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1.
We show that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2, q), q even, is at least q + 1 + $ \sqrt {q/6} $ provided that the set is not of even type. 相似文献
2.
Given a non-atomic, finite and complete measure space (,,µ)and a Banach space X, the modulus of continuity for a vectormeasure F is defined as the function F(t) = supµ(E)t |F|(E)and the space Vp,q(X) of vector measures such that t1/p'F(t) Lq((0,µ()],dt/t) is introduced. It is shown thatVp,q(X) contains isometrically Lp,q(X) and that Lp,q(X) = Vp,q(X)if and only if X has the RadonNikodym property. It isalso proved that Vp,q(X) coincides with the space of cone absolutelysumming operators from Lp',q' into X and the duality Vp,q(X*)=(Lp',q'(X))*where 1/p+1/p'= 1/q+1/q' = 1. Finally, Vp,q(X) is identifiedwith the interpolation space obtained by the real method (V1(X),V(X))1/p',q. Spaces where the variation of F is replaced bythe semivariation are also considered. 相似文献
3.
Hemisystems on the Hermitian Surface 总被引:2,自引:0,他引:2
The natural geometric setting of quadrics commuting with a Hermitiansurface of PG(3,q2), q odd, is adopted and a hemisystem on theHermitian surface H(3,q2) admitting the group P(4,q)is constructed, yielding a partial quadrangle PQ((q1)/2,q2,(q1)2/2) and a strongly regular graph srg((q3+1)(q+1)/2,(q2+1)(q1)/2,(q3)/2,(q1)2/2).For q>3, no partial quadrangle or strongly regular graphwith these parameters was previously known, whereas when q=3,this is the Gewirtz graph. Thas conjectured that there are nohemisystems on H(3,q2) for q>3, so these are counterexamplesto his conjecture. Furthermore, a hemisystem on H(3,25) admitting3.A7.2 is constructed. Finally, special sets (after Shult) andovoids on H(3,q2) are investigated. 相似文献
4.
Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition 总被引:2,自引:0,他引:2
de Pablo Arturo; Quiros Fernando; Rossi Julio D. 《IMA Journal of Applied Mathematics》2002,67(1):69-98
We study non-negative solutions of the porous medium equationwith a source and a nonlinear flux boundary condition, ut =(um)xx + up in (0, ), x (0, T); (um)x (0, t) = uq (0,t) for t (0, T); u (x, 0) = u0 (x) in (0, ), where m > 1,p, q > 0 are parameters. For every fixed m we prove thatthere are two critical curves in the (p, q-plane: (i) the criticalexistence curve, separating the region where every solutionis global from the region where there exist blowing-up solutions,and (ii) the Fujita curve, separating a region of parametersin which all solutions blow up from a region where both globalin time solutions and blowing-up solutions exist. In the caseof blow up we find the blow-up rates, the blow-up sets and theblow-up profiles, showing that there is a phenomenon of asymptoticsimplification. If 2q < p + m the asymptotics are governedby the source term. On the other hand, if 2q > p + m theevolution close to blow up is ruled by the boundary flux. If2q = p + m both terms are of the same order. 相似文献
5.
Multiple Blocking Sets and Arcs in Finite Planes 总被引:3,自引:0,他引:3
This paper contains two main results relating to the size ofa multiple blocking set in PG(2, q). The first gives a verygeneral lower bound, the second a much better lower bound forprime planes. The latter is used to consider maximum sizes of(k, n)-arcs in PG(2, 11) and PG(2, 13), some of which are determined.In addition, a summary is given of the value of mn(2, q) forq 13. 相似文献
6.
Integer Solutions are found to the equations t23(a2,b2, (a + b)2, (ab)2) = p2, q2, r2, s2. These lead surprisinglyto solutions to the equations u2 + (c2, d2, (c + d)2, (c d)2) = p2, q2, v2, w2, with the same values of p and q. 相似文献
7.
