共查询到20条相似文献,搜索用时 518 毫秒
1.
In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135,
1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal
and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree.
This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed
measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L
p
solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure
Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L
∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding
Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic. 相似文献
2.
Lance Nielsen 《Acta Appl Math》2010,110(1):409-429
In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are
not necessarily analytic at the origin in ℂ
n
. The method of disentangling follows Feynman’s heuristic rules from in (Feynman in Phys. Rev. 84:18–128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and
Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ
n
while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that
the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established. 相似文献
3.
Esther Ezra 《Discrete and Computational Geometry》2011,45(1):45-64
We show that the combinatorial complexity of the union of n infinite cylinders in ℝ3, having arbitrary radii, is O(n
2+ε
), for any ε>0; the bound is almost tight in the worst case, thus settling a conjecture of Agarwal and Sharir (Discrete Comput. Geom.
24:645–685, 2000), who established a nearly-quadratic bound for the restricted case of nearly congruent cylinders. Our result extends, in a significant way, the result of Agarwal and Sharir (Discrete Comput. Geom. 24:645–685, 2000), in particular, a simple specialization of our analysis to the case of nearly congruent cylinders yields a nearly-quadratic
bound on the complexity of the union in that case, thus significantly simplifying the analysis in Agarwal and Sharir (Discrete
Comput. Geom. 24:645–685, 2000). Finally, we extend our technique to the case of “cigars” of arbitrary radii (that is, Minkowski sums of line-segments and
balls) and show that the combinatorial complexity of the union in this case is nearly-quadratic as well. This problem has
been studied in Agarwal and Sharir (Discrete Comput. Geom. 24:645–685, 2000) for the restricted case where all cigars have (nearly) equal radii. Based on our new approach, the proof follows almost
verbatim from the analysis for infinite cylinders and is significantly simpler than the proof presented in Agarwal and Sharir
(Discrete Comput. Geom. 24:645–685, 2000). 相似文献
4.
In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145–210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms
arising in the analytic torsion due to the boundary, using generalizations of the Cheeger–Müller theorem. We use a formula
proved by Brüning and Ma (GAFA 16:767–873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary
(Lück, J Diff Geom 37:263–322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion
for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also
consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695–714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529–533, 2009). 相似文献
5.
In this paper, we study a variation of the equations of a chemotaxis kinetic model and investigate it in one dimension. In
fact, we use fractional diffusion for the chemoattractant in the Othmar–Dunbar–Alt system (Othmer in J Math Biol 26(3):263–298,
1988). This version was exhibited in Calvez in Amer Math Soc, pp 45–62, 2007 for the macroscopic well-known Keller–Segel model in all space dimensions. These two macroscopic and kinetic models are related
as mentioned in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009, Chalub, Math Models Methods Appl Sci, 16(7 suppl):1173–1197, 2006, Chalub, Monatsh Math, 142(1–2):123–141, 2004, Chalub, Port Math (NS), 63(2):227–250, 2006. The model we study here behaves in a similar way to the original model in two dimensions with the spherical symmetry assumption
on the initial data which is described in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009. We prove the existence and uniqueness of solutions for this model, as well as a convergence result for a family of numerical
schemes. The advantage of this model is that numerical simulations can be easily done especially to track the blow-up phenomenon. 相似文献
6.
We introduce an iterative sequence for finding the solution to 0∈T(v), where T
:
E⇉E
* is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal.
3:239–249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417–429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an
estimate of the convergence rate of the algorithm. An application to minimization problems is given.
This work was partially supported by the National Natural Sciences Grant 10671050 and the Heilongjiang Province Natural Sciences
Grant A200607. The authors thank the referees for useful comments improving the presentation and Professor K. Kohsaka for
pointing out Ref. 7. 相似文献
7.
We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average
Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton
method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295,
2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study. 相似文献
8.
