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1.
1.IntroductionWeshallassumefamiliaritywithmatroidtheory--foranintroduction,andforthedefinitionoftermsnotdefinedinthispaper,see[31.Edmonds'matroidpartitiontheoremisaveryimportanttheorem,whichhasmanyapplications.Twoclassicresultsof[4,5],whichconcernwithpackingandcoveringoftheedgesetofagraphwithkedge--disjointspanningtrees,canbeeasilydeducedfromit(see[3],PP.125--127).Inthepresentpaperwewillpresentamatroidapproachtotheproblemoftreedecompositionraisedrecently(see[6,7]).Ourmainaimistogivealternati… 相似文献
2.
John De Cicco 《Annali di Matematica Pura ed Applicata》1962,57(1):339-403
Summary The properties of a physical system Sk where k ≠−1, of ∞2n−1 trajectories C. in a Riemannian space Vn are developed. The intrinsic differential equations and the equations of Lagrange, of a physical system Sk, are derived. The Lagrangian function L and the Hamiltonian function H, are studied in the conservative case. Also included
are systems of the type (G), curvature trajectories, and natural families. The Appell transformation T of a dynamical system
S
0
in a Riemannian space Vn, is obtained. Finally, contact transformations and the transformation theory of a physical system Sk where k ≠−1, are considered in detail.
To Enrico Bompiani on his scientific Jubilee
Kasner,Differential geometric aspecte of dynamics, The Princeton Colloquium Lectures, 1909. Published by the ? American Mathematical Society, Providence, Rhode Island, 1913,
and reprinted 1934. 相似文献
3.
A. V. Stolyarov 《Journal of Mathematical Sciences》2011,177(5):716-724
In this paper, we study the internal geometry of a hypersurface V
n−1 embedded in a projectively metric space K
n
, n ≥ 3, and equipped with fields of geometric-objects { Gni,Gi } \left\{ {G_n^i,{G_i}} \right\} and { Hni,Gi } \left\{ {H_n^i,{G_i}} \right\} in the sense of Norden and with a field of a geometric object { Hni,Hn } \left\{ {H_n^i,{H_n}} \right\} in the sense of Cartan. For example, we have proved that the projective-connection space P
n−1,n−1 induced by the equipment of the hypersurface Vn - 1 ì Kn, n 3 3 {V_{n - 1}}\; \subset \;{K_n},\;n \geq 3 , in the sense of Cartan with the field of a geometrical object { Hni,Hn } \left\{ {H_n^i,{H_n}} \right\} is flat if and only if its normalization by the field of the object { Hni,Gi } \left\{ {H_n^i,{G_i}} \right\} in the tangent bundle induces a Riemannian space R
n−1 of constant curvature K = −1/c. 相似文献
4.
Ignacy Kotlarski 《Annali di Matematica Pura ed Applicata》1966,74(1):129-134
Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x1, x2, …, xn be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals fk(t) = E[ei(t,x
k)], (k=1, 2, …, n): let y1=x1 + xn, y2=x2 + xn, …, yn−1=xn−1 + xn.
If the characteristic functional f(t1, t2, …, tn−1) of the random variables (y1, y2, …, yn−1) does not vanish, then the joint distribution of (y1, y2, …, yn−1) determines all the distributions of x1, x2, …, xn up to change of location. 相似文献
5.
A. Dubickas 《Journal of Mathematical Sciences》2006,137(2):4654-4657
Let g and m be two positive integers, and let F be a polynomial with integer coefficients. We show that the recurrent sequence
x0 = g, xn = x
n−1
n
+ F(n), n = 1, 2, 3,…, is periodic modulo m. Then a special case, with F(z) = 1 and with m = p > 2 being a prime number,
is considered. We show, for instance, that the sequence x0 = 2, xn = x
n−1
n
+ 1, n = 1, 2, 3, …, has infinitely many elements divisible by every prime number p which is less than or equal to 211 except
for three prime numbers p = 23, 47, 167 that do not divide xn. These recurrent sequences are related to the construction of transcendental numbers ζ for which the sequences [ζn!], n = 1, 2, 3, …, have some nice divisibility properties. Bibliography: 18 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 76–82. 相似文献
6.
We establish integral formulas of Minkowski's type for compact spacelike hypersurfaces in de sitter spaceS
1
n+1
(1) and give their applications to the case of constantr-th mean curvature (r=1,2,…,n−1). Whenr=1 we recover Montiel's result.
Li Haizhong is supported by NNSFC No.19701017 and Basic Science Research Foundation of Tsinghua University and Chen Weihua
is supported by NNSFC No. 19571005 相似文献
7.
