共查询到20条相似文献,搜索用时 15 毫秒
1.
Let Ks be the canonical bundle on a non singular projective surface S (over an algebraically closed field F, char F=p) and L be a very ample line bundle on S. Suppose (S,L) is not one of the following pairs: (P2,O(e)), e=1,2, a quadric, a scroll, a Del Pezzo surface, a conic bundle. Then
- (Ks?L)2 is spanned at each point by global sections. Let \(\phi :S \to P^N _F \) be the map given by the sections Γ(Ks?L)2, and let φ=s o r its Stein factorization.
- r:S→S′=r(S) is the contraction of a finite number of lines, Ei for i=1,...r, such that Ei·Ei=KS·Ei=?L·Ei=?1.
- If h°(L)≥6 and L·L≥9, then s is an embedding.
2.
LetK be a field of characteristicp>0 andF/K be an algebraic function field. We obtain several results on Galois extensionsE/F with an elementary Abelian Galois group of orderp n.
- E can be generated overF by some elementy whose minimal polynomial has the specific formT pn?T?z.
- A formula for the genus ofE is given.
- IfK is finite, then the genus ofE grows much faster than the number of rational points (as [E∶F] → ∞).
- We present a new example of a function fieldE/K whose gap numbers are nonclassical.
3.
Consider a family of stars. Take a new vertex. Join one end-vertex of each star to this new vertex. The tree so obtained is known as abanana tree. It is proved that the banana trees corresponding to the family of stars
- (K1,1, K1,2,…, K1,t ?1, (α + l) K1,t, K1,t + 1, …, K1,n), α ? 0
- (2K1,1, 2K1,2,…, 2K1,t? 1, (α + 2)K1,t, 2K1,t + 1, …, 2K1,n), 0 ? α <t and
- (3K1,t, 3K1,2, …, 3K1,n) are graceful.
4.
Moshe Jarden 《Israel Journal of Mathematics》1974,18(3):279-307
We consider here a hilbertian fieldk and its Galois group (k s/k). For a natural numbere we prove that almost all (σ) ∈ (ks/k)e have the following properties. (1) The closedsubgroup 〈σ〉 which is generated by σ1, …, σe is a free pro-finite group withe generators. (2) LetK be a proper subfield of the fixed fieldk s (σ) of 〈σ〉, …, σe ink s, which containsk. Then the group (k s/K) cannot be topologically generated by less thene+1 elements. (3) There does not exist a τ ∈ (k/k), τ≠1, of finite order such that [k s (σ):k s (σ, τ)]<∞. (4) Ife=1, there does not exist a fieldk?K?k s (σ) such that 1<[k s (σ):K]<∞. Here “almost all” is used in the sense of the Haar measure of the compact group (ks/k)e. 相似文献
5.
LetR be a semiprime algebra over a fieldK acted on by a finite-dimensional Lie superalgebraL. The purpose of this paper is to prove a series of going-up results showing how the structure of the subalgebra of invariantsR Lis related to that ofR. Combining several of our main results we have: Theorem: Let R be a semiprime K-algebra acted on by a finite-dimensional nilpotent Lie superalgebra L such that if characteristic K=p then L is restricted and if characteristic, K=0 then L acts on R as algebraic derivations and algebraic superderivations.
- If RL is right Noetherian, then R is a Noetherian right RL-module. In particular, R is right Noetherian and is a finitely generated right RL-module.
- If RL is right Artinian, then R is an Artinian right RL-module. In particular, R is right Artinian and is a finitely generated right RL-module.
- If RL is finite-dimensional over K then R is also finite-dimensional over K.
- If RL has finite Goldie dimension as a right RL-module, then R has finite Goldie dimension as a right R-module.
- If RL has Krull dimension α as a right RL-module, then R has Krull dimension α as a right RL-module. Thus R has Krull dimension at most α as a right R-module.
- If R is prime and RL is central, then R satisfies a polynomial identity.
- If L is a Lie algebra and RL is central, then R satisfies a polynomial identity.
6.
Jean Oesmer Loyola 《Semigroup Forum》1997,54(1):375-380
We show that for any regular ring (R, +, -), the following conditions are equivalent:
- (R, -) is inverse.
- (R, -) isE-solid.
- (R, -) is locally inverse.
- (R, -) is locallyE-solid.
7.
Sylvie Guerre 《Israel Journal of Mathematics》1986,56(3):361-380
Let 1≦q<p<2. We construct a bounded sequence (X n ) n∈N inL q which defines a typeσ onL q , such that:
- (X n ) n∈N is equivalent to the unit vector basis ofl p .
- The l-conic classK 1(σ) generated byσ is not relatively compact for the topology of uniform convergence on bounded sets ofL q .
- (X n ) n∈N has no almost exchangeable subsequence after any change of density.
8.
