共查询到20条相似文献,搜索用时 31 毫秒
1.
Kurt Leichtweiß 《Journal of Geometry》2003,78(1-2):92-121
Analogue to the definition $K + L := \bigcup_{x\in K}(x + L)$ of the
Minkowski addition in the euclidean geometry it is proposed to define the
(noncommutative) addition $K \vdash L := \bigcup_{0\, \leqsl\, \rho\,\leqsl\,
a(\varphi),0\,\leqsl\,\varphi\,<\, 2\pi}T_{\rho}^{(\varphi)}(L)$ for compact,
convex and smoothly bounded sets K and
L in the hyperbolic plane $\Omega$
(Kleins model). Here $\rho = a(\varphi)$ is the representation of the boundary
$\partial$ K in geodesic polar coordinates
and $T_{\rho}^{(\varphi)}$ is the hyperbolic translation of $\Omega$ of length
$\rho$ along the line through the origin o of
direction $\varphi$. In general this addition does not preserve
convexity but nevertheless we may prove as main results: (1) $o \in$ int
$K, o \in$ int L and K,L horocyclic convex imply the strict
convexity of $K \vdash L$, and (2) in this case there exists a hyperbolic mixed
volume $V_h(K,L)$ of K and L which has a representation by a suitable
integral over the unit circle. 相似文献
2.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
3.
It has been shown earlier by the first author that for any nonzero perturbation of the integers $\lambda_n=n+o(1), \lambda_n\ne n$, there is a \textit{generator,} that is a function $\varphi\in L^2(\mathbf{R})$ such that the system of translates $\{\varphi(x-\lambda_n)\}$ is complete in $L^2(\mathbf{R})$. We ask if $\varphi$ can be chosen with fast decay. We prove that in general it cannot. On the other hand, if the perturbations are quasianalytically small, than it can, and this decay restriction is sharp. A certain class of complex measures which we call shrinkable is introduced, and it is shown that the zeros sets of such measures do dot admit generators with fast decay. 相似文献
4.
We investigate the Laplacian on a smooth bounded open set Rn with Wentzell-Robin boundary condition $\beta u+\frac{\partial u}{\partial \nu} + \Delta u=0$ on the boundary . Under the assumption $\memb$ C() with $\geq$ 0 , we prove that generates a differentiable positive contraction semigroup on $C(\bar{\Omega})$ and study some monotonicity properties and the asymptotic behaviour. 相似文献
5.
We extend the results for 2-D Boussinesq equations from ℝ2 to a bounded domain Ω. First, as for the existence of weak solutions, we transform Boussinesq equations to a nonlinear evolution
equation U
t
+ A(t, U) = 0. In stead of using the methods of fundamental solutions in the case of entire ℝ2, we study the qualities of F(u, υ) = (u · ▽)υ to get some useful estimates for A(t, U), which helps us to conclude the local-in-time existence and uniqueness of solutions. Second, as for blow-up criterions,
we use energy methods, Sobolev inequalities and Gronwall inequality to control
and
by
and
. Furthermore,
can control
by using vorticity transportation equations. At last,
can control
. Thus, we can find a blow-up criterion in the form of
.
相似文献
6.
Real valued M-estimators
in a statistical model 1 with observations
are replaced by
-valued M-estimators
in a new model with observations
where
are regressors,
is a structural parameter and
a structural function of the new model. Sufficient conditions for the consistency of
are derived, motivated by the sufficiency conditions for the simpler parent estimator
The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If F
has a natural exponential density ex–b( x ) then our pseudolinear model with u = (g o )–1 reduces to the well known generalized linear model, provided () = db()/d and g is the so-called link function of the generalized linear model. General results are illustrated for special pairs and leading to some classical M-estimators of mathematical statistics, as well as to a new class of generalized -quantile estimators. 相似文献
7.
A. F. Taraskin 《Journal of Mathematical Sciences》1991,53(1):78-86
For observations of independent random quantities in the series scheme we study the asymptotic behavior of the logarithm of the likelihood ratio. We find conditions for it to be asymptotically infinitely divisible. and in the parametric case we find for it the decomposition
in which () is a random variable converging in distribution to an infinitely divisible law with zero mean, finite dispersion, and Kolmogorov function
foru in some subset of the real axis, while
n
(u; )0 in probability.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 76–83, 1986. 相似文献
8.
Let
for anyf H(R), where
(x): =
–1(x–1). Then (x) P
(x + h) for some h R and > 0; P denotes the Poisson kernel.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 82–89, 1989. 相似文献
9.
We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2-periodic functions x with bounded variation of the derivative x, namely
where q (0, ), p [1, ], and = min{1/2, p/q(p + 1)}. 相似文献
10.
Letf be analytic in a hyperbolic region . The Bloch constant
f
off is defined by
, where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and
where
. Then for allf withf() , we have
f
1/(). In this paper we study the extremal functions defined by
f
=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China. 相似文献
11.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
12.
Jong Soo Jung Yeol Je Cho Shin Min Kang Byung Soo Lee Balwant Singh Thakur 《Czechoslovak Mathematical Journal》2000,50(2):379-396
Let (, ) be a measurable space and C a nonempty bounded closed convex separable subset of p-uniformly convex Banach space E for some p > 1. We prove random fixed point theorems for a class of mappings T: × C C satisfying: for each x, y C, and integer n 1,
where a, b, c: [0, ) are functions satisfying certain conditions and T
n(, x) is the value at x of the n-th iterate of the mapping T(, ·). Further we establish for these mappings some random fixed point theorems in a Hilbert space, in L
p spaces, in Hardy spaces H
p and in Sobolev spaces H
k,p for 1 < p < and k 0. As a consequence of our main result, we also extend the results of Xu [43] and randomize the corresponding deterministic ones of Casini and Maluta [5], Goebel and Kirk [13], Tan and Xu [37], and Xu [39, 41]. 相似文献
13.
