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1.
Juan B. Gil 《Mathematische Nachrichten》2003,250(1):25-57
The operator e–tA and its trace Tr e–tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A–λ)–1. The main step consists in approximating this family by a parametrix of A – λ constructed within a suitable parameter–dependent calculus. 相似文献
2.
Let S be an abelian *–semigroup in ℚk. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of S (i.e. S is perfect). To characterize perfectness for any abelian *–semigroupis a challenging, but not yet generally solved problem. In this paper, we characterize the structure of involutions on an abelian *–semigroup which is a subset of ℚk, and show that any conelike *–semigroups in ℚk are perfect. 相似文献
3.
Let W be an integrable positive Hermitian q × q–matrix valued function on the dual group of a discrete abelian group G such that W–1 is integrable. Generalizing results of T. Nakazi [N] and of A. G. Miamee and M. Pourahmadi [MiP] for q = 1 we establish a correspondence between trigonometric approximation problems in L2(W) and certain approximation problems in L2(W–1). The result is applied to prediction problems for q–variate stationary processes over G , inparticular, to the case G = ℤ. 相似文献
4.
We prove that a weak solution u = (u 1, u 2, u 3) to the Navier–Stokes equations is strong, if any two components of u satisfy Prodi–Ohyama–Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L 6, ∞. 相似文献
5.
Takayuki Kubo 《Mathematical Methods in the Applied Sciences》2005,28(11):1341-1357
We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n?3. Our proof is based on Lp–Lq estimates of the Stokes semigroup. We apply Lp–Lq estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
K. Rottbrand 《Mathematical Methods in the Applied Sciences》1996,19(15):1217-1224
A Wiener–Hopf equation in L2 being equivalent [5] to a boundary value problem (of the first kind) for a wave-scattering Sommerfeld half-plane Σ=ℝ+×{0} which faces two different media Ω-: x2<0, Ω+: x2>0, as a special configuration in [3], is solved by canonical Weiner–Hopf factorization of its L2-regular scalar symbol γo=γo- γo+. The factors are calculated by solving a Riemann–Hilbert boundary value problem on the semi-infinite branch cuts of tj(ξ):=(ξ2−k2j)1/2, kj∈ℂ++ for j=1,2: taken parallel to the imaginary axis. The procedure following this idea is known as the Wiener–Hopf–Hilbert(–Hurd) method [2] and requires the evaluation of elliptic-type integrals. Formula (3.7) seems not to be contained in tables of integrals. 相似文献
7.
M. R. Weber 《Mathematische Nachrichten》2009,282(10):1478-1487
In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U–1 exists, VU–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Yukihide Takayama 《代数通讯》2013,41(11):4744-4750
The Hirokado variety is a Calabi–Yau threefold in characteristic 3 that is not liftable either to characteristic 0 or the ring W 2 of the second Witt vectors. Although Deligne–Illusie–Raynaud type Kodaira vanishing cannot be applied, we show that H 1(X, L ?1) = 0, for an ample line bundle such that L 3 has a non-trivial global section, holds for this variety. 相似文献
9.
For a quasi-Hopf algebra H, a left H-comodule algebra and a right H-module coalgebra C we will characterize the category of Doi–Hopf modules C ?(H) in terms of modules. We will also show that for an H-bicomodule algebra and an H-bimodule coalgebra C the category of generalized Yetter–Drinfeld modules (H) C is isomorphic to a certain category of Doi–Hopf modules. Using this isomorphism we will transport the properties from the category of Doi–Hopf modules to the category of generalized Yetter–Drinfeld modules. 相似文献
10.
M. Arad A. Yakhot G. Ben-Dor 《Numerical Methods for Partial Differential Equations》1997,13(4):375-391
The coefficients for a nine–point high–order accuracy discretization scheme for a biharmonic equation ∇ 4u = f(x, y) (∇2 is the two–dimensional Laplacian operator) are derived. The biharmonic problem is defined on a rectangular domain with two types of boundary conditions: (1) u and ∂2u/∂n2 or (2) u and ∂u/part;n (where ∂/part;n is the normal to the boundary derivative) are specified at the boundary. For both considered cases, the truncation error for the suggested scheme is of the sixth-order O(h6) on a square mesh (hx = hy = h) and of the fourth-order O(h4xh2xh2y h4y) on an unequally spaced mesh. The biharmonic equation describes the deflection of loaded plates. The advantage of the suggested scheme is demonstrated for solving problems of the deflection of rectangular plates for cases of different boundary conditions: (1) a simply supported plate and (2) a plate with built-in edges. In order to demonstrate the high–order accuracy of the method, the numerical results are compared with exact solutions. © John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 375–391, 1997 相似文献
11.
