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1.
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.
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.
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 nR 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.
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.
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.
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.
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.
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.
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, sn/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.
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 nR and an integerk≡[0,1,n], we show that the set ∑k defined by
  相似文献   

20.
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
where the right-hand side is defined by the generalized superposition , and the argument transformation g(x) in the form of the functional
defined on the space of continuous test functions . The quality of optimization is evaluated by the integral functional
The minimizing sequence for the minimization problem J(g) inf G on the set G = g L 2(Q): g ( ) } of pointwise-bounded transformations is constructed by the gradient projection method combined with special projection-difference approximations of the direct and the conjugate initial boundary-value problems, which allow for possible irreversibility of the argument transformation and its generalized specification. Numerical optimization results are discussed using two examples of localized objective functions u 1(x, t).  相似文献   

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