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1.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
2.
We construct integral operators Rr and Hr on a regular q-pseudoconcave CR manifoldM such that
for f∈C
(0,r)
∞
(M) and prove sharp estimates in a special Lipschitz scale. 相似文献
3.
Qikeng Lu 《中国科学A辑(英文版)》1998,41(10):1061-1067
Let the coordinatex=(x
0,x
1,x
2,x
3) of the Minkowski spaceM
4 be arranged into a matrix
Then the Minkowski metric can be written as
. Imbed the space of 2 × 2 Hermitian matrices into the complex Grassmann manifoldF(2,2), the space of complex 4-planes passing through the origin ofC
2×4. The closure
ofM
4 inF(2,2) is the compactification ofM
4. It is known that the conformal group acts on
. It has already been proved that onF(2,2) there is anSu(2)-connection
whereZ is a 2 × 2 complex matrix andZ
†the complex conjugate and transposed matrix ofZ. Restrict this connection to
which is anSu(2)-connection on
. It is proved that its curvature form
satisfies the Yang-Mills equation
.
Project partially supported by the National Natural Science Foundation of China (Grant No. 19131010) and Fundamental Research
Bureau of CAS. 相似文献
4.
LetW be an open Riemann surface and
ap-sheeted (1<p<∞) unlimited covering surface ofW. Denote by Δ1 (resp.,
) the minimal Martin boundary ofW (resp.,
). For ζ ∈ Δ, let
ζ be the (cardinal) number of the set of pionts
which lie over ζ and
the class of open connected subsetsM ofW such thatM∪{ζ} is a minimal fine neighborhood of ζ. Our main result is the following:
, where
is the number of components of π-1
M and π is the projection of
ontoW. Moreover, some applications of the above results are discussed whenW is the unit disc. 相似文献
5.
Summary Let Mm,
m be two m-dimensional compact oriented hypersurfaces of class C3 immersed in a Riemannian manifold Rm+1 of constant sectional curvature. Suppose that Rm+1 admits a one-parameter continuous group G of conformal transformations satisfying a certain condition (which holds automatically
when G is a group of isometric transformations). Suppose further that there is a1 − 1 transformation Tτ ∈ G between Mm and
m such that
for each P ∈ Mm and each
m. If the r-th mean curvature for any r, 1 ⩽ r ⩽ m, of Mm at each point P ∈ Mm is equal to that of
m at the corresponding point
, together with other conditions, then Mm and
m are congruent mod G. This is a generalization of a joint theorem ofH. Hopf andY. Katsurada [5] in which G is a group of isometric transformations.
Entrata in Redazione il 13 Giugno 1975.
The first author was partially supported by the National Science Foundation grant GP-33944. 相似文献
6.
L. I. Danilov 《Theoretical and Mathematical Physics》2000,124(1):859-871
The absolute continuity of the spectrum for the periodic Dirac operator
, is proved given that A∈C(R
n;R
n)⊂H
loc
q(R
n;R
n), 2q>n−2, and also that the Fourier series of the vector potential A:R
n→R
n is absolutely convergent. Here,
are continuous matrix functions and
for all anticommuting Hermitian matrices
.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 3–17, July, 2000. 相似文献
7.
We obtain new exact inequalities of the form
for functions defined on the axis R or the semiaxis R
+ in the case where
for functions defined on the axis R in the case where
and for functions of constant sign on R or R
+ in the case where
and in the case where
.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 291–302, March, 2006. 相似文献
8.
Stephen H. Hechler 《Israel Journal of Mathematics》1973,14(2):115-148
For every uncountable cardinal κ define a metric spaceS to be κ-superuniversal iff for every metric spaceU of cardinality κ, every partial isometry intoS from a subset ofU of cardinality less than κ can be extended to all ofU. We prove that any such space must have cardinality at least
, and for each regular uncountable cardinal κ, we construct a κ-superuniversal metric space of cardinality
, It is proved that there is a unique κ-superuniversal metric space of cardinality κ iff
. Several decomposition theorems are also proved, e.g., every κ-superuniversal space contains a family of
disjoint κ-superuniversal subspaces. Finally, we consider some applications to more general topological spaces, to graph
theory, and to category theory, and we conclude with a list of open problems. 相似文献
9.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1986,38(1):195-204
Summary LetX be a positive random variable with the survival function
and the densityf. LetX have the moments μ=E(X) and μ2=E(X
2) and put ε=|1-μ2/2μ2|. Put
and
. It is proved that the following inequalities hold:
, for allx>0, ifq(x) is monotone and that
, ifq
1
(x) is monotone. It is also shown that Brown's inequality
which holds wheneverq
1
(x) is increasing is not valid in general whenq
1 is decreasing.