THINNINGOFPOINTPROCESSES,REVISITEDHESHENGWU(何声武)(DepartmentofMathematicalStatistics,EastChinaNormalUniversityShanghai200062,C... 相似文献
9.
Yuri Bilu 《Israel Journal of Mathematics》1995,90(1-3):235-252
LetK be an algebraic number field,S?S \t8 a finite set of valuations andC a non-singular algebraic curve overK. Letx∈K(C) be non-constant. A pointP∈C(K) isS-integral if it is not a pole ofx and |x(P)| v >1 impliesv∈S. It is proved that allS-integral points can be effectively determined if the pair (C, x) satisfies certain conditions. In particular, this is the case if
- x:C→P 1 is a Galois covering andg(C)≥1;
- the integral closure of $\bar Q$ [x] in $\bar Q$ (C) has at least two units multiplicatively independent mod $\bar Q$ *.
10.
с. Б. кОжыРЕВ 《Analysis Mathematica》1985,11(4):311-329
A continuous real valued function defined on an intervalD is called crinkly iff the setf ?1(У) ∩I is uncountable for each interval \(I \subseteqq D\) and number \(y \in (\mathop {\inf }\limits_I f,\mathop {\sup }\limits_I f)\) . The main result of the paper consists in the following assertion. Let the closed segment [0, 1] be represented as a union of four measurable, mutually nonintersecting setsE 1,Е 2,E 3,E 4. Then, for each functionH(δ) such thatH(δ)→ + ∞ andδH(δ)→0 asδ→0, there exists a crinkly functionf possessing the following five properties:
- a.e. onE 1:D + f(x)=D-f(x)=+∞,D + f(x)=D?f(x)=?∞;
- a.e. onE 2:D + f(x)=+∞,D?f(x)=?∞,D +f(x)=D-f(x)=0;
- a.e. onE 3:D + f(x)=?∞,D ? f(x)=+∞,D + f(x)=D?f(x)=0;
- a.e. onE 4:Df(x)=0;
- the modulus of continuityΩ off on [0, 1] satisfies $$\omega (\delta ,f,[0,1]) \leqq \delta H(\delta ).$$
11.
Wu Shengjian 《数学学报(英文版)》1994,10(2):168-178
Letf(z) be an entire function of order λ and of finite lower order μ. If the zeros off(z) accumulate in the vicinity of a finite number of rays, then
- λ is finite;
- for every arbitrary numberk 1>1, there existsk 2>1 such thatT(k 1 r,f)≤k 2 T(r,f) for allr≥r 0. Applying the above results, we prove that iff(z) is extremal for Yang's inequalityp=g/2, then
- every deficient values off(z) is also its asymptotic value;
- every asymptotic value off(z) is also its deficient value;
- λ=μ;
- $\sum\limits_{a \ne \infty } {\delta (a,f) \leqslant 1 - k(\mu ).} $
12.
Е. П. Долженко 《Analysis Mathematica》1978,4(4):247-268
Exact estimates are obtained for integrals of absolute values of derivatives and gradients, for integral moduli of continuity and for major variations of piecewise algebraic functions (in particular, for polynomials, rational functions, splines, etc.). These results are applied to the problems of approximation theory and to the estimates of Laurent and Fourier coefficients. Typical results:
- IfE is a measurable subset of the circle or of a line in thez-plane andR(z) is a rational function of degree ≦n, ¦R(z)¦≦ (z∈E), then ∝E ¦R′(z)¦dz¦≦ 2πn; the latter estimate is exact forn=0, 1, ... and everyE with positive measure;
- Iff(x 1,x 2, ...,x m) is a real valued piecewise algebraic function of order (n, k) on the unit ballD?R m (in particular, a real valued rational function of order ≦n), and ¦f¦≦1 onD, then ∝D¦gradf¦dx≦2π m/2n/Π(m/2); herem≧1, n≧0, 1≦k<∞;
- LetE=Π={z∶¦z¦=1}, and letc m(R) be the mth Laurent coefficient ofR onΠ,C m(n)=sup{¦cm(R)¦}, where sup is taken over allR from 1), then 1/7 min {n/¦m¦, 1} ≦C m(n) ≦ min {n/¦m¦, 1}.
13.
Jiuying Dong 《Journal of Applied Mathematics and Computing》2010,34(1-2):485-493
The theory of vertex-disjoint cycles and 2-factor of graphs has important applications in computer science and network communication. For a graph G, let σ 2(G):=min?{d(u)+d(v)|uv ? E(G),u≠v}. In the paper, the main results of this paper are as follows:
- Let k≥2 be an integer and G be a graph of order n≥3k, if σ 2(G)≥n+2k?2, then for any set of k distinct vertices v 1,…,v k , G has k vertex-disjoint cycles C 1,C 2,…,C k of length at most four such that v i ∈V(C i ) for all 1≤i≤k.
