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.     

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.     

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.     

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.     

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   

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.     

On measures integrating all functions of a given vector lattice

LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.     

Parametrices for a class of differential operators with multiple characteristics

Summary In this paper we give the construction of a parametrix for a class of differential operators of the type ²/t²–t^2k+1 + t^q(/x_i), k N, q N, qk.     

Nonlinear semigroups and age-dependent population models

Summary This paper treats the nonlinear age-dependent population problem (1)(0,a)=(a), a I; (2)(t, 0)=F((t, ·)), t0; (3) ,t0,where I is the age range of the population, (t, ·) is the unknown age density at time t, is the known initial age distribution, and the functionals F and G are nonlinear. The problems of existence, uniqueness, continuous dependence upon initial values, and the positivity of solutions are investigated using the method of nonlinear semigroups.Supported in part by the National Science Foundation Grant NSF 75-06332A01.     

Parametrices for operators of tricomi type

Sunto Si costruisce una parametrice per il problema di Dirichlet relativo ad operatori P del tipo (1/i(/t))² + t_x, nella regione t0. Tenuto conto che per tali operatori è nota la parametrice del problema di Cauchy nella regione t 0, ciò consente di costruire una soluzione (modO ) dell'equazione Pu=f , t (–T, T), T>0.     

Siegel's formula for genus 2

Let S be a semi-integral, symmetric, positive-definite m x m matrix; mn1. By the Siegel fundamental formula we mean the identity between the Siegel theta series of genus n, associated with the genus of the matrix S, and the correspond ing Eisenstein-Siegel series (C. L. Siegel, Lectures on the Analytical Theory of Quadratic Forms, 3rd rev. edition, Peppmüller, Göttingen, 1963). The validity of the mentioned formula for m/2n+1 is an open problem in the general case. In this paper we prove Siegel's formula for n=2, m=6.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 210–215, 1978.     

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.     

On automorphisms of prime order of a Riemann surface as matrices

Let A be an element of prime order of GL(g,) (g2). We prove that A is a representation on the space of differentials of some automorphism of a Riemann surface of genus g if and only if A satisfies the Eichler trace formula.     

On the Ranked Excursion Heights of a Kiefer Process

Let (K(s,t), 0s1, t1) be a Kiefer process, i.e., a continuous two-parameter centered Gaussian process indexed by [0,1]×₊ whose covariance function is given by (K(s₁,t₁) K(s₂,t₂))=(s₁s₂-s₁s₂)t₁t₂, 0s₁, s₂1, t₁, t₂ 0. For each t>0, the process K(·,t) is a Brownian bridge on the scale of . Let M ₁ ^* (t) M ₂ ^* (t) M _j ^* (t) 0 be the ranked excursion heights of K(,t). In this paper, we study the path properties of the process tM _j ^* (t). Two laws of the iterated logarithm are established to describe the asymptotic behaviors of M _j ^* (t) as t goes to infinity.     

Kato's equality and spectral decomposition for positive C0-groups

Let A be the generator of a C₀-semigroup {T(t); t0} defined on a Banach lattice E. It is shown that T(t) is a lattice homomorphism for all t>0 if and only if A satisfies <¦x¦, Ax>= (xD(A), x D(A)) (where q: EE is the evaluation mapping). This equality is used to obtain a spectral decomposition for generators of positive groups.     

A functional inequality for real-analytic functions

Summary Forf ( C ⁿ() and 0 t x letJ _n (f, t, x) = (–1)ⁿ f(–x)f ⁽ⁿ⁾(t) +f(x)f ⁽ⁿ⁾ (–t). We prove that the only real-analytic functions satisfyingJ _n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e ^x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ ₀ (f, x, x) 0 and ₀ ^x (x – t)^{n – 1}J_n(f, t, x)dt 0 (n 1).     

Discrete reflection groups in Lobachevskii spaces of large dimension

It is proved that, in a Lobachevskii space of dimension 62, there do not exist discrete groups generated by reflections in hyperplanes and having a bounded fundamental polyhedron. There is a reference to a published paper of the author in which the same (result) is proved for Lobachevskii spaces of dimensions 40.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 62–68.     

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.     

Lower semicontinuity of attractors of gradient systems and applications

Summary For 0₀, let T(t), t0, be a family of semigroups on a Banach space X with local attractors A. Under the assumptions that T₀(t) is a gradient system with hyperbolic equilibria and T(t) converges to T₀(t) in an appropriate sense, it is shown that the attractors {A, 0₀} are lower-semicontinuous at zero. Applications are given to ordinary and functional differential equations, parabolic partial differential equations and their space and time discretizations. We also give an estimate of the Hausdorff distance between A and A₀, in some examples.Research supported by U.S. Army Research Office DAAL-03-86-K-0074 and the National Science Foundation DMS-8507056.     

Compact interval spaces in which all closed subsets are homeomorphic to clopen ones,II

A topological spaceX whose topology is the order topology of some linear ordering onX, is called aninterval space. A space in which every closed subspace is homeomorphic to a clopen subspace, is called aCO space and a space isscattered if every non-empty subspace has an isolated point. We regard linear orderings as topological spaces, by equipping them with their order topology. IfL andK are linear orderings, thenL ^*, L+K, L · K denote respectively the reverse ordering ofL, the ordered sum ofL andK and the lexicographic order onL x K (so · 2=+). Ordinals are considered as linear orderings, and cardinals are initial ordinals. For cardinals , l 0, letL(K,)=K+1+*.Theorem: Let X be a compact interval scattered space. Then X is a CO space if and only if X is homeomorphic to a space of the form +1+_{1 L(K i i), where is any ordinal, n , for every ii},_i are regular cardinals and K_ii, and if n>0, then max({K_i:i相似文献