On the homogeneous ideal of projectively normal curves

Summary Fix integers k, d, g with g0, dg+3, k>0, 2k<(d–g), d(g(k+1)/k) + k+1. Here we prove that for a general curve X of genus g and a general L Pic^d(X), L is normally presented.     

A note on a nonlinear eigenvalue problem

Summary In this paper a necessary and sufficient condition for the existence of negative eigenvalues for the problem-u – u=(x)¦u¦^p–2u in u¦=0 is given. Here Rⁿ is supposed a smooth bounded domain, 0 a bounded nonnegative function, (₁, ₂), ₁ and ₁ being the first and the second eigenvalue of - in with zero Dirichlet boundary data, p2 and, if n 3, p < 2n¦(n–2). Moreover in the linear case (p=2) a uniqueness result is proved.Work supported by G.N.A.F.A. and by M.P.I, of Italy Fondi 40% Equazioni Differenziali e Calcolo delle Variazioni and Fondi 60% Analisi matematica.     

Lefschetz type theorem

Summary Let X=Cⁿ / be a toroidal group of rank =n+m. If X is compact, then it is a complex torus. In the compact case, we have the theorem of Lefschetz which asserts that if L is a positive line bundle over a complex torus X, then gives an embedding of X for any integer l3. This theorem is generalized to noncompact toroidal groups in this paper. In fact, we prove the following: (I) In the case of rank =n+1, H⁰(X, (Ll)) gives an embedding of a toroidal group X for l3, if L is positive. (II) In the case of rank =n+m, 2m相似文献   

On the postulation of a general projection of a curve inP N,N⩾4

Summary Fix a curve X of genus g and L Pic ^d (X). Let _L(X) be the image of X through the complete linear system H⁰(X, L). Here we prove that a general projection of _L(X) intoP ^N has maximal rank if either (a) N4, 0gN–1, dg+N, or (b) dd (g, N) for suitable d(g, N).     

Distribution of the supremum of sums of independent variables with negative drift

Let {_n} be a sequence of identically distributed independent random variables,M₁=<0,M ₁ ² <;S ₀=0,S _n =₁+₂,+...+ _{n, n}1;¯ S=sup {S _n n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If _t ^P (₁x dx=0((t)), thenP(¯ St)– 1/¦¦ _t P (₁x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks.     

Isotone solutions of parametric linear complementarity problems

The parametric linear complementarity problem is given by the conditions:q + p + Mz 0, 0,z 0,z ^T (q + p + Mz) = 0. Under the assumption thatM is a P-matrix, Cottle proved that the solution mapz() of the above problem is montonically nondecreasing in the parameter for every nonnegativeq and everyp if and only ifM is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.     

On the diameters of some classes of analytic functions. I

In the spaces of analytic functionsE _q (), q1, introduced by V. I. Smirnov, where is a bounded simply connected domain in the plane with sufficiently smooth boundary , we obtain order estimates of diameters of the classesW ^r E _p () (p1, and r is a natural number 2) for distinct p and q.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 324–333, March, 1992.     

On blocking sets in symmetric BIBD's with λ⩾2

Blocking sets in symmetric BIBD's with 2 are defined and bounds for their sizes are found. Thus, some results known in projective planes are generalized to symmetric BIBD's.     

Unique determination of the convolutions of measures in Rm,m⩾2, by their restriction to a set

Restrictions are indicated on a complex-valued measure in the spaceR ^m ,m 2., under which the n-fold convolution ^n*,n 2, is uniquely determined by its values on any semispacex ₁<r, rR.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 86–90, 1988.     

Isomorphisms of unitary groups over associative rings

Automorphisms of unitary linear groups u (n,,q) over the ring are found to be standard on an elementary unitary subgroup in the case when the hyperbolic rank of the form q is strictly greater than one and n5 (for a commutative ring, n4).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im V. A. Steklova AN SSSR, Vol. 132, pp. 97–109, 1983.     

Sur l'homotopie rationnelle des espaces fonctionnels

Let X be a nilpotent space such that it exists k1 with H^p (X,) = 0 p > k and H^k (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of Y^X (resp. is isomorphic as Lie algebra, to H^* (X,) (_* (Y) ) (resp.⁺ (X,) (_* (Y) )). If X is formal and Y -formal, then the spaces Y^X and are -formal. Furthermore, if dim _* (Y) is infinite and dim H^* (Y,Q) is finite, then the sequence of Betti numbers of grows exponentially.     