Bimahonian distributions 总被引:1,自引:0,他引:1
Barcelo Helene; Reiner Victor; Stanton Dennis 《Journal London Mathematical Society》2008,77(3):627-646
Motivated by permutation statistics, we define, for any complexreflection group W, a family of bivariate generating functionsW(t, q). They are defined either in terms of Hilbert seriesfor W-invariant polynomials when W acts diagonally on two setsof variables or, equivalently, as sums involving the fake degreesof irreducible representations for W. It is shown that W(t,q) satisfies a bicyclic sieving phenomenon whichcombinatorially interprets its values when t and q are certainroots of unity. 相似文献
8.
This paper proves that for every Lipschitz function f : RnRm,m < n, there exists at least one point of -differentiabilityof f which is in the union of all m-dimensional affine subspacesof the form q0 +span{q1,q2,...,qm}, where qj (j = 0,1,...,m)are points in Rn with rational coordinates. 2000 MathematicsSubject Classification 26B05, 26B35. 相似文献
9.
The authors consider the question of recovering the coefficientq from the equation ut uxx + q(x)u = fj(x) with homogeneousinitial and boundary conditions. The nonhomogeneous source terms form a basis for L2(0,1).It is proved that a unique determination is possible from datameasurements consisting of either the flux at one end of thebar or the net flux leaving the bar, taken at a single fixedtime for each input source. An algorithm that allows efficientnumerical reconstruction of q(x) from finite data is given. 相似文献
10.
On the Centred Hausdorff Measure 总被引:2,自引:0,他引:2
Let v be a measure on a separable metric space. For t, q R,the centred Hausdorff measures µh with the gauge functionh(x, r) = rt(vB(x, r))q is studied. The dimension defined bythese measures plays an important role in the study of multifractals.It is shown that if v is a doubling measure, then µh isequivalent to the usual spherical measure, and thus they definethe same dimension. Moreover, it is shown that this is trueeven without the doubling condition, if q 1 and t 0 or ifq 0. An example in R2 is also given to show the surprisingfact that the above assertion is not necessarily true if 0 <q < 1. Another interesting question, which has been askedseveral times about the centred Hausdorff measure, is whetherit is Borel regular. A positive answer is given, using the aboveequivalence for all gauge functions mentioned above. 相似文献
11.
12.
Embedded Thick Finite Generalized Hexagons in Projective Space 总被引:1,自引:0,他引:1
We show that every embedded finite thick generalized hexagon of order (s, t) in PG(n,q) which satisfies the conditions
- s = q
- the set of all points of generates PG(n, q)
- for anypoint x of , the set of all points collinear in withx is containedin a plane of PG(n, q)
- for any point x of , the set of allpoints of not oppositex in is contained in a hyperplane ofPG,(n, q)
13.
This paper is devoted to the long-time behavior of solutionsto the Cauchy problem of the porous medium equation ut = (um) up in Rn x (0,) with (1 2/n)+ < m < 1and the critical exponent p = m + 2/n. For the strictly positiveinitial data u(x,0) = O(1 + |x|)k with n + mn(2 n + nm)/(2[2 m + mn(1 m)]) k < 2/(1 m), we prove that the solution of the above Cauchy problem convergesto a fundamental solution of ut = (um) with an additional logarithmicanomalous decay exponent in time as t . 相似文献
14.
Guglielmo Lunardon 《Geometriae Dedicata》1999,75(3):245-261
In Dedicata 16 (1984), pp. 291–313, the representation of Desarguesian spreads of the projective space PG(2t – 1, q) into the Grassmannian of the subspaces of rank t of PG(2t – 1, q) has been studied. Using a similar idea, we prove here that a normal spread of PG(rt – 1,q) is represented on the Grassmannian of the subspaces of rank t of PG(rt – 1, q) by a cap V
r, t
of PG(r
t
– 1, q), which is the GF(q)-scroll of a Segre variety product of t projective spaces of dimension (r – 1), and that the collineation group of PG(r
t
– 1, q) stabilizing V
r, t
acts 2-transitively on V
r, t
. In particular, we prove that V
3, 2 is the union of q
2 – q + 1 disjoint Veronese surfaces, and that a Hermitan curve of PG(2, q
2) is represented by a hyperplane section U of V
3, 2. For q 0,2 (mod 3) the algebraic variety U is the unitary ovoid of the hyperbolic quadric Q
+ (7, q) constructed by W. M. Kantor in Canad. J. Math., 5 (1982), 1195–1207. Finally we study a class of blocking sets, called linear, proving that many of the known examples of blocking sets are of this type, and we construct an example in PG(3, q
2). Moreover, a new example of minimal blocking set of the Desarguesian projective plane, which is linear, has been constructed by P. Polito and O. Polverino. 相似文献
15.