Ole Barndorff-Nielsen 《Probability Theory and Related Fields》1969,12(1):56-58
Summary Let P={P
: } be an exponential family of probability distributions with the canonical parameter and consider the one to one mapping : P
. It is shown that, under mild regularity assumptions, and
–1 are continuous with respect to the Lévy metric in P and Euclidean metric in . 相似文献
14.
A Comparison of Methods for Estimating the Extremal Index 总被引:1,自引:0,他引:1
The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements. 相似文献
15.
G. Oniani 《Georgian Mathematical Journal》1999,6(2):149-168
For the frame in n, let B2()()( n) be a family of all n-dimensional rectangles containing x and having edges parallel to the straight lines of , and let MB
2() be a maximal operator corresponding to B
2(). The main result of the paper is the following
Theorem.
For any function fL(1+1n+
L)(
n
) (n2) there exists a measure preserving and invertible mapping
n
n
such that
.This theorem gives a general solution of M. de Guzmán's problem that was previously studied by various authors. 相似文献
(1) |
1\} } M_{B_2 (\theta )} (fo\omega ) < \infty .$$ " align="middle" vspace="20%" border="0"> | (2) |
16.
Qi-Man Shao 《Probability Theory and Related Fields》1992,94(1):119-133
Summary Let {X(t),t 0} be a stationary Gaussian process withEX(t)=0,EX
2(t)=1 and covariance function satisfying (i)r(t) = 1 2212;C |t | + o (|t|)ast0 for someC>0, 0<2; (ii)r(t)=0(t
–2) as t for some >0 and (iii) supts|r(t)|<1 for eachs>0. Put (t)= sup {s:0 s t,X(s) (2logs)1/2}. The law of the iterated logarithm implies
a.s. This paper gives the lower bound of (t) and obtains an Erds-Rèvèsz type LIL, i.e.,
a.s. if 0<<2 and
. Applications to infinite series of independent Ornstein-Uhlenbeck processes and to fractional Wiener processes are also given.Research supported by the Fok Yingtung Education Foundation of China and by Charles Phelps Taft Postdoctoral Fellowship of the University of Cincinnati 相似文献
17.
Majorants and Extreme Points of Unit Balls in Bernstein Spaces 总被引:1,自引:1,他引:0
The Bernstein space B
p () (1
$$
" align="middle" border="0">
0) is the set of functions from L
p(
) having Fourier transforms (in the sense of generalized functions) with supports in the compact segment [- , ]. Every function f
has an analytic continuation onto the complex plane, which is an entire function of exponential type . The spaces B
p ()\, are conjugate Banach spaces. Therefore, the closed unit ball
in B
p () has a rich set of extreme (boundary) points:
coincides with the weakly * closed convex hull of its extreme points. Since, for 1< p< , B
p () is a uniformly convex space, only the balls
and
have nontrivially arranged sets of extreme points. In this paper, in terms of zeros of entire functions, we obtain necessary and sufficient conditions of extremeness for functions from
. 相似文献
18.
M. Burak Erdogan 《Journal of Fourier Analysis and Applications》1999,5(6):523-544
The function
, is a characteristic function of a probability distribution iff
. This distribution is absolutely continuous; for =0 it is symmetric. The latter case was introduced by Linnik in 1953 [13] and several applications were found later. The case 0 was introduced by Klebanov, Maniya, and Melamed in 1984 [9], while some special cases were considered previously by Laha [12] and Pillai [18]. In 1994, Kotz, Ostrovskii and Hayfavi [10] carried out a detailed investigation of analytic and asymptotic properties of the density of the distribution for the symmetric case =0. We generalize their results to the non-symmetric case 0. As in the symmetric case, the arithmetical nature of the parameter plays an important role, but several new phenomena appear. 相似文献
19.
Let R be a Dubrovin valuation ring of a simple Artinian ring Q and let Q[X,] be the skew polynomial ring over Q in an indeterminate X, where is an automorphism of Q. Consider the natural map from Q[X,]XQ[X,] to Q, where Q[X,]XQ[X,] is the localization of Q[X,] at the maximal ideal XQ[X,] and set
, the complete inverse image of R by . It is shown that
is a Dubrovin valuation ring of Q(X,) (the quotient ring of Q[X,]) and it is characterized in terms of X and Q. In the case where R is an invariant valuation ring, the given automorphism is classified into five types, in order to study the structure of
(the value group of
). It is shown that there is a commutative valuation ring R with automorphism which belongs to each type and which makes
Abelian or non-Abelian. Furthermore, some examples are used to show that several ideal-theoretic properties of a Dubrovin valuation ring of Q with finite dimension over its center, do not necessarily hold in the case where Q is infinite-dimensional.
Presented by A. VerschorenMathematics Subject Classifications (2000) 16L99, 16S36, 16W60. 相似文献
20.
Werner Georg Nowak 《Monatshefte für Mathematik》1986,102(2):169-173
Let (a) denote the Euler totient function in an arbitrary quadratic number fieldK and defineE
K
(x) andH
K
(x) as the error terms in the asymptotic formulae for
and
, respectively, summation being extended over all ideals a with 1N(a)x. In this paper the asymptotic behaviour of
n=1
N
E
K
(n) and
n=1
N
H
K
(n)H
K
(itn) is studied. This generalizes results ofPillai andChowla [5] on the classical case.
Herrn Professor E. Hlawka zum siebzigsten Geburtstag gewidmet 相似文献
Herrn Professor E. Hlawka zum siebzigsten Geburtstag gewidmet 相似文献