In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S1 and a linear differential equations system in the Minkowski space M3. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number. 相似文献
In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others. 相似文献
A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational
inequalities is given in this paper. Several examples are constructed to analyze the results.
This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program,
and the KOSEF Brain Pool Program. 相似文献
The non-commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one [Phys. Lett. B 498 (2001) 277, hep-th/0203125, hep-th/0303090].
Due to the U(1) gauge invariance, the Seiberg–Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) θ-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are identical, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the “energy crisis”.
A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small. 相似文献
In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result,
we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium
problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical
program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and
systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints.
This research was supported by the National Science Council of the Republic of China. 相似文献
X-ray reflectivity (XRR), X-ray fluorescence (XRF) and small angle X-ray scattering (SAXS) techniques are used to the monitoring of Cu/porous low κ processes, which are developed for the next generation (≤65 nm) integrated circuits. Sensitivity of XRR and XRF is sufficient to detect drifts of the copper barrier layer, copper seed layer and Cu CMP (chemical-mechanical polishing) processes. Their metrology key parameters comply with production requirements. SAXS allows determining the pore structure of low κ films: average pore size and pore size distribution. 相似文献