Recently, Li et al. (Comput. Optim. Appl. 26:131–147, 2004) proposed a regularized Newton method for convex minimization problems. The method retains local quadratic convergence property
without requirement of the singularity of the Hessian. In this paper, we develop a truncated regularized Newton method and
show its global convergence. We also establish a local quadratic convergence theorem for the truncated method under the same
conditions as those in Li et al. (Comput. Optim. Appl. 26:131–147, 2004). At last, we test the proposed method through numerical experiments and compare its performance with the regularized Newton
method. The results show that the truncated method outperforms the regularized Newton method.
The work was supported by the 973 project granted 2004CB719402 and the NSF project of China granted 10471036. 相似文献
9.
Two natural extensions of Jensen’s functional equation on the real line are the equations f(xy) + f(xy
−1) = 2f(x) and f(xy) + f(y
−1
x) = 2f(x), where f is a map from a multiplicative group G into an abelian additive group H. In a series of papers (see Ng in Aequationes Math 39:85–99, 1990; Ng in Aequationes Math 58:311–320, 1999; Ng in Aequationes Math 62:143–159, 2001), Ng solved these functional equations for the case where G is a free group and the linear group
GLn(R), R=\mathbbZ,\mathbbR{{GL_n(R), R=\mathbb{Z},\mathbb{R}}} , is a quadratically closed field or a finite field. He also mentioned, without a detailed proof, in the above papers and
in (see Ng in Aequationes Math 70:131–153, 2005) that when G is the symmetric group S
n
, the group of all solutions of these functional equations coincides with the group of all homomorphisms from (S
n
, ·) to (H, + ). The aim of this paper is to give an elementary and direct proof of this fact. 相似文献
10.
Peter E. Kloeden Andreas Neuenkirch Raffaella Pavani 《Annals of Operations Research》2011,189(1):255-276
We adopt the multilevel Monte Carlo method introduced by M. Giles (Multilevel Monte Carlo path simulation, Oper. Res. 56(3):607–617,
2008) to SDEs with additive fractional noise of Hurst parameter H>1/2. For the approximation of a Lipschitz functional of the terminal state of the SDE we construct a multilevel estimator
based on the Euler scheme. This estimator achieves a prescribed root mean square error of order ε with a computational effort of order ε
−2. 相似文献
11.
The paper is devoted to the applications of convexifactors to bilevel programming problem. Here we have defined ∂
∗-convex, ∂
∗-pseudoconvex and ∂
∗-quasiconvex bifunctions in terms of convexifactors on the lines of Dutta and Chandra (Optimization 53:77–94, 2004) and Li and Zhang (J. Opt. Theory Appl. 131:429–452, 2006). We derive sufficient optimality conditions for the bilevel programming problem by using these functions, and we establish
various duality results by associating the given problem with two dual problems, namely Wolfe type dual and Mond–Weir type
dual. 相似文献
12.
In the paper, the authors discuss two kinds of consequence operations characterized axiomatically. The first one are consequence
operations of the type Cn
+ that, in the intuitive sense, are infallible operations, always leading from accepted (true) sentences of a deductive system to accepted (true) sentences of the deductive
system (see Tarski in Monatshefte für Mathematik und Physik 37:361–404, 1930, Comptes Rendus des Séances De la Société des Sciences et des Lettres de Varsovie 23:22–29, 1930; Pogorzelski and Słupecki in Stud Logic 9:163–176, 1960, Stud Logic 10:77–95, 1960). The second kind are dual consequence operations of the type Cn
− that can be regarded as anti-infallible operations leading from non-accepted (rejected, false) sentences of a deductive system to non-accepted (rejected, false)
sentences of the system (see Słupecki in Funkcja Łukasiewicza, 33–40, 1959; Wybraniec-Skardowska in Teoria zdań odrzuconych, 5–131, Zeszyty Naukowe Wyższej Szkoły Inżynierskiej w Opolu, Seria Matematyka
4(81):35–61, 1983, Ann Pure Appl Logic 127:243–266, 2004, in On the notion and function of rejected propositions, 179–202, 2005). The operations of the types Cn
+ and Cn
− can be ordinary finitistic consequence operations or unit consequence operations. A deductive system can be characterized
in two ways by the following triple:
${ll}{\rm by\,the\,triple}:\hspace{1.4cm}
(+ , -)\hspace{0,6cm} 13.
