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1.
Let A be a set of positive integers with gcd (A) = 1, and let p A (n) be the partition function of A. Let c 0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p A (n)/c 0 n and lim sup log p A (n)/c 0 n . In particular, if A has asymptotic density > 0, then log p A (n) c0n. Conversely, if > 0 and log p A (n) c 0 n, then the set A has asymptotic density .  相似文献   

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An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G 0 where 0 andG 0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L 1-algebra, Fourier transforms of abelian groups are given and their properties are studied.  相似文献   

4.
Let {X t} t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇn|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with ().  相似文献   

5.
A family of subtrees of a graphG whose edge sets form a partition of the edge set ofG is called atree decomposition ofG. The minimum number of trees in a tree decomposition ofG is called thetree number ofG and is denoted by(G). It is known that ifG is connected then(G) |G|/2. In this paper we show that ifG is connected and has girthg 5 then(G) |G|/g + 1. Surprisingly, the case wheng = 4 seems to be more difficult. We conjecture that in this case(G) |G|/4 + 1 and show a wide class of graphs that satisfy it. Also, some special graphs like complete bipartite graphs andn-dimensional cubes, for which we determine their tree numbers, satisfy it. In the general case we prove the weaker inequality(G) (|G| – 1)/3 + 1.  相似文献   

6.
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.  相似文献   

7.
We give a general criterion for the intrinsic ultracontractivity of Dirichlet Laplacians – D on domainsD ofR d d 3, based on the Lieb's formula. It applies to various classes of domains (e.g. John, Hölder andL p-averaging domains) and gives new conditions for intrinsic ultracontractivity in terms of the Minkowski dimension of the boundary D. In particular, isotropic self-similar fractals and domains satisfying a c-covering condition are considered.  相似文献   

8.
The number of subgroups of type and cotype in a finite abelian p-group of type is a polynomialg with integral coefficients. We prove g has nonnegative coefficients for all partitions and if and only if no two parts of differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certain order-preserving surjections that associate to each subgroup a vector dominated componentwise by . The nonzero components of (H) are the parts of , the type of H; if no two parts of differ by more than one, the nonzero components of – (H) are the parts of , the cotype of H. In fact, we provide an order-theoretic characterization of those isomorphism types of finite abelian p-groups all of whose Hall polynomials have nonnegative coefficients.  相似文献   

9.
Let R(r, m) be the rth order Reed-Muller code of length 2 m , and let (r, m) be its covering radius. We prove that if 2 k m - r - 1, then (r + k, m + k) (r, m + 2(k - 1). We also prove that if m - r 4, 2 k m - r - 1, and R(r, m) has a coset with minimal weight (r, m) which does not contain any vector of weight (r, m) + 2, then (r + k, m + k) (r, m) + 2k(. These inequalities improve repeated use of the known result (r + 1, m + 1) (r, m).This work was supported by a grant from the Research Council of Wright State University.  相似文献   

10.
Jiang  Jifa  Wang  Yi 《Positivity》2003,7(3):185-194
The authors study the -limit set dichotomy of the Kolmogorov systems i=xi f i(x)x i0, 1in with the cooperative and irreducible hypotheses and obtain the quasiconvergence almost everywhere when n=3, which gives an affirmative answer to the open problem by Smith [9, p.72] in the case of n=3.  相似文献   

11.
We argue extensively in favor of our earlier choice of the in and out states (among the solutions of a wave equation with one-dimensional potential). In this connection, we study the nonstationary and stationary families of complete sets of solutions of the Klein–Gordon equation with a constant electric field. A nonstationary set Pv consists of the solutions with the quantum number p v=p 0 v–p3. It can be obtained from the nonstationary set P3 with the quantum number p 3 by a boost along the x 3 axis (in the direction of the electric field) with the velocity –v. By changing the gauge, we can bring the solutions in all sets to the same potential without changing quantum numbers. Then the transformations of solutions in one set (with the quantum number p v) to the solutions in another set (with the quantum number p v) have group properties. The stationary solutions and sets have the same properties as the nonstationary ones and are obtainable from stationary solutions with the quantum number p 0 by the same boost. It turns out that each set can be obtained from any other by gauge manipulations. All sets are therefore equivalent, and the classification (i.e., assigning the frequency sign and the in and out indices) in any set is determined by the classification in the set P3, where it is obvious.  相似文献   

12.
{p mn } - 00>0, (1, 1) (1.1) (1.2). {s mn } J p - ( bJ p -lims mn =), (1.3) 0<x,y<1 p s (, )/p(x, y) x, y 1-. {r mn } - , (1.5) 0<, <1. N rp - , (1.6). , bJ p -lims mn = bJ q -lim(N rps) mn =. J p - . , .  相似文献   

13.
Summary A totally umbilical pseudo-Riemannian submanifold with the parallel mean curvature vector field is said to be an extrinsic sphere. A regular curve in a pseudo-Riemannian manifold is called a circle if it is an extrinsic sphere. LetM be ann-dimensional pseudo-Riemannian submanifold of index (0n) in a pseudo-Riemannian manifold with the metricg and the second fundamental formB. The following theorems are proved. For 0 = +1 or –1, 1 = +1, –1 or 0 (2–2 0+ 12n–2–2) and a positive constantk, every circlec inM withg(c, c) = 0 andg( c c, c c) = 1 k 2 is a circle in iffM is an extrinsic sphere. For 0 = +1 or –1 (–0n–), every geodesicc inM withg(c, c) = 0 is a circle in iffM is constant isotropic and B(x,x,x) = 0 for anyx T(M). In this theorem, assume, moreover, that 1n–1 and the first normal space is definite or zero at every point. Then we can prove thatM is an extrinsic sphere. When = 0 orn, this fact does not hold in general.  相似文献   

14.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

. . .  相似文献   

15.
We discuss the evaluation of the Hilbert transformf –1 1 (t-)–1 w(, )(t)dt,–1<<1, of the Jacobi weight functionw(, )(t)=(1–t))(1+t) by analytic and numerical means and also comment on the recursive computation of the quantitiesf –1 1 )(t–)–1 n (t;w (, )) w (, )(t)dt,n=0, 1, 2, ..., where n (·;w (, )) is the Jacobi polynomial of degreen.The work of the first author was supported in part by the National Science Foundation under grant DCR-8320561. The work of the second author was supported by the National Science Foundation under grant DMS-8419086.  相似文献   

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Zusammenfassung Es wird die Spannungsverteilung untersucht, die sich in einem breiten Balken mit konstanter Höhe unter einem konstanten Biegemoment ausbildet, wenn er eine kleine elliptische Einschliessung mit Zentrum auf der Neutralachse enthält. Insbesondere werden die Fälle eines sehr starren Einschlusses sowie eines elliptischen Loches im Detail diskutiert.
Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - x , y normal stress in Cartesian coordinates - xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h 1, 1/h 2 stretch ratios - e x + y dilatation - 2 rotation - M bending moment  相似文献   

18.
Summary Let A be the set of all points of the plane , visited by 2-dimensional Brownian motion before time 1. With probability 1, all points of A are twist points except a set of harmonic measure zero. Twist points may be continuously approached in \A only along a special spiral. Although negligible in the sense of harmonic measure, various classes of cone points are dense in A, with probability 1. Cone points may be approached in \A within suitable wedges.Research supported in part by NSF Grant DMS 8419377  相似文献   

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We consider the weak convergence of distribution functions (mx 1/ m)-1 m x,fx(m)x is a set (x 2) of strongly additive functions such that fx(p){0,1} for each prime number p.  相似文献   

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