The Institute of Statistical Mathematics 相似文献
10.
Let X = {X(t),t <σ} (σ is lifespan) be a birth and death process with explosion whose characteristic triple (Mα,MC,MD) of MX in terms of (α, C, D) and M. This means that a lot of given birth and death processes can be embedded in one and the same birth and death process. If κ∈ E and M = {κ},we decompose X into κX, κ∈ E. 相似文献
11.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
12.
Nakao HAYASHI Pavel I. NAUMKIN 《数学学报(英文版)》2006,22(5):1441-1456
We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut+uux-uxx+uxxx=0,x∈R,t〉0. We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that if the initial data u0 ∈H^s (R)∩L^1 (R), where s 〉 -1/2, then there exists a unique solution u (t, x) ∈C^∞ ((0,∞);H^∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u(t)=t^-1/2fM((·)t^-1/2)+0(t^-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L^1 (R), then the asymptotics are true u(t)=t^-1/2fM((·)t^-1/2)+O(t^-1/2-γ) where γ ∈ (0, 1/2). 相似文献
13.
O. V. Kulikova 《Journal of Mathematical Sciences》2007,142(2):1942-1948
Under the condition of asphericity of a quotient group
, mutual commutants of the form
in hyperbolic groups G are investigated together with the structure of central subgroups
in central extensions
of
. In particular, quotients of the form G/[g
m
, G] are considered, where g is an element of infinite order from a hyperbolic group G and m is sufficiently large (depending on g).
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 115–125, 2005. 相似文献
14.
A. M. Arkhipov 《Journal of Mathematical Sciences》2006,139(6):7013-7024
In this paper, we consider the Kuramoto-Sivashinskii equation on the multidimensional torus with a Riemannian metric:
where
. For this equation the theorem on energy transfer holds. It is formulated in the following way. Let
be the Fourier expansion of the function u. Denote by P
N
and P
N
⊥
the operators of rejection of the “leading” and, respectively, “lowest” terms of the Fourier expansion (harmonics), i.e.,
.
For any ρ > 0,N ∈ ℕ, s ≥ n/2+5, and λ ∈ (0, 1), there exists R such that for any function. ϕ ∈
lying outside the ball
in the ball
, there exists an instant of time t ∈ (0, 1) such that g
KS
t
ϕ=ψ and
. Here, R is a constant depending on the metric (g), n
s
is the sth Sobolev norm, and
is the C
1-norm.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
15.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
16.
Michael Christ 《Journal of Geometric Analysis》1991,1(3):193-230
For a large class of subharmonicφ, the equation
is studied in
. Pointwise upper bounds are derived for the distribution kernels of the canonical solution operator and of the orthogonal
projection onto the space of entire functions inH. Existence theorems inL
p norms are derived as a corollary. A class of counterexamples, related to the failure of
to be analytic-hypoelliptic on certain CR manifolds, is discussed.
Communicated by Steven Krantz 相似文献
17.
We construct differential operators Kg(z), Lg(z),
, and
such that they map arbitrary holomorphic functions in a simply connected domain D in the complex plane z=x+iy into regular
solutions of the equation
We give examples of applications of the constructed differential operators to a solution of the main boundary-value problems
of mathematical physics. Bibliography: 1 title.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 19997, pp. 1–8. 相似文献
18.
LetD be a strictly pseudoconvex domain inC
n
. We prove that
, ϕ a
(0,1)-form, admits solutions inL
p
(∂D), 1≤p<∞ and in BMO, under certain Wolff type conditions of ϕ. Some such results (for 1<p<∞) have previously been obtained by Amar in the ball, but under slightly stronger hypotheses. As a corollary we obtain aH
p
-corona result for two generators.
Partially supported by the Swedish Natural Sciences Research Council. 相似文献
19.
Given a semi-convex functionu: ω⊂R
n→R and an integerk≡[0,1,n], we show that the set ∑k defined by
相似文献
20.
Numerical Optimization of the Two-Dimensional Transformation of Arguments in the Functional-Differential Diffusion Equation 总被引:1,自引:1,他引:0
We consider the optimization of the two-dimensional transformation
of the spatial arguments of the sought function in the mixed initial boundary-value problem for the functional-differential diffusion equation
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