Li Banghe 《Commentarii Mathematici Helvetici》1982,57(1):135-144
Under the assumption of (f, M
n
,N
2n−1) being trivial, the classification of immersions homotopic tof: M
n
→N
2n−1 is obtained in many cases. The triviality of (f, M
n
,P
2n−1) is proved for anyM
n
andf.
LetM, N be differentiable manifolds of dimensionn and2n−1 respectively. For a mapf: M → N, denote byI[M, N]
f
the set of regular homotopy classes of immersions homotopic tof. It has been proved in [1] that, whenn>1,I[M, N]
f
is nonempty for anyf. In this paper we will determine the setI[M, N]
f
in some cases.
For example, ifN=P
2n−1 or more generally, the lens spacesS
m
2n−1
=Z
m
/S
2n−1,M is any orientablen-manifold or nonorientable butn≡0, 1, 3 mod 4, then, for anyf, theI[M, N]
f is determined completely.
WhenN=R
2n−1, the setI[M, N] of regular homotopy classes of all immersions has been enumerated by James and Thomas in [2] and McClendon in [3] forn>3. Applying our results toN=R
2n−1 we obtain their results again, except for the casen≡2 mod 4 andM nonorientable.
Whenn=3, McClendon's results cannot be used. Our results include the casesn=3,M orientable or not (for orientableM, I[M, R5] is known by Wu [4]). 相似文献
8.
Giuliano Mazzanti 《Annali dell'Universita di Ferrara》1972,17(1):143-147
Riassunto Si dà la definizione di classe ?localmente filtrale?. Si diceche K è una classe localmente filtrale se per ogni n∈ω, per ogni
A
0,...,A
n−1, εK e per ogni famiglia di sotto-insiemi Vi di Ai (i∈n) con Vi finiti, la classe {B
0,...,B
n−1 delle algebre generate da V0, ..., Vn−1 è costituita da algebre finite ed è filtrale.
Si dimostra che seK è localmente filtrale alloraV
L(K)=IR
L
DS(K) e si dà un teorema di caratterizzazione per queste classi.
Lavoro eseguito nell'ambito dei gruppi di ricerca matematici del C.N.R. per l'anno 1970–71. 相似文献
Summary We define a ?classe localmente filtrale? as follows: LetK be a class of similar algebras;K is a ?classe localmente filtrale? if for andn ∈ ω and for anyA 0,...,A n−1 ink and for any family of finite subsetsV i ofA i(i∈n), the class {B 0,...,B n−1 of algebras generated byV o, ...,V n−1 consists of finite algebras and is ?filtrale?. We show that ifK is ?localmente filtrale? thenV L (K)=IR L DS(K) and we give a characterization theorem for these classes.
Lavoro eseguito nell'ambito dei gruppi di ricerca matematici del C.N.R. per l'anno 1970–71. 相似文献
9.
A. V. Stolyarov 《Russian Mathematics (Iz VUZ)》2010,54(11):56-65
In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a
regular hypersurface V
n−1 embedded into a projective-metric space K
n
, n ≥ 3, intrinsically induces a dual projective-metric space $
\bar K_n
$
\bar K_n
. 2) An invariant analytical condition is established under which a normalization of a hypersurface V
n−1 ⊂ K
n
(a tangential hypersurface $
\bar V_{n - 1}
$
\bar V_{n - 1}
⊂ $
\bar K_n
$
\bar K_n
) by quasitensor fields H
n
i
, H
i
($
\bar H_n^i
$
\bar H_n^i
, $
\bar H_i
$
\bar H_i
) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R
n−1 and $
\bar R_{n - 1}
$
\bar R_{n - 1}
are spaces of the same constant curvature $
K = - \tfrac{1}
{c}
$
K = - \tfrac{1}
{c}
. 3) Geometric interpretations of the obtained analytical conditions are given. 相似文献
10.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献
11.
We deal with (n−1)-generated modules of smooth (analytic, holomorphic) vector fieldsV=(X
1,..., Xn−1) (codimension 1 differential systems) defined locally on ℝ
n
or ℂ
n
, and extend the standard duality(X
1,..., Xn−1)↦(ω), ω=Ω(X1,...,Xn−1,.,) (Ω−a volume form) betweenV′s and 1-generated modules of differential 1-forms (Pfaffian equations)—when the generatorsX
i are linearly independent—onto substantially wider classes of codimension 1 differential systems. We prove that two codimension
1 differential systemsV and
are equivalent if and only if so are the corresponding Pfaffian equations (ω) and
provided that ω has1-division property: ωΛμ=0, μ—any 1-form ⇒ μ=fω for certain function germf. The 1-division property of ω turns out to be equivalent to the following properties ofV: (a)fX∈V, f—not a 0-divisor function germ ⇒X∈V (thedivision property); (b) (V
⊥)⊥=V; (c)V
⊥=(ω); (d) (ω)⊥=V, where ⊥ denotes the passing from a module (of vector fields or differential 1-forms) to its annihilator.