In this article we use linear spline approximation of a non-linear Riemann–Hilbert problem on the unit disk. The boundary condition for the holomorphic function is reformulated as a non-linear singular integral equation A(u) = 0, where A : H 1(Γ) → H 1(Γ) is defined via a Nemytski operator. We approximate A by A n : H 1(Γ) → H 1(Γ) using spline collocation and show that this defines a Fredholm quasi-ruled mapping. Following the results of (A.I. ?nirel'man, The degree of quasi-ruled mapping and a nonlinear Hilbert problem, Math. USSR-Sbornik 18 (1972), pp. 373–396; M.A. Efendiev, On a property of the conjugate integral and a nonlinear Hilbert problem, Soviet Math. Dokl. 35 (1987), pp. 535–539; M.A. Efendiev, W.L. Wendland, Nonlinear Riemann–Hilbert problems for multiply connected domains, Nonlinear Anal. 27 (1996), pp. 37–58; Nonlinear Riemann–Hilbert problems without transversality. Math. Nachr. 183 (1997), pp. 73–89; Nonlinear Riemann–Hilbert problems for doubly connected domains and closed boundary data, Topol. Methods Nonlinear Anal. 17 (2001), pp. 111–124; Nonlinear Riemann–Hilbert problems with Lipschitz, continuous boundary data without transversality, Nonlinear Anal. 47 (2001), pp. 457–466; Nonlinear Riemann–Hilbert problems with Lipschitz-continuous boundary data: Doubly connected domains, Proc. Roy. Soc. London Ser. A 459 (2003), pp. 945–955.), we define a degree of mapping and show the existence of the spline solutions of the fully discrete equations A n (u) = 0, for n large enough. We conclude this article by discussing the solvability of the non-linear collocation method, where we shall need an additional uniform strong ellipticity condition for employing the spline approximation. 相似文献
12.
The global wellposedness in Lp(?) for the Chern–Simons–Dirac equation in the 1+1 space and time dimension is discussed. We consider two types of quadratic nonlinearity: the null case and the non-null case. We show the time global wellposedness for the Chern–Simon–Dirac equation in the framework of Lp(?), where 1≤p≤∞ for the null case. For the scaling critical case, p = 1, mass concentration phenomena of the solutions may occur in considering the time global solvability. We invoke the Delgado–Candy estimate which plays a crucial role in preventing concentration phenomena of the global solution. Our method is related to the original work of Candy (2011), who showed the time global wellposedness for the single Dirac equation with cubic nonlinearity in the critical space L2(?). 相似文献
13.
Xiaojing Yang 《Mathematische Nachrichten》2004,268(1):102-113
In this paper, the boundedness of all solutions of the nonlinear differential equation (φp(x′))′ + αφp(x+) – βφp(x–) + f(x) = e(t) is studied, where φp(u) = |u|p–2 u, p ≥ 2, α, β are positive constants such that = 2w–1 with w ∈ ?+\?, f is a bounded C5 function, e(t) ∈ C6 is 2πp‐periodic, x+ = max{x, 0}, x– = max{–x, 0}. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
A Priori Error Estimates of Crank–Nicolson Finite Volume Element Method for a Hyperbolic Optimal Control Problem
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Xianbing Luo 《Numerical Methods for Partial Differential Equations》2016,32(5):1331-1356
In this article, a Crank–Nicolson linear finite volume element scheme is developed to solve a hyperbolic optimal control problem. We use the variational discretization technique for the approximation of the control variable. The optimal convergent order O(h2 + k2) is proved for the numerical solution of the control, state and adjoint‐state in a discrete L2‐norm. To derive this result, we also get the error estimate (convergent order O(h2 + k2)) of Crank–Nicolson finite volume element approximation for the second‐order hyperbolic initial boundary value problem. Numerical experiments are presented to verify the theoretical results.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1331–1356, 2016 相似文献
15.
Donald W. Robinson 《Linear and Multilinear Algebra》2013,61(1-2):135-141
Let B be a realn–by–n, invertible matrix. Sharp lower bounds are determined for the dimension of the space {A: A1 = BAB?1 } of real matrices A which are similar under B to their transposes A′ . In particular, it is shown that this dimension is at least the greatest integer in (n + l)/2. 相似文献
16.
