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1.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ...,
n
) = 1(1) + ... +
n
(
n
), where
i
(
i
) are ordinary moduli of continuity that depend on one variable. In the case where
i
(
i
) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L
2 for (1, ...,
n
) = 1(1) + ... +
n
(
n
); (ii) in the integral metric L
p (p 1) for (1, ...,
n
) = c
11 + ... + c
n
n
; (iii) in the integral metric L
(2, ..., 2, 2r) (r = 2, 3, ...) for (1, ...,
n
) = 1(1) + ... +
n – 1(
n – 1) + c
n
n
. 相似文献
2.
Wolfgang Reichel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):822-838
We consider the equation
(pu)-qu+wu
= f
in (0,1) subject to homogenous boundary conditions at
x = 0
and
x = 1, e.g.,
u(0)
= u(1) = 0. Let
1
be the first eigenvalue of the corresponding Sturm-Liouville problem. If
f 0
but
0 then it is known that there exists
> 0 (independent on
f) such that for
(1,
1 + ]
any solution
u
must be negative. This so-called
uniform anti-maximum principle
(UAMP)
goes back to Clément, Peletier [4]. In this paper we
establish the sharp values of
for which (UAMP) holds. The same phenomenon, including sharp values of
, can be shown for the radially symmetric
p-Laplacian on balls and annuli in
n
provided
1 n <
p. The results are illustrated by
explicitly computed examples. 相似文献
3.
Gert K. Pedersen 《Inventiones Mathematicae》1978,45(3):299-305
For each*-derivation of a separableC
*-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x. 相似文献
4.
Blow-up rates for parabolic systems 总被引:7,自引:0,他引:7
Keng Deng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(1):132-143
Let
n
be a bounded domain andB
R
be a ball in
n
of radiusR. We consider two parabolic systems: ut=u +f(), i= +g(u) in × (0,T) withu=v=0 on × (0,T) andu
t
=u, v
t
=v inB
r
× (0,T) withe/v=f (v), e/v=g(u) onB
R
× (0,T). Whenf(v) andg(u) are power law or exponential functions, we establish estimates on the blow-up rates for nonnegative solutions of the systems. 相似文献
6.
Yiqiang Zhou 《Algebra Colloquium》2000,7(3):305-318
For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(RR) = Jac(R/Soc(RR)) and show, among others, the following results:
The research was partially supported by the NSERC of Canada under Grant OGP0194196.2000 Mathematics Subject Classification: 16L30, 16E50 相似文献
(1) | (R) is the largest -small right ideal of R. |
(2) | R is -semiregular if and only if R/(R) is a von Neumann regular ring and idempotents of R(R) lift to idempotents of R. |
(3) | R is -semiperfect if and only if R/(R) is a semisimple ring and idempotents of R/(R) lift to idempotents of R. |
(4) | R is -perfect if and only if R/Soc(RR) is a right perfect ring and idempotents of R/(R) lift to idempotents of R. |
7.
Using the well known properties of thes-stage implicit Runge-Kutta methods for first order differential equations, single step methods of arbitrary order can be obtained for the direct integration of the general second order initial value problemsy=f(x, y, y),y(x
o)=y
o,y(x
o)=y
o. These methods when applied to the test equationy+2y+
2
y=0, ,0, +>0, are superstable with the exception of a finite number of isolated values ofh. These methods can be successfully used for solving singular perturbation problems for which f/y and/or f/y are negative and large. Numerical results demonstrate the efficiency of these methods. 相似文献
8.
We construct the CR invariant canonical contact form can(J) on scalar positive spherical CR manifold (M,J), which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold ()/, where is a convex cocompact subgroup of AutCRS2n+1=PU(n+1,1) and () is the discontinuity domain of . This contact form can be used to prove that ()/ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent ()<n (respectively, ()>n, or ()=n). This generalizes Nayatanis result for convex cocompact subgroups of SO(n+1,1). We also discuss the connected sum of spherical CR manifolds. 相似文献
9.
Yimin Xiao 《Journal of Theoretical Probability》1997,10(4):849-866
Let X(t) (tR) be a real-valued centered Gaussian process with stationary increments. We assume that there exist positive constants
0, C
1, and c
2 such that for any tR and hR with |h|0
and for any 0r<min{|t|, 0}
where
is regularly varying at zero of order (0 < < 1). Let be an inverse function of near zero such that (s)=(s) log log(1/s) is increasing near zero. We obtain exact estimates for the weak -variation of X(t) on [0,a]. 相似文献
10.
Stephan Ruscheweyh 《Numerische Mathematik》1984,45(2):227-240
Summary Given a complex polynomialp we determine a functionf
p
: such that |p(f
p
(z))||p(z)|,z withk<1. This result is used to introduce a global root-finding algorithm for polynomials. 相似文献
11.
