共查询到20条相似文献,搜索用时 31 毫秒
1.
Marco Schlichting 《Mathematische Zeitschrift》2006,253(1):97-134
We define negative K-groups for exact categories and for ``derived categories' in the framework of Frobenius pairs, generalizing definitions
of Bass, Karoubi, Carter, Pedersen-Weibel and Thomason. We prove localization and vanishing theorems for these groups. Dévissage (for noetherian abelian categories), additivity, and resolution hold. We show that the first negative K-group of an abelian category vanishes, and that, in general, negative K-groups of a noetherian abelian category vanish. Our methods yield an explicit non-connective delooping of the K-theory of exact categories and chain complexes, generalizing constructions of Wagoner and Pedersen-Weibel. Extending a theorem
of Auslander and Sherman, we discuss the K-theory homotopy fiber of ε⊕→ ε and its implications for negative K-groups. In the appendix, we replace Waldhausen's cylinder functor by a slightly weaker form of non-functorial factorization
which is still sufficient to prove his approximation and fibration theorems. 相似文献
2.
Mohamed Ben Ayed Khalil El Mehdi 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):485-509
This paper is concerned with a biharmonic equation under the Navier boundary condition
, u > 0 in Ω and u = Δu = 0 on ∂Ω, where Ω is a smooth bounded domain in
, n ≥ 5, and ε > 0. We study the asymptotic behavior of solutions of (P
−ε) which are minimizing for the Sobolev quotient as ε goes to zero. We show that such solutions concentrate around a point
x
0 ∈Ω as ε → 0, moreover x
0 is a critical point of the Robin’s function. Conversely, we show that for any nondegenerate critical point x
0 of the Robin’s function, there exist solutions of (P
−ε) concentrating around x
0 as ε → 0. Finally we prove that, in contrast with what happened in the subcritical equation (P
−ε), the supercritical problem (P
+ε) has no solutions which concentrate around a point of Ω as ε → 0.
Work finished when the authors were visiting Mathematics Department of the University of Roma “La Sapienza”. They would like
to thank the Mathematics Department for its warm hospitality. The authors also thank Professors Massimo Grossi and Filomena
Pacella for their constant support. 相似文献
3.
Eduard Marušić-Paloka Igor Pažanin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(1):81-99
In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its
ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→
0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved. 相似文献
4.
We consider a class of Markov chain models that includes the highly reliable Markovian systems (HRMS) often used to represent
the evolution of multicomponent systems in reliability settings. We are interested in the design of efficient importance sampling
(IS) schemes to estimate the reliability of such systems by simulation. For these models, there is in fact a zero-variance
IS scheme that can be written exactly in terms of a value function that gives the expected cost-to-go (the exact reliability,
in our case) from any state of the chain. This IS scheme is impractical to implement exactly, but it can be approximated by
approximating this value function. We examine how this can be effectively used to estimate the reliability of a highly-reliable
multicomponent system with Markovian behavior. In our implementation, we start with a simple crude approximation of the value
function, we use it in a first-order IS scheme to obtain a better approximation at a few selected states, then we interpolate
in between and use this interpolation in our final (second-order) IS scheme. In numerical illustrations, our approach outperforms
the popular IS heuristics previously proposed for this class of problems. We also perform an asymptotic analysis in which
the HRMS model is parameterized in a standard way by a rarity parameter ε, so that the relative error (or relative variance) of the crude Monte Carlo estimator is unbounded when ε→0. We show that with our approximation, the IS estimator has bounded relative error (BRE) under very mild conditions, and
vanishing relative error (VRE), which means that the relative error converges to 0 when ε→0, under slightly stronger conditions. 相似文献
5.
Saâd Benbachir 《Numerical Algorithms》1999,21(1-4):57-77
The main aim of this work is to look for the periodic solutions of the nonintegrable Hamiltonian system of Ollongren in the
neighborhood of the origin. We apply a functional algorithm derived from the method of Lindstedt-Poincaré. We first show that
the system admits six main periodic families and then, by means of the computer algebra system “Mathematica”, compute the
series corresponding to these families up to O(ε14A29) as well as to their periods up to O(ε15A30), where A is the zeroth-order amplitude and έ is a perturbative parameter. Reducing the system to one degree of freedom we
also prove that the period of the two “oblique” periodic families is rigorously equal to a Gauss hypergeometric series. Moreover,
we study numerically the convergence of the L-P series and test the validity of these series using a numerical integration
technique. Finally, we compare our results with those of a geometrical method and a Lie series method.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Phoolan Prasad 《Proceedings Mathematical Sciences》2000,110(4):431-447
Using a method of expansion similar to Chapman-Enskog expansion, a new formal perturbation scheme based on high frequency
approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears.
