Zur Kennzeichnung der Kollineationen zwischen Quadriken

In projective spaces Pⁿ(K), Pⁿ(K) over commutative fields K, K of characteristic 2 we consider the quadrics Q^n–1Pⁿ(K), Q,^n–1Pⁿ(K) which have the same rank and index and each of which is different from its singularity space. A one-to-one correspondence of Q^n–1 onto Q'^n–1 can be extended uniquely to a collineation of Pⁿ(K) onto Pⁿ(K) if and only if satisfies the following condition: maps the (n–2)-dimensional quadrics of Q,^n–1 of maximal rankonto (n–2)-dimensional quadrics of Q^n–1 of maximal rank (Theorem 1).

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Herrn Prof. Dr. Helmut Karzel zum 60. Geburtstag gewidmet     

On meromorphic solutions of algebraic differential equations in angular domains

We obtain asymptotic estimates of meromorphic solutions to the differential equationP _n (z, , )=P _n–1 (z, , ,..., ^(m) ) in the angular domain P={z: arg z · }. Here P_n(z, w, w) is a polynomial in all variables, and of degree n with respect to w and w; P_n–1(z, w, w, ..., w^(m)) is a polynomial in all variables, and of degree n –1 with respect to w, w, ..., w^(m) In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 514–523, April, 1992.     

The trace to subsets ofR n of Besov spaces in the general case

R ⁿ. , , , F R ⁿ, F , R ⁿ R ⁿ . ^p,q (Rⁿ), >0, 1, q, — ( ) Rⁿ. , ^p,q (Rⁿ) ^F Rⁿ. , q B ^p,q (F), = – (n–)/, >0, — « », ad — F, . , . : , F=R ^d,F— « » F— R ⁿ, « », F. .

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This work has been supported in part by the Swedish Natural Science Research Council.     

On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -      

On the asymptotic equivalence ofL pmetrics for convergence to normality

Summary This paper is concerned with the rate of convergence to zero of theL _pmetrics _np1p, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that the _np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1p, p, _np/_np is universally bounded away from zero and infinity asn.     

Weight functions on the Kneser graph and the solution of an intersection problem of Sali

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.     

Multiple wiener integrals and nonlinear functionals of a nuclear space valued Wiener process

In this work we develop techniques for the study of nonlinear functionals of a -valued Wiener processW _t, where is the dual of a countably Hilbert nuclear space. We construct stochastic integrals and multiple Wiener integrals of operator-valued processes with respect toW _t. The Wiener decomposition of the space of -valued nonlinear functionals ofW _t is established. We also obtain multiple stochastic integral expansions and representations of -valued nonlinear functionals ofW _t as operator-valued stochastic integrals of Itô type.This research was partially supported by CONACYT grants 22537 and PCEXCNA-040651, and Air Force Office of Scientific Research No. F49620 85 C 0144.Presently at CIMAT, A.P. 402 Guanajuato 36000, GTO, México.     

Problems with one quarter

In this paper two sequences of oscillation criteria for the self-adjoint second order differential equation (r(t)u(t)) + p(t)u(t) = 0 are derived. One of them deals with the case dt/r(t) = , and the other with the case dt/r(t) < .This work was supported by the grant VGA of Slovak Republic No. 1/7466/20.     

Hasse-Witt matrices of Fermat curves

Let m be an integer with m3. Let K and K be perfect fields of characteristic p and p such that (p,m)=1 and (p,m)=1, respectively. Moreover let A and A be algebraic function fields over K and K defined by x^m+y^m=a(0, ak) and x^m+y^m=a(a0 ak), respectively. Put g=(m–1)(m–2)/2. Denote by M(K,p,a) and M(K,p,a) the Hasse-Witt matrices of A and A with respect to the canonical bases of holomorphic differentials. Then we show that if p+p0(mod.m) then rank M(K,p,a)+rank M(K,p,a)=g and if pp1 (mod.m) then rank M(K,p,a)=rank M(K,p,a).     

Decomposing symmetric exchanges in matroid bases

LetB,B be bases of a matroid, withX B, X B. SetsX,X are asymmetric exchange if(B – X) X and(B – X) X are bases. SetsX,X are astrong serial B-exchange if there is a bijectionf: X X, where for any ordering of the elements ofX, sayx _i ,i = 1, , m, bases are formed by the sets B₀ = B, B_i = (B_i–1 – x_i) f(x _i), fori = 1, , m. Any symmetric exchangeX,X can be decomposed by partitioning X = _i=1 ^m Y_i, X = _i=1 ^m Y_i, X, where (1) bases are formed by the setsB ₀ =B, B _i = (B _i–1 –Y _i ) Y _i ; (2) setsY _i ,Y _i are a strong serialB _i–1 -exchange; (3) properties analogous to (1) and (2) hold for baseB and setsY _i ,Y _i .     

