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1.
In [3] U. Ott introduced a Bruck-Ryser abstract theorem concerning lattices of an R-module. As one of the applications of this theorem, he obtained a new proof of the Bruck-Ryser theorem for finite projective planes and studied p-curves in a projective plane. In this paper, we apply the Bruck-Ryser abstract theorem in order to give a new proof of the Bruck-Ryser-Chowla theorem for symmetric (v, k, )-design with (v, k, )=1, and to study p-curves in arbitrary symmetric designs.  相似文献   

2.
The paper is concerned with the problem of stability of equilibrium figures of a uniformly rotating, viscous, incompressible, self-gravitating liquid subjected to capillary forces at the boundary. It is shown that a rotationally symmetric equilibrium figure F is exponentially stable if the functional G defined on the set of domains close to F and satisfying the conditions of volume invariance (||=|F|) and the barycenter position attains its minimum for =F. The proof is based on the direct analysis of the corresponding evolution problem with initial data close to the regime of a rigid rotation.  相似文献   

3.
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional : n , such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map n n , which is functional increasing (i.e. for each x n (which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)( u))( 2(u))... n (u)). Under quite general conditions one finds that the sequence { n (u)} n converges tov=v(u). As a consequence one obtains the inequality (u)(v).  相似文献   

4.
Summary LetC be the symmetric cusp {(x, y)2:–x yx ,x0} where >1. In this paper we decide whether or not reflecting Brownian motion inC has a semimartingale representation. Here the reflecting Brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary. Our results carry through for a wide class of asymmetric cusps too.  相似文献   

5.
Summary A class of stochastic evolution equations with additive noise and weakly continuous drift is considered. First, regularity properties of the corresponding Ornstein-Uhlenbeck transition semigroupR t are obtained. We show thatR t is a compactC 0-semigroup in all Sobolev spacesW n,p which are built on its invariant measure . Then we show the existence, uniqueness, compactness and smoothing properties of the transition semigroup for semilinear equations inL p() spaces and spacesW 1,p . As a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to . It is shown also that the density of this measure with respect to is inL p() for allp1.This work was done during the first author's stay at UNSW supported by ARC Grant 150.346 and the second author's stay at ód University supported by KBN Grant 2.1020.91.01  相似文献   

6.
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   

7.
Summary D. Gilat has shown that any non-negative submartingale (X, .) is equal in law to the absolute value of a martingale (M, .). This result may be strenthened so that the pairs (X,.) and (¦M¦,.) are synonomous. In this paper the question of uniqueness of M is considered. Conditions on a local martingale (M, .) are found that lead to an explicit formula for the finite-dimensional distributions of M in terms of the Doob-Meyer decomposition of the local martingale X. In many cases of interest the conditions on M are unnecessary. For example, if X is the pth power of an Itô integral it is shown that (M) is unique if p> 1 but not in general if p=1.  相似文献   

8.
Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.  相似文献   

9.
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d 2(), where runs through certain finite sets of integers ofK.  相似文献   

10.
A proof of the following conjecture of Jungnickel and Tonchev on quasi-multiple quasi-symmetric designs is given: Let D be a design whose parameter set (v,b,r,k,) equals (v,sv,sk,k, s) for some positive integer s and for some integers v,k, that satisfy (v-1) = k(k-1) (that is, these integers satisfy the parametric feasibility conditions for a symmetric (v,k,)-design). Further assume that D is a quasi-symmetric design, that is D has at most two block intersection numbers. If (k, (s-1)) = 1, then the only way D can be constructed is by taking multiple copies of a symmetric (v,k, )-design.  相似文献   

11.
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have ; this measure defines an indefinite integral over the measure onL 2 (T, ,). We prove that if { n (t)} n =1/ is an orthonormal basis inL 2 and n (e)=e n (t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL 2 is uniquely expandable in a series(e)= n =1/ n n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies n =1/ n /2 <. In the caseL 2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L 2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998.  相似文献   

12.
, (n), - (P n ), P n (A n )>0P n (A n )0,n. [15] - , . , P n P n T n T n .  相似文献   

13.
Summary We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)(f(x) d) A (f(x) d, d d = 1. Iff is an arbitrary nonnegativeL x function, this holds if 0, is convex andA = 1. Iff is monotone the measure need not be positive for (J) to hold for all convex withA = 1. If has higher monotonicity, e.g., is also convex, then we get a version of (J) withA < 1 and measures that need not be positive.  相似文献   

14.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z (n) and k(n, ) z (n).  相似文献   

15.
LetR be a commutative ring with 1 andM anR-module. If:M R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM *, where the isomorphism is given by the adjoint of.  相似文献   

16.
Summary LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R R is called a symmetric bi-derivation if, for any fixedy R, the mappingx D(x, y) is a derivation. The purpose of this paper is to prove two results concerning symmetric bi-derivations on prime rings. The first result states that, ifD 1 andD 2 are symmetric bi-derivations on a prime ring of characteristic different from two and three such thatD 1(x, x)D 2(x,x) = 0 holds for allx R, then eitherD 1 = 0 orD 2 = 0. The second result proves that the existence of a nonzero symmetric bi-derivation on a prime ring of characteristic different from two and three, such that [[D(x, x),x],x] Z(R) holds for allx R, whereZ(R) denotes the center ofR, forcesR to be commutative.  相似文献   

17.
18.
Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier.  相似文献   

19.
Let (P, ) and (P, ) be linear spaces satisfying the exchange axiom with dim P=dim P . Then a bijection :PP which maps collinear points onto collinear points is an isomorphism. Also a surjection :PP which maps any three non-collinear points to non-collinear points is an isomorphism. This assertion is not true if dim P is not finite.  相似文献   

20.
Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A * and the Palm version A 0 corresponding to A *. Let (T i ,i) be the inter-point distance sequence in A and (T i 0 ,i) in A 0. We prove that forj, the sequence (T i+j,i) converges in distribution to (T i 0 ,i). If the intensity function is periodic then the convergence is in variation.  相似文献   

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