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81.
In this article we give a complete global classification of the class QSess of planar, essentially quadratic differential systems (i.e. defined by relatively prime polynomials and whose points at infinity are not all singular), according to their topological behavior in the vicinity of infinity. This class depends on 12 parameters but due to the action of the affine group and re-scaling of time, the family actually depends on five parameters. Our classification theorem (Theorem 7.1) gives us a complete dictionary connecting very simple integer-valued invariants which encode the geometry of the systems in the vicinity of infinity, with algebraic invariants and comitants which are a powerful tool for computer algebra computations helpful in the route to obtain the full topological classification of the class QS of all quadratic differential systems. 相似文献
82.
Isothermal vapour—liquid equilibria have been determined for 2-butanone + acetonitrile at 333.67 K, and for 2-butanone + 1,2-dichloroethane and acetonitrile + 1,2-dichloroethane at 333.15 K using a dynamic method. The apparatus used in these studies for the precise measurement of complete vapour—liquid equilibrium data is described and the reliability and accuracy of the measured data are considered in terms of the activity coefficients and of the dependences of the molar excess Gibbs energies on composition. Experimental inaccuracies are estimated for statistical treatment of the data both in terms of correlations and in consistency tests. 相似文献
83.
84.
According to a result of Wigner and von Neumann, the dimension of the set
of n × n real symmetric matrices with multiple eigenvalues is equal to N −2, where N = n(n+1)/2. This value is determined
by counting the number of free parameters in the spectral decomposition of a matrix. We show that the same dimension is obtained
if
is interpreted as an algebraic variety. Bibliography: 4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 34–46. 相似文献
85.
Firanescu G Hermsdorf D Ueberschaer R Signorell R 《Physical chemistry chemical physics : PCCP》2006,8(36):4149-4165
Large molecular aggregates with sizes ranging from subnanometers to microns are ubiquitous. As atmospheric aerosols they influence our climate, in interstellar space they are discussed as reactive sites, and in medicine small particles are considered as promising candidates to achieve a targeted drug delivery. The present contribution is focused on the characterization of the physical-chemical properties of these particles and on their targeted generation. One of the greatest challenges is to understand the properties of these aggregates on a molecular level. The latter point is discussed in detail focussing on the vibrational dynamics of these particles. 相似文献
86.
We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions. 相似文献
87.
In this article, we study the Lotka–Volterra planar quadratic differential systems. We denote by LV systems all systems which can be brought to a Lotka–Volterra system by an affine transformation and time homotheties. All
these systems possess invariant straight lines. We classify the family of LV systems according to their geometric properties encoded in the configurations of invariant straight lines which these systems
possess. We obtain a total of 65 such configurations which are distinguished, roughly speaking, by the multiplicity of their
invariant lines and by the multiplicities of the singularities of the systems located on these lines. We determine an algebraic
subvariety of
\mathbbR12{\mathbb{R}^{12}} which contains all these systems and we find the bifurcation diagram of the configurations of LV systems within this algebraic subvariety, in terms of polynomial invariants with respect to the group action of affine transformations
and time homotheties. This geometric classification will serve as a basis for the full topological classification of LV systems. 相似文献
88.
Joan C. Artés Jaume Llibre Dana Schlomiuk Nicolae Vulpe 《Journal of Fixed Point Theory and Applications》2013,14(2):555-618
In this work we classify, with respect to the geometric equivalence relation, the global configurations of singularities, finite and infinite, of quadratic differential systems possessing exactly three distinct finite simple singularities. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddles) of different orders. Such distinctions are, however, important in the production of limit cycles close to the foci (or loops) in perturbations of the systems. The notion of geometric equivalence relation of configurations of singularities allows us to incorporate all these important geometric features which can be expressed in purely algebraic terms. The geometric classification of all configurations of singularities, finite and infinite, of quadratic systems was initiated in a work published in 2013 when the classification was done for systems with total multiplicity m f of finite singularities less than or equal to one. That work was continued in an article which is due to appear in 2014 where the geometric classification of configurations of singularities was done for the case m f = 2. In this article we go one step further and obtain the geometric classification of singularities, finite and infinite, for the subclass mentioned above. We obtain 147 geometrically distinct configurations of singularities for this family. We give here the global bifurcation diagram of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for this class of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants, a fact which gives us an algorithm for determining the geometric configuration of singularities for any quadratic system in this particular class. 相似文献
89.
The Josephson effect in the superconductor/ferromagnet/superconductor (SFS) graphene Josephson junction is studied using the Dirac Bogoliubov-de Gennes (DBdG) formalism. It is shown that the SFS graphene junction drives 0–π transition with the increasing of p=h0L/vF?, which captures the effects of both the exchange field and the length of the junction; the spin-down current is dominant. The 0 state is stable for p 〈 pc (critical value pc ≈ 0.80) and the π state is stable for p 〉 pc, where the free energy minima are at φg=0 and φg=π, respectively. The coexistence of the 0 and π states appears in the vicinity of pc. 相似文献
90.
In the integrated circuit manufacturing process, the critical area extraction is a bottleneck to the layout optimization and the integrated circuit yield estimation. In this paper, we study the problem that the missing material defects may result in the open circuit fault. Combining the mathematical morphology theory, we present a new computation model and a novel extraction algorithm for the open critical area based on the net flow-axis. Firstly, we find the net flow-axis for different nets. Then, the net flow-edges based on the net flow-axis are obtained. Finally, we can extract the open critical area by the mathematical morphology. Compared with the existing methods, the nets need not to divide into the horizontal nets and the vertical nets, and the experimental results show that our model and algorithm can accurately extract the size of the open critical area and obtain the location information of the open circuit critical area. 相似文献