Über Untergruppen Endlicher Algebraischer Gruppen

Let k be a commutative ring, GG finite affine algebraic k-groups, and HH the dual Hopfalgebras of the affine algebras of G resp. G. The main results of this paper are: (I) If k is semilocal (e.g. k a field) there is an H-linear, HH-colinear, unitary, augmented isomorphism HHH H, where HH is the coalgebra belonging to G/G. (II) If the k-submodule of the fixelements of (HH)^* is isomorphic to k (e.g. k principal or semilocal), then HH is a Frobeniusextension of the second kind.     

Formula for the differentiation of operator-valued functions depending on a parameter

A study of the convergence of the differentiation formula (f(A))=f (A)A+f ^m(A)/21[AA]+f ^m(A)/3l[[AA]A]'+... where [XY]=XY–YX, and A=A(t) is a function of the real variable t with values in a Banach algebra.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 207–218, August, 1971.The author wishes to thank A. G. Aslanyan for his comments concerning this work.     

Admissibility of linear estimators of regression coefficients under quadratic loss

For the general fixed effects linear model:Y=X+, N(0,V),V0, we obtain the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS in the class of all estimators under the loss function (d -S)D(d -S), whereD0 is known. For the general random effects linear model: =XV ₁₁ X+XV ₁₂+V ₂₁ X+V ₂₂0, we also get the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS+Q in the class of all estimators under the loss function (d -S -Q)D(d -S -Q), whereD0 is known.     

On local uniqueness of the solution of boundary-value problems

In this paper we present conditions under which differentiability of the mappings F: ACⁿ(I) Lⁿ(I) and :ACⁿ(I) Rⁿ at x₀ ACⁿ(I) and the uniqueness of the solution of the boundaryvalue problem u = F(x₀)(u), (x₀)(u) = 0 imply local uniqueness of the solution x₀ of the boundary-value problem x = F(x), (x) = 0.Translated from Matematicheskie Zametki, Vol. 15, No. 6, pp. 891–895, June, 1974.The author thanks A. Ya. Lepin for the help he has given him in the preparation of this paper.     

K1 of Twisted Rings of Polynomials

We prove that for an arbitrary endomorphism of a ring R the group K1(R[t]) splits into the direct sum of K1(R) and Ñil (r;). Moreover, for any such R and Ñil (R; ) is isomorphic to Ñil (R ; ) for some ring R with : R R – an isomorphism.     

Circularity of Finite Groups without Fixed Points

Let be a fixed point free group given by the presentation where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d.     

Parties d'ensembles B-normaux

For a given subset A of the set R of real numbers, we defined M(A) as the infimum of all the lengths of the finite intervals I such that there exists a sequence of real numbers in I such that A is the associated normal set B(). We prove that if A is a subset of A, such that all the multiples k.a' belongs to A (for each non zero integer k and each element a of A), then M(A) is less or equal to 2.M(A). Thus the family of the subsets A such that M(A) is finite is closed under intersection and finite union.     

A Generalization of the Hausdorff-Young Theorem

Considering mixed-norm sequence spaces lp,q, p, q 1, C. N. Kellogg proved the following theorem: if 1 < p 2 then lp,2 and lp,2 , where 1/p + 1/p = 1. This result extends the Hausdorff-Young Theorem.We introduce here multiple mixed-norm sequence spaces , examine their properties and characterize the multipliers of spaces of the form lp,[s;n],q, with the index s repeated n times. By an interpolation-type argument we prove that (l,[2;n],2, lp,[1;n],1) for 1 < p 2. Using these results we obtain a further generalization of the Hausdorff-Young Theorem: if 1 < p 2 then lp,[2;n] and lp,[2;n] for each n = 0, 1, 2, ¨. The spaces lp,[2;n] decrease and lp,[2;n] increase properly with n for 1 < p < 2 and 1/p + 1/p = 1. We also extend a theorem of J. H. Hedlund on multiplers of Hardy spaces and deduce other results.     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

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Verschärfung einer Ungleichung von Ky Fan

Summary In this paper we prove the following:IfA _n ,G _n andH _n (resp.A _n ,G _n andH _n ) denote the arithmetic, geometric and harmonic means ofa ₁,, a _n (resp. 1 –a ₁,, 1 –a _n ) and ifa _i (0, 1/2],i = 1,,n, then(G _n /G _n ) ⁿ (A _n /A _n ) ^n-1 H _n /H _n , (^*) with equality holding forn = 1,2. Forn 3 equality holds if and only ifa ₁ = =a _n . The inequality (^*) sharpens the well-known inequality of Ky Fan:G _n /G _n A _n /A _n .