Rikard Olofsson 《Annales Henri Poincare》2010,11(7):1285-1302
We study the eigenfunctions of the quantized cat map, desymmetrized by Hecke operators. In the papers (Olofsson in Ann Henri
Poincaré 10(6):1111–1139, 2009; Math Phys 286(3):1051–1072, 2009) it was observed that when the inverse of Planck’s constant is a prime exponent N = p
n
, with n > 2, half of these eigenfunctions become large at some points, and half remains small for all points. In this paper we study
the large eigenfunctions more carefully. In particular, we answer the question of for which q the L
q
norms remain bounded as N goes to infinity. The answer is q ≤ 4. 相似文献
14.
Jean-Marie Mirebeau 《Constructive Approximation》2010,32(2):339-383
Given a function f defined on a bounded domain Ω⊂ℝ2 and a number N>0, we study the properties of the triangulation TN\mathcal{T}_{N} that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the norm X=L
p
for 1≤p≤∞, and we consider Lagrange finite elements of arbitrary polynomial degree m−1. We establish sharp asymptotic error estimates as N→+∞ when the optimal anisotropic triangulation is used, recovering the results on piecewise linear interpolation (Babenko
et al. in East J. Approx. 12(1), 71–101, 2006; Babenko, submitted; Chen et al. in Math. Comput. 76, 179–204, 2007) and improving the results on higher degree interpolation (Cao in SIAM J. Numer. Anal. 45(6), 2368–2391, 2007, SIAM J. Sci. Comput. 29, 756–781, 2007, Math. Comput. 77, 265–286, 2008). These estimates involve invariant polynomials applied to the m-th order derivatives of f. In addition, our analysis also provides practical strategies for designing meshes such that the interpolation error satisfies
the optimal estimate up to a fixed multiplicative constant. We partially extend our results to higher dimensions for finite
elements on simplicial partitions of a domain Ω⊂ℝ
d
. 相似文献
15.
It is known that Jacobi’s last multiplier is directly connected to the deduction of a Lagrangian via Rao’s formula (Madhava
Rao in Proc. Benaras Math. Soc. (N.S.) 2:53–59, 1940). In this paper we explicitly demonstrate that it also plays an important role in Hamiltonian theory. In particular, we apply
the recent results obtained by Torres del Castillo (J. Phys. A Math. Theor. 43:265202, 2009) and deduce the Hamiltonian of a second-order ODE of the Lienard type, namely, [(x)\ddot]+f(x)[(x)\dot]2+g(x)=0\ddot{x}+f(x){\dot{x}}^{2}+g(x)=0. In addition, we consider cases where the coefficient functions may also depend on the independent variable t. We illustrate our construction with various examples taken from astrophysics, cosmology and the Painlevé-Gambier class of
differential equations. Finally we discuss the Hamiltonization of third-order equations using Nambu-Hamiltonian mechanics. 相似文献
16.
In this paper, we analyze the outer approximation property of the algorithm for generalized semi-infinite programming from
Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). A simple bound on the regularization error is found and used to formulate a feasible numerical method for generalized semi-infinite programming with convex lower-level problems. That is, all iterates of the
numerical method are feasible points of the original optimization problem. The new method has the same computational cost
as the original algorithm from Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). We also discuss the merits of this approach for the adaptive convexification algorithm, a feasible point method for standard
semi-infinite programming from Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007). 相似文献
17.