Ya. V. Kurylev 《Journal of Mathematical Sciences》1987,38(1):1633-1641
We consider the propagation of concentrated wave packets along space-time rays for the case of frequency-dependent velocity: c=co(x,t)+c1(x,t,), 1. The complex ray method is applied to construct formal asymptotic expansions. It is shown that these packets may propagate only at certain medium-determined frequencies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 104–115, 1985.In conclusion, I would like to thank I. A. Molotkov for proposing the problem and for useful comments and A. P. Kachalov for fruitful discussion. 相似文献
12.
S. A. Telyakovskii 《Mathematical Notes》1993,54(3):940-945
Asymptotic estimates for the integral modulus of continuity of order s of the Dirichlet kernel and the conjugate Dirichlet kernel are obtained. For example, if k/2, then
s
(D
k
,)=2
s
+1/2sin
s
k/2 log(1+k/s)+O(2
s
sin
s
k/2)holds uniformly with respect to all the parameters.Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 98–105, September, 1993. 相似文献
13.
E. P. Fadeeva 《Journal of Mathematical Sciences》1991,53(1):87-94
We present an explicit solution of the problem of optimal linear filtering: the recovery of the useful signal(s) at the instantt+, (>0,<0, or=0) from known values of the received signal(s)=(s)+(s) in the past, i.e., at the instantt–s, s0. In doing so we assume the random processes(s) and /gr(s) are stationary and jointly stationary, while the stationary process of noise (s) with zero mean is assumed to be mutually correlated and jointly stationary with the process(s) under the assumption that there exists a common spectral densityf() for these processes.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 83–91, 1986. 相似文献
14.
Karl Dilcher 《Aequationes Mathematicae》1994,48(1):55-85
Summary We study a class of generalized gamma functions
k
(z) which relate to the generalized Euler constants
k
(basically the Laurent coefficients of(s)) as (z) does to the Euler constant. A new series expansion for
k
is derived, and the constant term in the asymptotic expansion for log
k
(z) is studied in detail. These and related constants are numerically computed for 1 k 15. 相似文献
15.
S. V. Petras 《Journal of Mathematical Sciences》1984,24(3):380-386
The behavior of the poles zn(), n=1,2,... of the scattering matrix of the operatorl
u=–u(x), x , (u/n)+(x)u|=0 as 0 is considered. It is proved that |zn()–zn|=0((1/2)qn), where qn is the order of the pole of the scattering matrix for the operator 0u=–u, u/=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981. 相似文献
16.
V. M. Badkov 《Mathematical Notes》1973,13(5):453-459
For the polynomials {pn(t)}
0
, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)
v=1
m
, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
2)
and 3)
with the conditions that
on [–1, 1] and (H,)–1 L2(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973. 相似文献
17.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z
(n) and k(n, ) z
(n). 相似文献
18.
This article is the first in a series of three articles that discuss a particular class of minihypers and its applications. Proving that for small and < N, a {v
+ 1, v
; N, q}-minihyper consists of a sum of -spaces, we show that the excess points of an s-cover with excess of PG(N, q), (s + 1)|(N + 1), form a sum of s-spaces, and that no maximal partial s-spreads with deficiency of PG(N, q), (s + 1)|(N + 1), exist. The case q square will be studied in greater detail in [7] and further applications of these classification results on this class of minihypers will be published in [8]. 相似文献
19.
Willy Kellenberger 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(4):647-651
Summary In order to determine the roots of a polynomialp, a sequence of numbers {x
k} is constructed such that the associated sequence {|p(x
k)|} decreases monotonically. To determine a new iteration pointx
k+1 such that |p(x
k+1)|<-|p(x
k)| ( is a positive real constant, <1, depending only on the degree ofp), we determine a circleK aroundx
k which contains no root ofp and compute the values ofp atN points which are distributed equally on the circumference ofK (N again depends only on the degree ofp); at least one of theN points is shown to satisfy the given condition. Computing the function values by means of Fourier synthesis according to Cooley-Tukey [2] and combining our iteration step with the normal step of the method of Nickel [1], we obtain a numerically safe and fast algorithm for determining the roots of arbitrary polynomials. 相似文献
20.
Ryoichi Shimizu Yasunori Fujikoshi 《Annals of the Institute of Statistical Mathematics》1997,49(2):285-297
Let Z be a random variable with the distribution function G(x) and let s be a positive random variable independent of Z. The distribution function F(x) of the scale mixture X = sZ is expanded around G(x) and the difference between F(x) and its expansion is evaluated in terms of a quantity depending only on G and the moments of the powers of the variable of the form s/gr - 1, where (> 0) and (= ±1) are parameters indicating the types of expansion. For = -1, the bound is sharp under some extra conditions. Sharp bounds for errors of the approximations of the scale mixture of the standard normal and some gamma distributions are given either by analysis ( = -1) or by numerical computation ( = 1). 相似文献