共查询到20条相似文献,搜索用时 46 毫秒
1.
Tim Römer 《manuscripta mathematica》2001,104(1):39-48
In this paper we consider the category of squarefree modules over the polynomial ring and an exact duality functor, which
is an extension of the Alexander dual of a simplicial complex. We give a relationship between the squarefree components of
local cohomology groups of a squarefree module and the Tor groups of its dual. With this result it is shown that a squarefree
module is sequentially Cohen–Macaulay if and only if the dual is componentwise linear.
Received: 7 June 1999 / Revised version: 6 September 2000 相似文献
2.
Yunkang Li 《Numerische Mathematik》1995,70(4):473-485
Summary.
This paper deals with the subject of
numerical stability for the neutral functional-differential equation
It is proved that numerical solutions generated by
-methods
are convergent if . However, our numerical experiment suggests
that they are divergent when is large. In
order to obtain convergent numerical solutions when
,
we use
-methods to obtain approximants
to some high order derivative
of the exact solution, then we use the Taylor expansion with integral
remainder to obtain approximants to the exact solution. Since
the equation under consideration has unbounded time lags, it
is in general difficult to investigate numerically the long time
dynamical behaviour of the exact solution due to limited computer
(random access) memory. To avoid this problem we
transform the equation under consideration into a neutral
equation with constant time lags. Using the
later equation as a test model, we prove that the linear
-method
is -stable, i.e., the numerical
solution tends to zero for
any constant stepsize as long as
and , if and only
if , and that the
one-leg -method is -stable if
. We also
find out that inappropriate stepsize causes spurious solution in the
marginal case where and .
Received May 6, 1994 相似文献
3.
Kai Diethelm 《Numerical Functional Analysis & Optimization》2013,34(7-8):745-757
Sard's classical generalization of the Peano kernel theorem provides an extremely useful method for expressing and calculating sharp bounds for approximation errors. The error is expressed in terms of a derivative of the underlying function. However, we can apply the theorem only if the approximation is exact on a certain set of polynomials. In this paper, we extend the Peano-Sard theorem to the case that the approximation is exact for a class of generalized polynomials (with non-integer exponents). As a result, we obtain an expression for the remainder in terms of a fractional derivative of the function under consideration. This expression permits us to give sharp error bounds as in the classical situation. An application of our results to the classical functional (vanishing on polynomials) gives error bounds of a new type involving weighted Sobolev-type spaces. In this way, we may state estimates for functions with weaker smoothness properties than usual. The standard version of the Peano-Sard theory is contained in our results as a special case. 相似文献
4.
Summary. The method of shortest residuals (SR) was presented by Hestenes and studied by Pytlak. If the function is quadratic, and
if the line search is exact, then the SR method reduces to the linear conjugate gradient method. In this paper, we put forward
the formulation of the SR method when the line search is inexact. We prove that, if stepsizes satisfy the strong Wolfe conditions,
both the Fletcher-Reeves and Polak-Ribière-Polyak versions of the SR method converge globally. When the Wolfe conditions are
used, the two versions are also convergent provided that the stepsizes are uniformly bounded; if the stepsizes are not bounded,
an example is constructed to show that they need not converge. Numerical results show that the SR method is a promising alternative
of the standard nonlinear conjugate gradient method.
Received June 25, 1996 / Revised version received April 1, 1997 / Published online July 28, 1999 相似文献
5.
Takuya Tsuchiya 《Numerische Mathematik》1999,84(1):121-141
Summary. Finite element solutions of strongly nonlinear elliptic boundary value problems are considered. In this paper, using the
Kantorovich theorem, we show that, if the Fréchet derivative of the nonlinear operator defined by the boundary value problem
is an isomorphism at an exact solution, then there exists a locally unique finite element solution near the exact solution.
Moreover, several a priori error estimates are obtained.
Received March 2, 1998 / Published online September 7, 1999 相似文献
6.
Let B be a block of the group algebra KG of a finite Group G over an algebraically closed field K. We prove that every degeneration of finite dimensional B-modules is given by short exact sequences if and only if B is of finite representation type.
Received: 7 July 1997 相似文献
7.
Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models. 相似文献
8.
9.
J. R. Wall 《Linear and Multilinear Algebra》1975,2(4):337-340
For a doubly stochastic matrix A, each of the equations x:aty= A and X Aty=t is shown to have doubly stochastic solutions X and Y if and only if A lies in a subgroup of the semigroup of all doubly stochastic matrices of a given order. All elements of this semigroup which are left regular, right regular, or intra-regular are identified. 相似文献
10.
Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference
between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results.