Endre Boros Khaled Elbassioni Vladimir Gurvich Hans Raj Tiwary 《Annals of Operations Research》2011,188(1):63-76
Given a graph G=(V,E) and a weight function on the edges w:E→ℝ, we consider the polyhedron P(G,w) of negative-weight flows on G, and get a complete characterization of the vertices and extreme directions of P(G,w). Based on this characterization, and using a construction developed in Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190,
2008), we show that, unless P=NP, there is no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness
result of Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190, 2008) for non 0/1-polyhedra, and comes in contrast with the polynomiality of vertex enumeration for 0/1-polytopes (Bussiech and
Lübbecke in Comput. Geom., Theory Appl. 11(2):103–109, 1998). As further applications, we show that it is NP-hard to check if a given integral polyhedron is 0/1, or if a given polyhedron
is half-integral. Finally, we also show that it is NP-hard to approximate the maximum support of a vertex of a polyhedron
in ℝ
n
within a factor of 12/n. 相似文献
18.
Jean-Marie Mirebeau 《Numerische Mathematik》2012,120(2):271-305
Given a function f defined on a bounded polygonal domain
W ì \mathbbR2{\Omega \subset \mathbb{R}^2} and a number N > 0, we study the properties of the triangulation TN{\mathcal{T}_N} that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W
1, p
semi-norm for 1 ≤ p < ∞, and we consider Lagrange finite elements of arbitrary polynomial order m − 1. We establish sharp asymptotic error estimates as N → +∞ when the optimal anisotropic triangulation is used. A similar problem has been studied in Babenko et al. (East J Approx.
12(1):71–101, 2006), Cao (J Numer Anal. 45(6):2368–2391, 2007), Chen et al. (Math Comput. 76:179–204, 2007), Cohen (Multiscale, Nonlinear and Adaptive Approximation. Springer, Berlin, 2009), Mirebeau (Constr Approx. 32(2):339–383, 2010), but with the error measured in the L
p
norm. The extension of this analysis to the W
1, p
norm is required in order to match more closely the needs of numerical PDE analysis, and it is not straightforward. In particular,
the meshes which satisfy the optimal error estimate are characterized by a metric describing the local aspect ratio of each
triangle and by a geometric constraint on their maximal angle, a second feature that does not appear for the L
p
error norm. Our analysis also provides with practical strategies for designing meshes such that the interpolation error satisfies
the optimal estimate up to a fixed multiplicative constant. 相似文献
19.
Wenchang Chu 《The Ramanujan Journal》2011,26(2):251-255
The general summation theorem for well-poised 5
F
4-series discovered by Dougall (Proc. Edinb. Math. Soc. 25:114–132, 1907) is shown to imply several infinite series of Ramanujan-type for 1/π and 1/π
2, including those due to Bauer (J. Reine Angew. Math. 56:101–121, 1859) and Glaisher (Q. J. Math. 37:173–198, 1905) as well as some recent ones by Levrie (Ramanujan J. 22:221–230, 2010). 相似文献
20.
Hong Oh Kim Rae Young Kim Yeon Ju Lee Jungho Yoon 《Advances in Computational Mathematics》2010,33(3):255-283
We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family
has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system (Wei et al., IEEE Trans Image Proc 7:1000–1013, 1998). Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though
the construction of the new biorthogonal wavelet systems, in fact, starts from a new class of quasi-interpolatory subdivision
schemes, we find that the refinement masks accidently coincide with the ones by Cohen et al. (Comm Pure Appl Math 45:485–560,
1992, §6.C) (or Daubechies 1992, §8.3.5), which are designed for the purpose of generating biorthogonal wavelets close to orthonormal cases. However, the
corresponding mathematical analysis is yet to be provided. In this study, we highlight the connection between the quasi-interpolatory
subdivision schemes and the masks by Cohen, Daubechies and Feauveau, and then we study the fundamental properties of the new
biorthogonal wavelet systems such as regularity, stability, linear independence and accuracy. 相似文献
|