996
Cytogenetic analysis of a human renal oncocytoma revealed a near-haploid chromosome number of 36 with the loss of chromosomes 1, 2, 3, 6, 8, 9, 15, 17, 21, and 22. Review of the literature disclosed that this cytogenetic configuration is extremely rare in solid human tumors and that no renal oncocytomas with near-haploid stemline karyotype have been described. These results are compared with the other published cases of oncocytoma.
Three dimensional reconstruction to visualize atrial fibrillation activation patterns on curved atrial geometry
2021
BackgroundThe rotational activation created by spiral waves may be a mechanism for atrial fibrillation (AF), yet it is unclear how activation patterns obtained from endocardial baskets are influenced by the 3D geometric curvature of the atrium or ‘unfolding’ into 2D maps. We develop algorithms that can visualize spiral waves and their tip locations on curved atrial geometries. We use these algorithms to quantify differences in AF maps and spiral tip locations between 3D basket reconstructions, projection onto 3D anatomical shells and unfolded 2D surfaces.MethodsWe tested our algorithms in N = 20 patients in whom AF was recorded from 64-pole baskets (Abbott, CA). Phase maps were generated by…
Magnetic Heusler Compounds
2013
Abstract Heusler compounds are a remarkable class of intermetallic materials with 1:1:1 (often called Half-Heusler) or 2:1:1 composition comprising more than 1500 members. New properties and potential fields of applications emerge constantly; the prediction of topological insulators is the most recent example. Surprisingly, the properties of many Heusler compounds can easily be predicted by the valence electron count or within a rigid band approach. The wide range of the multifunctional properties of Heusler compounds is reflected in extraordinary magnetooptical, magnetoelectronic, and magnetocaloric properties. Co 2 -Heusler compounds are predicted and proven half-metallic ferromagnets sho…
Disorder-induced vibrational anomalies from crystalline to amorphous solids
2021
The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening th…