Orbits of edge-to-edge tilings by equilateral triangles,squares and regular hexagons

An edge-to-edge tiling of the Euclidian plane by equilateral triangles, squares and regular hexagons is said to be of type (t,s,h) if there are exactly t orbits of triangles, s orbits of squares and h orbits of hexagons under the symmetry group of the tiling. We prove that there exist tilings of type (t,s,h) for every t 92, s 2, h 43. We completely determine the values of t and h for which tilings of type (t,1,h) exist.     

On blocking sets in affine planes

Denote by _q an affine plane of order q. In the desarguesian case _q=AG(2,q), q 5(q= p^h, p prime), we prove that the smallest cardinality of a blocking set is 2q–1. In any arbitrary affine plane _q (desarguesian or not) with q5, for any integer k with 2q–1 k(q–1)², we construct a blocking set S with ¦S¦=k. For an irreducible blocking set S of _q we determine the upper bound S [qq]+1. We prove that if _q contains a blocking set S which is irreducible with its complementary blocking set, then necessarily _q=AG(2, 4) and S is uniquely determined. Finally we introduce techniques to obtain blocking sets in AG(2, q) and in PG(2, q).Research partially supported by G.N.S.A.G.A. (CNR)     

Perturbation of a self-adjoint operator by a subordinate symmetric operator

The following variant of Rellich's theorem is proved. Let A,B be operators in a Hilbert space, A=A^*, BB^* and D(B)D(A). We assume that (Bu,u)(Au,u), uD(A) for some> –1. Then the operator A + B with domain of definition D(A) is self-adjoint.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 196–198, 1985.     

A geometric condition for an l.c.K. manifold to be Kähler

We prove that a necessary and sufficient condition for a locally conformal Kähler manifold(M ⁿ , g), n 2, to be Kähler is thatM admits through every one of its points a minimal Kahler submanifold of complex dimensionp2.     

Quasimonotonicity,regularity and duality for nonlinear systems of partial differential equations

Summary We prove partial regularity for the vector-valued differential forms solving the system (A(x, ))=0, d=0, and for the gradient of the vector-valued functions solving the system div A(x, Du)=B(x, u, Du). Here the mapping A, with A(x, w) (1+ + ¦¦²)^{(p – 2)/2} (p2), satisfies a quasimonotonicity condition which, when applied to the gradient A(x, )=Df(x, ) of a real-valued functionf, is analogous to but stronger than quasiconvexity for f. The case 1相似文献   

Quadratic forms of closed manifolds

In this paper it is shown that for any integral-valued unimodular quadratic form and any number n of the form 8k + 4 (where k1), there exists a smooth closed n-dimensional manifold with this quadratic form. The proof is based on the construction (with the help of the plumbing construction) of smooth closed three-connected eight-dimensional manifolds with given form.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 104–108, 1982.     

On square-full numbers in short intervals

It is shown that the number of square-full numbers in the interval is asymptotically equal to for every in the range 1/6>0.14254, which extends P.Shiu's range 1/6>0.1526.     

Random symmetric polynomials

Let {Q⁽ⁿ⁾(x₁,...,x_n)} be a sequence of symmetric polynomials having a fixed degree equal to k. Let {X_n1,...,X_nn}, n k, be some sequence of series of random variables (r.v.). We form the sequence of r.v. Y_n=Q⁽ⁿ⁾(X_n1, ... X_nn), n k One obtains limit theorems for the sequence Y_n, under very general assumptions.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 170–188, 1986.     

Distribution of the number of nonappearing lengths of cycles in a random mapping

One-to-one random mappings of the set 1, 2,..., n onto itself are considered. Limit theorems are proved for the quantities _i, 0in, max _i, min _i, where _i is the number of 0in components of the vector ( ₁, ₂,..., _n) which are equal to i, 0< i< n, and ar is the number of components of dimension r of the random mapping.Translated from Matematicheskle Zametki, Vol. 23, No. 6, pp. 895–898, June, 1978.The author is grateful to V. P. Chistyakov and V. E. Stepanov for many useful remarks.