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101.
In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u| weighted HLS inequality in Theorem 1.1 and the |z| weighted HLS inequality in Theorem 1.5 (where we have denoted u=(z,t) as points on the Heisenberg group). Then we provide regularity estimates of positive solutions to integral systems which are Euler–Lagrange equations of the possible extremals to the Stein–Weiss inequalities. Asymptotic behavior is also established for integral systems associated to the |u| weighted HLS inequalities around the origin. By these a priori estimates, we describe asymptotically the possible optimizers for sharp versions of these inequalities. 相似文献
102.
Nicholas J. Daras 《Numerical Algorithms》1999,20(4):285-301
Padé-type approximation is the rational function analogue of Taylor’s polynomial approximation to a power series. A general
method for obtaining Padé-type approximants to Fourier series expansions of harmonic functions is defined. This method is
based on the Newton-Cotes and Gauss quadrature formulas. Several concrete examples are given and the convergence behavior
of a sequence of such approximants is studied.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
103.
104.
《Journal of Pure and Applied Algebra》2022,226(12):107137
We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the notion of bifinal object and prove that a (lax) bilimit is a limiting bifinal object in the 2-category of (lax) cones. Everything is developed in the context of marked 2-categories, so that the machinery can be applied to different levels of laxity, including pseudo-limits. 相似文献
105.
Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA
N, N
, withA nonsingular, andb
N
are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure. 相似文献
106.
Summary. In shape optimization problems, each computation of
the cost function by the finite element method
leads to an expensive analysis. The use of the second order derivative
can help to reduce the number of analyses. Fujii ([4], [10])
was the first to study this problem. J. Simon [19] gave the second order
derivative for the Navier-Stokes
problem, and the authors describe in [8], [11], a method which gives an
intrinsic expression of the first and second order derivatives on the
boundary
of the involved domain.
In this paper we study higher order derivatives. But one can ask
the following questions:
-- are they expensive to calculate?
-- are they complicated to use?
-- are they imprecise?
-- are they useless?
\medskip\noindent
At first sight, the answer seems to be positive, but classical results of
V. Strassen [20] and J. Morgenstern [13] tell us that the higher order
derivatives are not expensive to calculate, and can be computed
automatically. The purpose of this paper is to give an answer to the third
question by proving that the higher order derivatives of a function can be
computed with the same precision as the function itself.
We prove also that the derivatives so computed are
equal to the derivatives of the discrete problem (see Diagram 1). We
call the discrete
problem the finite dimensional problem processed by the computer. This result
allows the use of automatic differentiation ([5], [6]), which works only on
discrete problems.
Furthermore, the computations of Taylor's expansions
which are proposed at the end of this paper, could be a partial answer to
the last question.
Received January 27, 1993/Revised version received July 20, 1993 相似文献
107.
A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...ksuch that (x
1)...(xk). Let P
nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P
nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x
t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + k, k) , where k 0 as k. Alternatively, the largest k such that every regression on P
nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)–2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element. 相似文献
108.
In this paper we shall first introduce the Pascal k-eliminated functional matrices Pn,k[xyz] and CPn,k[xyz]. Then, using these matrices we obtain several important combinatorial identities. Finally, using the matrix inversion of Pn,k[xyz] and CPn,k[xyz], we derive an interesting formula for Eulerian numbers [7] 相似文献
109.
In this paper we generalize the construction - introduced by Gagliardi and Grasselli in the closed case - of a coloured-graph
representing the product of two manifolds, starting by two coloured graphs representing the manifolds themselves, to the boundary
case. In particular we study the genus of the graph product of low dimensional manifold ( resp. n-spheres ) with m-disks.
Received September 28, 1998; in final form January 5, 2000 / Published online October 11, 2000 相似文献
110.
An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C *-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000 相似文献