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1.
Provided the non-negative function
allows for a generalized Hardy-Sobolev inequality, existence and uniqueness of global weak solutions of the possibly degenerate parabolic PDE
, subject to homogeneous Dirichlet boundary conditions, is proved. The maximum/minimum principle holds. The associated entropy decays exponentially as t with a rate not exceeding 2/C, where C is the constant arising in the generalized Hardy-Sobolev inequality.A.U. acknowledges support from the DFG Forschungszentrum Mathematics for Key Technologies, project D10 (Berlin) and from the EU Research Network HYKE.M.R. acknowledges the hospitality of the mathematical department, Universität Kaiserslautern, where this work was carried out. 相似文献
2.
Richard Urzúa Luz 《Bulletin of the Brazilian Mathematical Society》2003,34(2):287-302
Let a minimal affine
-action on the torus
T
q
,
p 2 and
q 1. The cohomology of
(see definition below) depends on both the algebraic properties
of the induced action on H
1(T
q
,
) and the arithmetical
properties of the translation cocycle. We give a Diophantine
condition that characterizes those affine actions whose first
cohomology group is finite dimensional. In this case it is
necessarily isomorphic to
. Thus the
-action
F
obtained by suspension of is parameter
rigid, i.e., any other
-action with the same
orbit foliation is smoothly conjugate to a reparametrization of
F
by
an automorphism of
.*Partially supported by CNPq fellowship by Fondecyt Grant
1000047 and DGICT-UCN and fundación Andes, Chile. 相似文献
3.
We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes. 相似文献
4.
Let G be the complex general linear group and its Lie algebra equipped with a factorizable Lie bialgebra structure; let Uħ() be the corresponding quantum group. We construct explicit Uħ()-equivariant quantization of Poisson orbit bundles O
λ → O
μ in *. 相似文献
5.
Let áA, B | Am=1, Bn=At, BAB-1=Ar?\langle A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB^{-1}=A^\rho\rangle
where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d. 相似文献
6.
Gonchar V. Yu. Tanatarov L. V. Chechkin A. V. 《Theoretical and Mathematical Physics》2002,131(1):582-594
The properties of stationary solutions of the one-dimensional fractional Einstein--Smoluchowski equation with a potential of the form x
2m+2, m=1,2,..., and of the Riesz spatial fractional derivative of order , 12, are studied analytically and numerically. We show that for 1<2, the stationary distribution functions have power-law asymptotic approximations decreasing as x
–(+2m+1) for large values of the argument. We also show that these distributions are bimodal. 相似文献
7.
We consider solutions of the class of ODEs y=6y
2–x
, which contains the first Painlevé equation (PI) for =1. It is well known that PI has a unique real solution (called a tritronquée solution) asymptotic to
and decaying monotonically on the positive real line. We prove the existence and uniqueness of a corresponding solution for each real nonnegative 1. 相似文献
8.
Guyan Robertson 《K-Theory》2001,22(3):251-269
Let be a torsionfree lattice in G=PGL(n+1,
, where n 1 and
is a nonArchimedean local field. Then acts on the Furstenberg boundary G/P, where P is a minimal parabolic subgroup of G. The identity element I in the crossedproduct C
*algebra C(G/P) generates a class [I] in the K
0 group of C(G/P) . It is shown that [I] is a torsion element of K
0 and there is an explicit bound for the order of [I]. The result is proved more generally for groups acting on affine buildings of type Ã
n. For n=1, 2 the Euler–Poincaré characteristic () annihilates the class [I]. 相似文献
9.
There have been many results obtained so far for the mean square of the (absolute) value of the Dirichlet L-function L(s,) in the critical strip 0<<1, especially on the critical line , but relatively few results were known for discrete mean value of |L(1,)|2 till W. Zhang had published papers improving the error term step by step, which have recently been superseded by M. Katsurada and K.Matsumoto in which they succeeded in deriving an asymptotic formula for 0|L(1,)|2. The object of our paper is to point out a structural property contained in the formation of the mean square, to find out the niryana–the true body of the above sum.Dedicated to Professor Jean Louis Nicolás on his sixtieth birthdayin final form: 7 October 2003 相似文献
10.
Bullough R. K. Bogolyubov N. M. Kapitonov V. S. Malyshev C. Timonen J. Rybin A. V. Varzugin G. G. Lindberg M. 《Theoretical and Mathematical Physics》2003,134(1):47-61
We evaluate finite-temperature equilibrium correlators
for thermal time ordered Bose fields
to good approximations by new methods of functional integration in d=1,2,3 dimensions and with the trap potentials V(r)0. As in the translationally invariant cases, asymptotic behaviors fall as
to longer-range condensate values for and only for d=3 in agreement with experimental observations; but there are generally significant corrections also depending on
due to the presence of the traps. For d=1, we regain the exact translationally invariant results as the trap frequencies 0. In analyzing the attractive cases, we investigate the time-dependent c-number Gross–Pitaevskii (GP) equation with the trap potential for a generalized nonlinearity –2c||2n
and c<0. For n=1, the stationary form of the GP equation appears in the steepest-descent approximation of the functional integrals. We show that collapse in the sense of Zakharov can occur for c=0 and nd2 and a functional E
NLS[]0 even when V(r)0. The singularities typically arise as -functions centered on the trap origin r=0. 相似文献
11.
