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311.
In this paper we present an alternative algorithm for computing Poincaré-Lyapunov constants of simple monodromic singularities of planar analytic vector fields based on the concept of inverse integrating factor. Simple monodromic singular points are those for which after performing the first (generalized) polar blow-up, there appear no singular points. In other words, the associated Poincaré return map is analytic. An improvement of the method determines a priori the minimum number of Poincaré-Lyapunov constants which must cancel to ensure that the monodromic singularity is in fact a center when the explicit Laurent series of an inverse integrating factor is known in (generalized) polar coordinates. Several examples show the usefulness of the method. 相似文献
312.
We introduce a new reflection principle which we call “Fodor-type Reflection Principle” (FRP). This principle follows from but is strictly weaker than Fleissner's Axiom R. For instance, FRP does not impose any restriction on the size of the continuum, while Axiom R implies that the continuum has size ?ℵ2.We show that FRP implies that every locally separable countably tight topological space X is meta-Lindelöf if all of its subspaces of cardinality ?ℵ1 are (Theorem 4.3). It follows that, under FRP, every locally (countably) compact space is metrizable if all of its subspaces of cardinality ?ℵ1 are (Corollary 4.4). This improves a result of Balogh who proved the same assertion under Axiom R.We also give several other results in this vein, some in ZFC, others in some further extension of ZFC. For example, we prove in ZFC that if X is a locally (countably) compact space of singular cardinality in which every subspace of smaller size is metrizable then X itself is also metrizable (Corollary 5.2). 相似文献
313.
Ezio Venturino 《Journal of Computational and Applied Mathematics》2010,234(9):2883-191
In this paper we consider ecoepidemic models in which the basic demographics is represented by predator-prey interactions, with the disease modeled by an SEI system. At first we consider a basic Lotka-Volterra type of interaction. Then we also introduce competition for resources among individuals of the prey population. Several variations of the model are presented, in which the prey intra-specific population pressure assumes different forms, depending on the virulence of the disease. Indeed, the latter may affect the exposed and infected individuals so much that they may not be able to compete with the sound ones for resources. A further distinguishing feature of this investigation lies in the way in which the predator actively selects the prey for hunting. For instance in some cases predators may discard the diseased ones, as less palatable, while in other situations they would instead search expressly for the infected, since these are weaker individuals and thus easier to hunt. The equilibria of the systems are analyzed, showing that in some cases bifurcations arise, contrary to what happens to similar classical Holling type I ecoepidemic models. These persistent oscillations seem to be triggered by the number of subpopulations present in the system, which is larger than those introduced in the former models, counting also the latent class. Furthermore, adding predation to an SEI epidemic model has profound effects on the stability of its equilibria. In particular, once the predators are introduced into an SEI epidemic at a stable endemic equilibrium, their presence destabilizes this equilibrium making the previous stable conditions unrecoverable. 相似文献
314.
Juan Carlos De los Reyes Sergio González Andrade 《Journal of Computational and Applied Mathematics》2010,235(1):11-32
This paper is devoted to the numerical simulation of two-dimensional stationary Bingham fluid flow by semismooth Newton methods. We analyze the modeling variational inequality of the second kind, considering both Dirichlet and stress-free boundary conditions. A family of Tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified. By using Fenchel’s duality, optimality systems which characterize the original and regularized solutions are obtained. The regularized optimality systems are discretized using a finite element method with (cross-grid P1)-Q0 elements for the velocity and pressure, respectively. A semismooth Newton algorithm is proposed in order to solve the discretized optimality systems. Using an additional relaxation, a descent direction is constructed from each semismooth Newton iteration. Local superlinear convergence of the method is also proved. Finally, we perform numerical experiments in order to investigate the behavior and efficiency of the method. 相似文献
315.
We introduce the notion of the generalized Catalan matrix as a kind of lower triangular Toeplitz matrix whose nonzero elements involve the generalized Catalan numbers. Inverse of the linear combination of the Pascal matrix with the identity matrix is computed in Aggarwala and Lamoureux (2002) [1]. In this paper, continuing this idea, we invert various linear combinations of the generalized Catalan matrix with the identity matrix. A simple and efficient approach to invert the Pascal matrix plus one in terms of the Hadamard product of the Pascal matrix and appropriate lower triangular Toeplitz matrices is considered in Yang and Liu (2006) [14]. We derive representations for inverses of linear combinations of the generalized Catalan matrix and the identity matrix, in terms of the Hadamard product which includes the Generalized Catalan matrix and appropriate lower triangular Toeplitz matrix. 相似文献
316.
In a previous paper the authors introduced seven complete congruences on the lattice ev(I of e-varieties of regular semigroups of the form
P
:U
P
VPU=PV, whereP is drawn from a small set of e-varieties: left zero, right zero, rectangular bands, groups, left groups, right groups and completely simple semigroups. Four new complete congruences are introduced here of the form
P
:U
P
VPU=PV, whereP is one of the following classes of regular semigroups: left monoids, right monoids, monoids, idempotent generated semigroups. For each complete congruence on ev(I) and eachUev(I), the -class ofU is an interval [U
,U
] so that there is associated with each such congruence an idempotent operatorUU
on ev(I). This paper establishes numerous results concerning the commutativity of operators of this form.This work was supported in part by NSERC Grant 4044. 相似文献
317.
Dennis E. White 《Aequationes Mathematicae》1977,16(1-2):59-64
We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.This work was supported in part by NSF Contract GP-43010. 相似文献
318.
Zalman Rubinstein 《Aequationes Mathematicae》1981,23(1):108-117
Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered. 相似文献
319.
Dietrich Braess 《Numerische Mathematik》1981,37(3):387-404
Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.Dedicated to Professor Dr.Dr.h.c. Lothar Collatz on the occasion of his 70 th birthday 相似文献
320.
J. S. Huang 《Annals of the Institute of Statistical Mathematics》1981,33(1):131-134
For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0]<P [Y<X]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless
property relative to a continuous variable.
Research partially supported by NRC of Canada grants #A8057 and #T0500.
Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia. 相似文献