The transport equation for the amplitude has been deduced with an errorO(ε2) where ε is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet-Bruhat’s
theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading order
terms give the weakly nonlinear ray theory (WNLRT) of Prasad, which has been very successful in giving physically realistic
results and also in showing that the caustic of a linear theory is resolved when nonlinear effects are included. The weak
shock ray theory with infinite system of compatibility conditions also follows from this theory. 相似文献
7.
Quick Approximation to Matrices and Applications 总被引:1,自引:0,他引:1
m ×n matrix A with entries between say −1 and 1, and an error parameter ε between 0 and 1, we find a matrix D (implicitly) which is the sum of simple rank 1 matrices so that the sum of entries of any submatrix (among the ) of (A−D) is at most εmn in absolute value. Our algorithm takes time dependent only on ε and the allowed probability of failure (not on m, n).
We draw on two lines of research to develop the algorithms: one is built around the fundamental Regularity Lemma of Szemerédi
in Graph Theory and the constructive version of Alon, Duke, Leffman, R?dl and Yuster. The second one is from the papers of
Arora, Karger and Karpinski, Fernandez de la Vega and most directly Goldwasser, Goldreich and Ron who develop approximation
algorithms for a set of graph problems, typical of which is the maximum cut problem.
From our matrix approximation, the above graph algorithms and the Regularity Lemma and several other results follow in a simple
way.
We generalize our approximations to multi-dimensional arrays and from that derive approximation algorithms for all dense Max-SNP
problems.
Received: July 25, 1997 相似文献
8.
This paper considers multidimensional control problems governed by a first-order PDE system. It is known that, if the structure
of the problem is linear-convex, then the so-called ε-maximum principle, a set of necessary optimality conditions involving
a perturbation parameter ε > 0, holds. Assuming that the optimal controls are piecewise continuous, we are able to drop the
perturbation parameter within the conditions, proving the Pontryagin maximum principle with piecewise regular multipliers
(measures). The Lebesgue and Hahn decompositions of the multipliers lead to refined maximum conditions. Our proof is based
on the Baire classification of the admissible controls. 相似文献
9.
We consider the Stokes problem in an axisymmetric three-dimensional domain with data which are axisymmetric and have angular component equal to zero. We observe that the solution is also axisymmetric and the velocity has also zero angular component, hence the solution satisfies a system of equations in the meridian domain. The weak three-dimensional problem reduces to a two-dimensional one with weighted integrals. The latter is discretized by Taylor–Hood type finite elements. A weighted Clément operator is defined and approximation results are proved. This operator is then used to derive the discrete inf–sup condition and optimal a priori error estimates. 相似文献
10.
S. A. Kordyukova 《Theoretical and Mathematical Physics》2008,154(2):250-259
For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter ε for large times where
corrections to the approximation described by the Korteweg-de Vries equation must be taken into account. We reveal the appearance
of the Korteweg-de Vries hierarchy, which ensures the construction of an asymptotic representation up to the times t ≈ ε−2, where the Korteweg-de Vries approximation becomes inapplicable.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 294–304, February, 2008. 相似文献
11.
We consider the M/G/1 queue with an arrival rate λ that depends weakly upon time, as λ = λ(εt) where ε is a small parameter. In the asymptotic limit ε → 0, we construct approximations to the probability p
n(t)that η customers are present at time t. We show that the asymptotics are different for several ranges of the (slow) time scale Τ= εt. We employ singular perturbation techniques and relate the various time scales by asymptotic matching.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
B. Amaziane M. Goncharenko L. Pankratov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):592-611
The aim of this paper is to study the asymptotic behavior of the solution of a convection–diffusion equation in perforated
domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles.
Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find
the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection–diffusion
equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate
the methodology. 相似文献
13.