- Let k≥1 be an integer and G be a graph of order n≥3k, if σ 2(G)≥n+2k?2, then for any set of k distinct vertices v 1,…,v k , G has k vertex-disjoint cycles C 1,C 2,…,C k such that:
- v i ∈V(C i ) for all 1≤i≤k.
- V(C 1)∪???∪V(C k )=V(G), and
- |C i |≤4, 1≤i≤k?1.
14.
LetS be a locally compact (σ-compact) group or semi-group, and letT(t) be a continuous representation ofS by contractions in a Banach spaceX. For a regular probability μ onS, we study the convergence of the powers of the μ-averageUx=∫T(t)xdμ(t). Our main results for random walks on a groupG are:
- if μ is adapted and strictly aperiodic, and generates a recurrent random walk, thenU n (U-I) converges strongly to 0. In particular, the random walk is completely mixing.
- If μ×μ is ergodic onG×G, then for every unitary representationT(.) in a Hilbert space,U n converges strongly to the orthogonal projection on the space of common fixed points. These results are proved for semigroup representations, along with some other results (previously known only for groups) which do not assume ergodicity.
- If μ is spread-out with supportS, then $\left\| {\mu ^{n + K} - \mu ^n } \right\| \to 0$ if and only if e $ \in \overline { \cup _{j = 0}^\infty S^{ - j} S^{j + K} } .$ .
15.
16.
Stokes’ flow past a heterogeneous porous sphere has been studied, adopting the boundary conditions modified by Jones (1973) for curved surfaces at the interface of the free fluid region and porous material. The porous sphere is made up ofn + 1 concentric spheres of different permeability. The results for drag experienced by the sphere has been discussed and the following cases of interest are deduced:
- WhenK 1=K 2=...=K n+1=K.
- WhenK i is very small for eachi.
17.
We consider the problem
- u t=u xx+e u whenx ∈ ?,t > 0,
- u(x, 0) =u 0(x) whenx ∈ ?,
18.
В данной работе рассм атриваются классы фу нкцийf(z), голоморфные в област иa (?∞<a<b≦+∞) приp≧1 иs≧0, и у довлетворяющие одному из следующих условий:
- Еслиb≦+∞, то $$\int\limits_a^b {(\int\limits_{ - \infty }^{ + \infty } {\left| {f\left( {x + iy} \right)} \right|^p } dy)^s dx< + \infty .} $$
- Еслиb=+∞, иa=0, то $$\int\limits_0^u {(\int\limits_{ - \infty }^{ + \infty } {\left| {f\left( {x + iy} \right)} \right|^p } dy)^s dx \leqq \varrho \left( u \right), u > 0,} $$ где?(u) — функция опред еленного роста.
19.
A cycle of a bipartite graphG(V+, V?; E) is odd if its length is 2 (mod 4), even otherwise. An odd cycleC is node minimal if there is no odd cycleC′ of cardinality less than that ofC′ such that one of the following holds:C′ ∩V + ?C ∩V + orC′ ∩V ? ?C ∩V ?. In this paper we prove the following theorem for bipartite graphs: For a bipartite graphG, one of the following alternatives holds: -All the cycles ofG are even. -G has an odd chordless cycle. -For every node minimal odd cycleC, there exist four nodes inC inducing a cycle of length four. -An edge (u, v) ofG has the property that the removal ofu, v and their adjacent nodes disconnects the graphG. To every (0, 1) matrixA we can associate a bipartite graphG(V+, V?; E), whereV + andV ? represent respectively the row set and the column set ofA and an edge (i,j) belongs toE if and only ifa ij = 1. The above theorem, applied to the graphG(V+, V?; E) can be used to show several properties of some classes of balanced and perfect matrices. In particular it implies a decomposition theorem for balanced matrices containing a node minimal odd cycleC, having the property that no four nodes ofC induce a cycle of length 4. The above theorem also yields a proof of the validity of the Strong Perfect Graph Conjecture for graphs that do not containK 4?e as an induced subgraph. 相似文献
20.
Г. Г. ГЕВОРКЯН 《Analysis Mathematica》1990,16(2):87-114
In this paper some basis properties are proved for the series with respect to the Franklin system, which are analogous to those of the series with respect to the Haar system. In particular, the following statements hold:
- The Franklin series \(\mathop \Sigma \limits_{n = 0}^\infty a_n f_n (x)\) converges a.e. onE if and only if \(\mathop \Sigma \limits_{n = 0}^\infty a_n^2 f_n^2 (x)< + \infty \) a.e. onE;
- If the series \(\mathop \Sigma \limits_{n = 0}^\infty a_n f_n (x)\) , with coefficients ¦a n ¦↓0, converges on a set of positive measure, then it is the Fourier-Franklin series of some function from \(\bigcap\limits_{p< \infty } {L_p } \) ;
- The absolute convergence at a point for Fourier—Franklin series is a local property;
- If an integrable function (fx) has a discontinuity of the first kind atx=x 0, then its Fourier-Franklin series diverges atx=x 0.