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1.
LetX, Y be finite sets and suppose thatF is a collection of pairs of sets (F, G),FX,GY satisfying |FF|s, |GG|t and |FF|+|GG|s+t+1 for all (F, G),F, GF. Extending a result of Sali, we determine the maximum ofF.  相似文献   

2.
H P (R + 2 ) — R + 2 ={zC: Imz>0} p (R) — H p (R + 2 ). P k (f,x) — ë- — ,W k (f,x) — — R k, (f,x) — f H (R) (. §1,1)–3)); k (, f) p - . , fH p (R) 0<p1,kN; (1+)–1<p1, 0<<,kN.  相似文献   

3.
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GraßmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the 1-distance lines, 1=1,..., r, which are in 1–1-correspondence to the so-called generalized reguli of type (r, 1).To every chain geometry there are subspaces T and Z of the surrounding space ofG, such that forV=GT andW = VZ we have a projective representation of on V\W as pointset, where the chains of are exactly the r-distance lines on V\W.Dedicated to Prof.A. Barlotti on occasion of his 60 birthday  相似文献   

4.
Denoting by dimA the dimension of the affine hull of the setA, we prove that if {K i:i T} and {K i j :i T} are two finite families of convex sets inR n and if dim {K i :i S} = dim {K i j :i S}for eachS T such that|S| n + 1 then dim {K i :i T} = dim {K i : {i T}}.  相似文献   

5.
A bounded operatorT is called cellular-indecomposable ifL M {0} wheneverL andM are nonzero invariant subspaces forT. We prove that a cyclic subnormal operator is cellular-indecomposable if and only if it is quasi-similar to an analytic Toeplitz operator whose symbol is a weak-star generator ofH . This completes our previous work [5], [6].  相似文献   

6.
For the motion equations of Kelvin-Voight fluids one proves: 1) a global theorem for the existence and uniqueness of a solution (v;{ue}) of the initial-boundary value problem on the semiaxis t R+ from the class W 1 (R+); W 2 2 () H()) with initial condition vo(x) W 2 2 () H() when the right-hand side f(x, t) L(R +; L2()); 2) a global theorem for the existence and uniqueness of a solution (v; {ul}) on the entire axisR from the classW 1 (R; W 2 2 () H()) when the right-hand side f(x, t) L(R; L2()); 3) a global theorem for the existence of at least one solution (v; {ul}), periodic with respect to t with period , from the class W 1 (R +; W 2 2 () H()) when the right-hand side f(x, t) L(R +; L2()) is periodic with respect to t with period , and a local uniqueness theorem for such a solution; 4) a theorem for the existence and uniqueness in the small of a solution (v; {ul}), almost periodic with respect to t R, from V. V. Stepanov's class S 1 (R; W 2 2 ()H()) when the right-hand side f(x, t) S(R; L2()) is almost periodic with respect to t; 5) the linearization principle (Lyapunov's first method) is justified in the theory of the exponential stability of the solutions of an initial-boundary value problem in the space H() and conditions are given for the exponential stability of a stationary and periodic solution, with respect to t R, of the system (1).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 181, pp. 146–185, 1990.  相似文献   

7.
Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers k V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies 2 = 0 and ( k V) k–1 V We prove that ( k V)= ker k–1 V except when k=m+2. In the exceptional case, ( m+2 V) has codimension 2m in ker m V and we show that the quotient module ker m V/ m+2 V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in m V and multiplicity 0 in all other components of V.  相似文献   

8.
Let G be an infinite group generated by oblique reflections with respect to hyperplanes in the real space E m ; let II , II , II be the linear spans of dimensions , , of three G-orbits of directions of symmetry, where II II II =0 and dim(II + II + II ) < + +. Some singularities of the equation of an algebraic hypersurface invariant with respect to G are established. Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 34–38, 1992.  相似文献   

9.
We construct one parameter families of inclusions of nonhyperfinite type II1 factorsN s M s , with trivial relative commutant (N s )M s = and with the Jones' index [M s N s ]=s ranging over the sets{4 cos2/n|n4}[4, ), by using Markov traces on certain universal algebras associated to a given algebra and to the Jones' sequence of projections. This solves the problem of finding all possible values of indices of subfactors with trivial relative commutant in arbitrary type II1 factors, by showing that any numbers>4 can occur.This work was partially supported by an NSF grant DMS-8908281  相似文献   

10.
We consider the set of regular functions . We construct a Borel measure and a class of outer measures h onH. With these and h we show that: (HS)=0 and h (HS)=0, (S is the set of normed univalent functions). From h (HS)=0 follows—forh=t —that the Hausdorff—Billingsley-dimension ofHS is zero.  相似文献   

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