F. A. Rihan 《Computational Mathematics and Modeling》2008,19(3):292-303
Singular perturbation problems containing a small positive parameter ε occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. A uniformly
valid, reliable interpretable approximation of such problems is required. This paper provides sufficient conditions to ensure
the exponential stability of the analytical and numerical solutions of the singularly perturbed delay differential equations
with a bounded time-lag for suf.ciently small ε > 0. The Halanay inequality is used to prove the main results of the paper. A numerical example is provided to illustrate
the methodology and clarify the need for a stiff solver for numerical solutions of these problems. 相似文献
14.
Yu. N. Bibikov 《Mathematical Notes》1999,65(3):269-279
We consider small perturbations periodic in time of an oscillator whose restoring force has a leading term with exponent 3
or 1/3. The first case corresponds to oscillations with infinitesimal frequency and the second case to oscillations with infinite
frequency. The smallness of the perturbation is determined both by the smallness of the considered neighborhood of the equilibrium
point and by a small nonnegative parameter ε. For ε=0, the stability of the equilibrium point is studied. For ε>0, we find
conditions for an invariant two-dimensional torus to branch off with “soft” or “rigid” loss of stability with loss index 1/2.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 323–335, March, 1999. 相似文献
15.
We deal with consistent first order non-relativistic corrections (i.e. in the small parameter , where c is the speed of light) of the Dirac–Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ɛ) approximation of the Dirac equation. We suggest a coupling to the “magnetostatic”O(ɛ) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch
the semiclassical/nonrelativistic limits of this model.
(Received 22 May 2000) 相似文献
16.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system.
Research done in the University of Michigan-Ann Arbor, submission from Temasek Laboratories, National University of Singapore. 相似文献
17.
Stokes flow between corrugated plates in microdomains has been analyzed using a perturbation method. This approach used the incompressible Navier-Stokes equations, but the velocity-slip is present along the solid-fluid interface. For the slip flow regime, if we introduce Knudsen number (K
n) herein, 0.01 K
n 0.1, the total flow rate is increasing as a ratio of 1 + 6K
nto no-slip Stokes flow. If we consider fixedK
ncases, the corrugations still decrease the flow rate, consideringO(2) terms, and the decrease is maximum as the phase shift becomes 180 °. 相似文献
18.
MIXED FINITE ELEMENT METHOD FOR THE CONVECTION-DOMINATED DIFFUSION PROBLEMS WITH SMALL PARAMETER ε 总被引:2,自引:0,他引:2
CHENHUANZHEN 《高校应用数学学报(英文版)》1998,13(2):199-206
In rids paper a mixed finite element method for the convection-dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a sufficient condition for optimal error estimates is derived. The paper also shows that under some conditions,the standard finite dement method only gives a hounded solution,however the mixed finite element method gives a convergent one. 相似文献
19.
J. Müller 《Journal of Nonlinear Science》1999,9(2):149-168
Summary. We consider a reaction-diffusion equation that is homogeneous of degree one. This homogeneity is a symmetry. The dynamics
is factorized into trivial evolution due to symmetry and nontrivial behavior by a projection to an appropriate hypermanifold.
The resulting evolution equations are rather complex. We examine the bifurcation behavior of a stationary point of the projected
system. For these purposes we develop techniques for dimension reduction similar to the Ginzburg-Landau (GL) approximation,
the modulation equations. Since we are not in the classical GL situation, the remaining approximative equations have a quadratic
nonlinearity and the amplitude does not scale with ε but with ε
2
where ε
2
denotes the bifurcation parameter. Moreover, the symmetry requires that not only one but two equations are necessary to
describe the behavior of the system. We investigate traveling fronts for the modulation equations. This result is used to
analyze an epidemic model.
Received April 9, 1996; second revision received January 3, 1997; final revision received October 7, 1997; accepted January
19, 1998 相似文献
20.
We consider the problem of approximate range counting over a stream of d-dimensional points. In the data stream model the
algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary data
structure. The summary, whose size depends on the approximation parameter ε, can be used to count the number of points inside
a query range within additive error εn, where n is the size of the stream seen so far. We present several results, deterministic
and randomized, for both rectangle and halfspace ranges. 相似文献