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1.
Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.  相似文献   

2.
3.
Summary We prove that, for any Tychonoff X, the space Cp(X) is K-analytic if and only if it has a compact cover {Kp: p } such that Kp subset Kq whenever p,q and p q. Applying this result we show that if Cp(X) is K-analytic then Cp(X) is K-analytic as well. We also establish that a space Cp(X) is K-analytic and Baire if and only if X is countable and discrete.  相似文献   

4.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization.  相似文献   

5.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞.  相似文献   

6.
We show that the Lp-approximation order of surface spline interpolation equals m+1/p for p in the range 1 \leq p \leq 2, where m is an integer parameter which specifies the surface spline. Previously it was known that this order was bounded below by m + &frac; and above by m+1/p. With h denoting the fill-distance between the interpolation points and the domain , we show specifically that the Lp()-norm of the error between f and its surface spline interpolant is O(hm + 1/p) provided that f belongs to an appropriate Sobolev or Besov space and that \subset Rd is open, bounded, and has the C2m-regularity property. We also show that the boundary effects (which cause the rate of convergence to be significantly worse than O(h2m)) are confined to a boundary layer whose width is no larger than a constant multiple of h |log h|. Finally, we state numerical evidence which supports the conjecture that the Lp-approximation order of surface spline interpolation is m + 1/p for 2 < p \leq \infty.  相似文献   

7.
A finite group G is called p i -central of height k if every element of order p i of G is contained in the k th -term ζ k (G) of the ascending central series of G. If p is odd, such a group has to be p-nilpotent (Thm. A). Finite p-central p-groups of height p − 2 can be seen as the dual analogue of finite potent p-groups, i.e., for such a finite p-group P the group P1(P) is also p-central of height p − 2 (Thm. B). In such a group P, the index of P p is less than or equal to the order of the subgroup Ω1(P) (Thm. C). If the Sylow p-subgroup P of a finite group G is p-central of height p − 1, p odd, and N G (P) is p-nilpotent, then G is also p-nilpotent (Thm. D). Moreover, if G is a p-soluble finite group, p odd, and P ∈ Syl p (G) is p-central of height p − 2, then N G (P) controls p-fusion in G (Thm. E). It is well-known that the last two properties hold for Swan groups (see [11]).  相似文献   

8.
Let D be a 2-(v, k, 4) symmetric design and G be a flag-transitive point-primitive automorphism group of D with XGAut(X) where XPSL 2(q). Then D is a 2-(15, 8, 4) symmetric design with X = PSL 2(9) and X x = PGL 2(3) where x is a point of D.  相似文献   

9.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2(M) as h↓0. Let HM be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator.  相似文献   

10.
Let X be a Banach space, K be a scattered compact and T: B C(K)X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B C(K)**X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C 1,u -smooth noncompact operator from B c O which does not fix any (affine) basic sequence. P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503.  相似文献   

11.
We point out that the formalism of the trace map and reduction modulo p can be used to give a short proof for the fact first proved by Ogg that is not a Weierstrass point on X0(pM) where p is a prime not dividing M and the genus of X0(M) is zero.  相似文献   

12.
We prove that if q = p h , p a prime, do not exist sets U í AG(n,q){U {\subseteq} AG(n,q)}, with |U| = q k and 1 < k < n, determining N directions where
\fracqk - 1p - 1 < N £ \fracq+32 q k-1+ qk-2 +...+q2 + q \frac{{q^k} - 1}{p - 1} < N \le \frac{q+3}{2} q ^{k-1}+ q^{k-2} +\dots+q{^2} + q  相似文献   

13.
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D * is an FC-group, then D is a field. Let M be a maximal subgroup of GL n (D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M n (D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞.  相似文献   

14.
An automorphism α of a group G is called a commuting automorphism if each element x in G commutes with its image α(x) under α. Let A(G) denote the set of all commuting automorphisms of G. Rai [Proc. Japan Acad., Ser. A 91 (5), 57–60 (2015)] has given some sufficient conditions on a finite p-group G such that A(G) is a subgroup of Aut(G) and, as a consequence, has proved that, in a finite p-group G of co-class 2, where p is an odd prime, A(G) is a subgroup of Aut(G). We give here very elementary and short proofs of main results of Rai.  相似文献   

15.
A group G is said to be capable if it is isomorphic to the central factor group H/Z(H) for some group H. Let G be a nonabelian group of order p 2 q for distinct primes p and q. In this paper, we compute the nonabelian tensor square of the group G. It is also shown that G is capable if and only if either Z(G) = 1 or p < q and Gab=\mathbbZp×\mathbbZp{G^{\rm ab}=\mathbb{Z}_{p}\times\mathbb{Z}_{p}} .  相似文献   

16.
The modular Witt algebra W(p, n) and H(p, 2n) are defined on the polynomial rings Zp[x1,...,xn] and Zp[X1,...,xn, y1,...,yn] respectively. We generalize Zp[x1,...,xn] and Zp[x1,...,xn, y1,...,yn], so we get the generalized W-type and H-type modular Lie algebras. We find all the derivations of W(p, 1).AMS Subject Classification: Primary 17B40, 17B56.  相似文献   

17.
We prove the following statement, which is a quantitative form of the Luzin theorem on C-property: Let (X, d, μ) be a bounded metric space with metric d and regular Borel measure μ that are related to one another by the doubling condition. Then, for any function f measurable on X, there exist a positive increasing function η ∈ Ω (η(+0) = 0 and η(t)t a decreases for a certain a > 0), a nonnegative function g measurable on X, and a set EX, μE = 0 , for which
| f(x) - f(y) | \leqslant [ g(x) + g(y) ]h( d( x,y ) ), x,y ? X / E \left| {f(x) - f(y)} \right| \leqslant \left[ {g(x) + g(y)} \right]\eta \left( {d\left( {x,y} \right)} \right),\,x,y \in {{X} \left/ {E} \right.}  相似文献   

18.
As a counterpart to best approximation in normed linear spaces, the best coapproximation was introduced by Franchetti and Furi. In this paper, we shall consider the relation between coproximinality M in X and L p (S,M) in L p (S,X). Finally we give some results in cochebyshev subspaces and additional subspaces.  相似文献   

19.
This paper investigates the s-energy of (finite and infinite) well separated sequences of spherical designs on the unit sphere S 2. A spherical n-design is a point set on S 2 that gives rise to an equal weight cubature rule which is exact for all spherical polynomials of degree ≤n. The s-energy E s (X) of a point set of m distinct points is the sum of the potential for all pairs of distinct points . A sequence Ξ = {X m } of point sets X m S 2, where X m has the cardinality card(X m )=m, is well separated if for each pair of distinct points , where the constant λ is independent of m and X m . For all s>0, we derive upper bounds in terms of orders of n and m(n) of the s-energy E s (X m(n)) for well separated sequences Ξ = {X m(n)} of spherical n-designs X m(n) with card(X m(n))=m(n).   相似文献   

20.
In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an (x(q + 1), x; 2, q)-minihyper, with xq 2q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q 2qx, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers.  相似文献   

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