Jean-Claude Douai 《代数通讯》2013,41(9):3963-3968
Using the Tate–Poitou duality, Sansuc proved that the group III1(K, G) is stably K-birational invariant of G for a connected linear algebraic group defined over a number field K. In this paper, we consider the case where K is a function field, in one variable over a PAC field (K is a “good” field in sense Colliot–Thélène and Kunyavskii). We show that the group III1(K, G) is stably K-birational invariant when G is a connected reductive K-group. Since we no longer have the Tate–Poitou duality at our disposition, we use the flasque resolutions of Colliot–Thélène and Sansuc. En utilisant la dualité de Tate–Poitou, Sansuc a établi le caractère d'invariant stablement K-birationnel du groupe III1(K, G) pour un groupe algébrique linéaire connexe G défini sur un corps de nombres K. Dans cet article, nous considérons le cas où K est un corps de fonctions en une variable sur un corps PAC (K est un “bon” corps au sens de Colliot–Thélène et Kunyavskii). Nous montrons le caractère d'invariant stablement K-birationnel du groupe III1(K, G) pour un K-groupe réductif connexe G. Comme nous n'avons plus à notre disposition la dualité de Tate–Poitou, nous devons utiliser les résolutions flasques de Colliot–Thélène et Sansuc. 相似文献
17.
Yongge Tian 《International Journal of Mathematical Education in Science & Technology》2013,44(3):331-339
The standard reverse-order law for the Moore–Penrose inverse of a matrix product is (AB)??=?B ? A ?. The purpose of this article is to give a set of equivalences of this reverse-order law and other mixed-type reverse-order laws for the Moore–Penrose inverse of matrix products. 相似文献
18.
Guang‐Hua Gao Zhi‐Zhong Sun 《Numerical Methods for Partial Differential Equations》2013,29(5):1459-1486
This is the further work on compact finite difference schemes for heat equation with Neumann boundary conditions subsequent to the paper, [Sun, Numer Methods Partial Differential Equations (NMPDE) 25 (2009), 1320–1341]. A different compact difference scheme for the one‐dimensional linear heat equation is developed. Truncation errors of the proposed scheme are O(τ2 + h4) for interior mesh point approximation and O(τ2 + h3) for the boundary condition approximation with the uniform partition. The new obtained scheme is similar to the one given by Liao et al. (NMPDE 22 (2006), 600–616), while the major difference lies in no extension of source terms to outside the computational domain any longer. Compared with ones obtained by Zhao et al. (NMPDE 23 (2007), 949–959) and Dai (NMPDE 27 (2011), 436–446), numerical solutions at all mesh points including two boundary points are computed in our new scheme. The significant advantage of this work is to provide a rigorous analysis of convergence order for the obtained compact difference scheme using discrete energy method. The global accuracy is O(τ2 + h4) in discrete maximum norm, although the spatial approximation order at the Neumann boundary is one lower than that for interior mesh points. The analytical techniques are important and can be successfully used to solve the open problem presented by Sun (NMPDE 25 (2009), 1320–1341), where analyzed theoretical convergence order of the scheme by Liao et al. (NMPDE 22 (2006), 600–616) is only O(τ2 + h3.5) while the numerical accuracy is O(τ2 + h4), and convergence order of theoretical analysis for the scheme by Zhao et al. (NMPDE 23 (2007), 949–959) is O(τ2 + h2.5), while the actual numerical accuracy is O(τ2 + h3). Following the procedure used for the new obtained difference scheme in this work, convergence orders of these two schemes can be proved rigorously to be O(τ2 + h4) and O(τ2 + h3), respectively. Meanwhile, extension to the case involving the nonlinear reaction term is also discussed, and the global convergence order O(τ2 + h4) is proved. A compact ADI difference scheme for solving two‐dimensional case is derived. Finally, several examples are given to demonstrate the numerical accuracy of new obtained compact difference schemes. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
19.
We prove that the moduli space X(1,7) of (1,7)–polarized abelian surfaces with canonical level–structure is birational to the Fano 3–fold V22 of polar hexagons of the Klein quartic (7). In particular X(1,7) is rational and the birational map to ℙ3 is defined over ℚ. As a byproduct we obtain explicitely the equations of the (1,7)–very–ample–polarized abelian surfaces embedded in ℙ6. 相似文献
20.
A. Aguglia 《组合设计杂志》2003,11(2):79-88
An affine 2–(q3,q2, q + 1) design is constructed from a Buekenhout‐Metz unital of the affine plane AG(2,q2), with q > 2. It is also shown that such a design is isomorphic to the point‐plane design of the affine space AG(3,q). © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 79–88, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10010 相似文献