This work, investigates the asymptotics for Eulers q-exponentialEq(z), Ramanujans function Aq(z), Jacksons q-Besselfunction Jv(2) (z; q), the Stieltjes–Wigert orthogonalpolynomials Sn(x; q) and q-Laguerre polynomials Ln() (x; q)as q approaches 1. 相似文献
16.
David G. Glynn 《Geometriae Dedicata》1988,26(3):273-280
The problem is considered of constructing a maximal set of lines, with no three in a pencil, in the finite projective geometry PG(3, q) of three dimensions over GF(q). (A pencil is the set of q+1 lines in a plane and passing through a point.) It is found that an orbit of lines of a Singer cycle of PG(3, q) gives a set of size q
3 + q
2 + q + 1 which is definitely maximal in the case of q odd. A (q
3 + q
2 + q + 1)-cap contained in the hyperbolic (or Klein) quadric of PG(5, q) also comes from the construction. (A k-cap is a set of k points with no three in a line.) This is generalized to give direct constructions of caps in quadrics in PG(5, q). For q odd and greater than 3 these appear to be the largest caps known in PG(5, q). In particular it is shown how to construct directly a large cap contained in the Klein quadric, given an ovoid skew to an elliptic quadric of PG(3, q). Sometimes the cap is also contained in an elliptic quadric of PG(5, q) and this leads to a set of q
3 + q
2 + q + 1 lines of PG(3,q
2) contained in the non-singular Hermitian surface such that no three lines pass through a point. These constructions can often be applied to real and complex spaces. 相似文献
17.
The low-dimensional projective irreducible representations incross characteristics of the projective special linear groupPSLn(q) are investigated. If n 3 and (n, q) (3,2), (3,4), (4,2), (4,3), all such representationsof the first degree (which is (qn q)/(q 1) with = 0 or 1) and the second degree (which is (qn 1)/(q 1) come from Weil representations. We show thatthe gap between the second and the third degree is roughly q2n-4.1991 Mathematics Subject Classification: 20C20, 20C33. 相似文献
18.
A Hurwitz group is any non-trivial finite group that can be(2,3,7)-generated; that is, generated by elements x and y satisfyingthe relations x2 = y3 = (xy)7 = 1. In this short paper a completeanswer is given to a 1965 question by John Leech, showing thatthe centre of a Hurwitz group can be any given finite abeliangroup. The proof is based on a recent theorem of Lucchini, Tamburiniand Wilson, which states that the special linear group SLn(q)is a Hurwitz group for every integer n 287 and every prime-powerq. 2000 Mathematics Subject Classification 20F05 (primary);57M05 (secondary). 相似文献
19.
We prove that a GF(q)-linear Rédei blocking set of size q
t + q
t–1 + ··· + q + 1 of PG(2,q
t) defines a derivable partial spread of PG(2t – 1, q). Using such a relationship, we are able to prove that there are at least two inequivalent Rédei minimal blocking sets of size q
t + q
t–1 + ··· + q + 1 in PG(2,q
t), if t 4. 相似文献
20.
We classify all embeddings θ: PG(n, q) → PG(d, q), with $d \geqslant \tfrac{{n(n + 3)}}
{2}$d \geqslant \tfrac{{n(n + 3)}}
{2}, such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = ?n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point sets corresponding to subspaces of PG(n, q)). With an additional condition we generalize this result to the infinite case as well. 相似文献