We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.This revised version was published online in October 2004 with a corrected Received date. 相似文献
12.
Let M be a Riemannian manifold. A complete geodesic on M means that :(-,+)M is a normalized geodesic. In this paper, we prove that on (S2,g) with positive curvature, any two complete geodesics must intersect an infinite number of times, and a complete geodesic must self-intersect an infinite number of times. Mathematics Subject Classification (2000) 53C40 (53C22) 相似文献
13.
In this note we consider the Gross-Pitaevskii equation i
t
++(1–2)=0, where is a complex-valued function defined on N×, and study the following 2-parameters family of solitary waves: (x, t)=e
it
v(x
1–ct, x), where
and x denotes the vector of the last N–1 variables in
N
. We prove that every distribution solution , of the considered form, satisfies the following universal (and sharp) L
-bound:
This bound has two consequences. The first one is that is smooth and the second one is that a solution 0 exists, if and only if
. We also prove a non-existence result for some solitary waves having finite energy. Some more general nonlinear Schrödinger equations are considered in the third and last section. The proof of our theorems is based on previous results of the author ([7]) concerning the Ginzburg-Landau system of equations in
N
.Received May 31, 2002
Published online February 7, 2003 相似文献
14.
N. Watt 《Monatshefte für Mathematik》2004,141(1):45-81
For X,Y,>0, let and define I
8(X,Y,) to be the cardinality of the set. In this paper it is shown that, for >0, Y
2/X
3=O(), =O(Y
3/X
3) and X=O (Y
2), one has I
8(X,Y,)=O(X
2
Y
2+X
min (X
{3/2}
Y
3, X
{11/2}
Y
{–1})+X
min ({1/3}
X
2
Y
3, X
{14/3}
Y
{1/3})), with the implicit constant depending only on . There is a brief report on an application of this that leads, by way of the Bombieri-Iwaniec method for exponential sums, to some improvement of results on the mean squared modulus of a Dirichlet L-function along a short interval of its critical line. 相似文献
15.
Uri Elias 《Monatshefte für Mathematik》2004,142(3):205-225
The paper studies singular eigenvalue problems for the equation y
(n)
+p(x)y=0 with boundary conditions imposed on the derivatives y
(i)
at the points x=a and x=. We look for singular problems which are analogous to regular problems on a finite interval. It is characterized when each eigenfunction has a finite number of zeros and when the spectrum is discrete or continuous, respectively. 相似文献
16.
17.
A. V. Kotikov L. N. Lipatov A. I. Onishchenko V. N. Velizhanin 《Theoretical and Mathematical Physics》2007,150(2):213-224
We present results for the universal anomalous dimension γun(j) of Wilson twist-2 operators in the
supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting
the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis
of the integrability of the
supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 249–262, February, 2007. 相似文献
18.
Summary. We consider a fully discrete finite element approximation of the nonlinear cross-diffusion population model: Find ui, the population of the ith species, i=1 and 2, such that where ji and gi(u1,u2):=(i–iiui–ijuj)ui. In the above, the given data is as follows: v is an environmental potential, ci, ai are diffusion coefficients, bi are transport coefficients, i are the intrinsic growth rates, and ii are intra-specific, whereas ij, ij, are interspecific competition coefficients. In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d3. Finally some numerical experiments in one space dimension are presented.Mathematics Subject Classification (2000): 65M60, 65M12, 35K55, 92D25Acknowledgements. Part of this work was carried out while the authors participated in the 2003 programme {\it Computational Challenges in Partial Differential Equations} at the Isaac Newton Institute, Cambridge, UK. 相似文献
19.
Amnon Neeman 《K-Theory》2001,22(1-2):1-144
Let
be a triangulated category, and assume it admits at least one model. In this article, we define a K-theory for
. The main theorem is that, given any bounded i-structure on
, the K-theory of the heart agrees with the K-theory of
. An immediate consequence tells us that, if two Abelian categories occur as hearts of a triangulated category for two different t-structures, then their K-theories must be isomorphic.The proof was also sketched in previous articles in this series. The virtue of this article is in the careful detail in which it is written down. 相似文献
20.
Robert Schaback 《Constructive Approximation》2005,21(3):293-317
In many cases, multivariate interpolation by smooth radial basis
functions converges toward polynomial interpolants, when the
basis functions are scaled to become flat.
In particular, examples show and this paper proves that
interpolation by scaled Gaussians
converges toward the de Boor/Ron least polynomial interpolant.
To arrive at this result, a few new tools are necessary.
The link between radial basis functions
and multivariate polynomials is provided by
radial polynomials ||x-y||22l\|x-y\|_2^{2\ell} that already occur in the seminal paper by C.A. Micchelli
of 1986. We study the polynomial
spaces spanned by linear combinations of
shifts of radial polynomials and introduce the notion
of a discrete moment basis to define
a new well-posed multivariate polynomial interpolation process
which is of minimal degree and also least and degree-reducing
in the sense of de Boor and Ron.
With these tools at hand, we generalize
the de Boor/Ron interpolation process and show that it
occurs as the limit of interpolation by Gaussian
radial basis functions. As a byproduct, we get
a stable method for preconditioning the matrices arising
with interpolation by smooth radial basis functions. 相似文献