Received April 2, 1996 / Revised version received July 30, 1990 相似文献
11.
I. Fonseca G. Leoni R. Paroni 《Calculus of Variations and Partial Differential Equations》2003,17(3):283-309
It is proved that if , with p > 1, if is bounded in , , and if in then provided is 2-quasiconvex and satisfies some appropriate growth and continuity condition. Characterizations of the 2-quasiconvex envelope
when admissible test functions belong to BHp are provided.
Received: 10 October 2001 / Accepted: 8 May 2002 / Published online: 17 December 2002 相似文献
12.
KAM theorem of symplectic algorithms for Hamiltonian systems 总被引:5,自引:0,他引:5
Zai-jiu Shang 《Numerische Mathematik》1999,83(3):477-496
Summary. In this paper we prove that an analog of the celebrated KAM theorem holds for symplectic algorithms, which Channel and Scovel
(1990), Feng Kang (1991) and Sanz-Serna and Calvo (1994) suggested a few years ago. The main results consist of the existence
of invariant tori, with a smooth foliation structure, of a symplectic numerical algorithm when it applies to a generic integrable
Hamiltonian system if the system is analytic and the time-step size of the algorithm is s
ufficiently small. This existence result also implies that the algorithm, when it is applied to a generic integrable system,
possesses n independent smooth invariant functions which are in involution and well-defined on the set filled by the invariant tori in
the sense of Whitney. The invariant tori are just the level sets of these functions. Some quantitative results about the numerical
invariant tori of the algorithm approximating the exact ones of the system are also given.
Received December 27, 1997 / Revised version received July 15, 1998 / Published online: July 7, 1999 相似文献
13.
Andrzej Stachurski 《Numerische Mathematik》1981,38(2):209-218
Summary In this paper the problem of minimizing the functionalf:DR
n
R is considered. Typical assumptions onf are assumed. A class of Quasi-Newton methods, namely Huang's class of methods is used for finding an optimal solution of this problem. A new theorem connected with this class is presented. By means of this theorem some convergence results known up till now only for the methods which satisfy Quasi-Newton condition are extended, that is the results of superlinear convergence of variable metric methods in the cases of exact and asymptotically exact minimization and the so-called direct-prediction case. This theorem allows to interpretate one of the parameters as the scaling parameter. 相似文献
14.
Matías Menni 《Journal of Pure and Applied Algebra》2007,210(2):511-520
Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere-Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Grothendieck toposes whose exact completion is a Grothendieck topos.We also show that for any topological space X, the exact completion of is a topos if and only if X is discrete. The corollary in this case characterizes the Grothendieck toposes with enough points whose exact completions are toposes. 相似文献
15.
Ji?í Spurný 《Journal of Functional Analysis》2006,232(2):259-294
Let X be a compact convex subset of a locally convex space. We show that any bounded Baire-one function defined on can be extended to an affine Baire-one function on X if and only if X is a Choquet simplex and satisfies a certain topological property. 相似文献
16.
Hideo Kozono 《Mathematische Annalen》2001,320(4):709-730
Consider the nonstationary Stokes equations in exterior domains with the compact boundary . We show first that the solution decays like for all as . This decay rate is optimal in the sense that for some as occurs if and only if the net force exerted by the fluid on is zero.
Received: 15 June 2000 / Published online: 18 June 2001 相似文献
17.
By using the homogeneous balance principle, we derive a Backlund transformation (BT) to (3+1)-dimensionaI Kadomtsev-Petviashvili (K-P) equation with variable coefficients if the variable coefficients are linearly dependent. Based on the BT, the exact solution of the (3+1)-dimensional K-P equation is given. By the same method, we derive a BT and the solution to (2+1)-dimensional K-P equation. The variable coefficients can change the amplitude of solitary wave, but cannot change the form of solitary wave. 相似文献
18.
19.
Michał Kwieciński 《manuscripta mathematica》1998,97(2):163-173
We prove that a complex map is flat if and only if none of its fibred powers has vertical (isolated or embedded) components.
A commutative algebraic analogue of this statement follows: flatness is equivalent to torsion freeness of all tensor powers.
Received: 21 August 1997 / Revised version: 6 April 1998 相似文献
20.
R.V. Gurjar 《Mathematische Zeitschrift》2002,240(1):83-94
We give a new proof of the Cancellation Theorem for which says that if V is a smooth complex affine surface such that is isomorphic to then V is isomorphic to The proof is based on the topological method of Mumford-Ramanujam.
Received: 2 November 2000 / in final form: 10 September 2001 / Published online: 1 February 2002 相似文献