Supported by Polish KBN grant No 2 1090 91 01.
Partially supported by the fund for the promotion of research at the Technion, 100–942. 相似文献
12.
We obtain a sufficient condition for a subsetH of positive integers to satisfy that the equidistribution (mod 1) of the sequences (u
n+h
− u
n; n=1, 2, ···) for allh ∈H implies the equidistribution of (u
n). Our condition is satisfied, for example, for the following sets: (1)H={n − m; n ∈ I, m ∈ I, n>m}, whereI is any infinite subset of integers; (2)H={| ψ (n)|; ψ(n)≠0,n ∈ Z}, where ψ is a nonconstant polynomial with integral coefficients having at least one integral zero (modq) for allq=2, 3, ···; (3)H={p+1;p is a prime} andH={p − 1;p is a prime}. 相似文献
13.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):429-433
A sequence {X
n,n≧1} of independent and identically distributed random variables with continuous cumulative distribution functionF(x) is considered.X
j is a record value of this sequence ifX
j>max (X
1, …,X
j−1). Let {X
L(n) n≧0} be the sequence of such record values. Some properties ofX
L(n) andX
L(n)−XL(n−1) are studied when {X
n,n≧1} has the exponential distribution. Characterizations of the exponential distribution are given in terms of the sequence
{X
L(n),n≧0}
The work was partly completed when the author was at the Department of Statistics, University of Brasilia, Brazil. 相似文献
14.
The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations
that only depends on the path graph A
n − 1 on n − 1 nodes. Here we describe an algebra depending on an arbitrary graph Q, called the Brauer algebra of type Q, and study its structure in the cases where Q is a Coxeter graph of simply laced spherical type (so its connected components are of type A
n − 1, D
n
, E6, E7, E8). We find its irreducible representations and its dimension, and show that the algebra is cellular. The algebra is generically
semisimple and contains the group algebra of the Coxeter group of type Q as a subalgebra. It is a ring homomorphic image of the Birman-Murakami-Wenzl algebra of type Q; this fact will be used in later work determining the structure of the Birman-Murakami-Wenzl algebras of simply laced spherical
type. 相似文献
15.
William J. Firey 《Israel Journal of Mathematics》1976,24(3-4):274-281
A function over the convex coneK{inn}, of convex bodiesK in Euclideann-space (where addition is vector addition, positive scalar multiplication is dilatation), which is linear overK{inn}, increasing with respect to set inclusion, and zero at point bodies must be a mixed volumeV(K; đ, p−1;σ
1, …,σ
n−p). Heređ, takenp−1 times, is inK{inn} andσ
1, …,σ
n−pare pairwise orthogonal unit segments spanning the orthogonal complement of the affine hull ofđ. 相似文献
16.
Marston Morse 《Annali di Matematica Pura ed Applicata》1960,49(1):117-128
Summary Let M be a compact differentiable m-manifold of class Cm in En, n=2m+1. Let x=(x1, ..., xn) represent a point in En. The union of the direction c on the direction sphere Sn−1 in En such that the scalar product c · x defines a non-degenerate fonction on M is an open subset of Sn−1 whose complement θ has a Lebesgue measure zero on Sn−1. When M is non-compact θ can be everywhere dense on Sn−1, but still has Lebesgue measure zero.
To Giovanni Sansone on his 70th birth day. 相似文献
17.
Karel Svoboda 《Annali di Matematica Pura ed Applicata》1962,57(1):239-255
Résumé Dans un espace projectif S2n−i(n≥3) à 2n−1 dimensions, on étudie un système composé de n congruences non-paraboliques de droites L1, L2, ..., Ln qui jouissent de la propriété que chaque couple de congruences Li,L
i+1(i=1, 2, ..., n; Ln+i=Li) est stratifiable dans le sens de Li vers Li+1.
à M. Enrico Bompiani pour son Jubilé scientifique. 相似文献
18.
Laurent-Padé (Chebyshev) rational approximantsP
m
(w, w
−1)/Q
n
(w, w
−1) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP
m
/Q
n
matches that of a given functionf(w, w
−1) up to terms of orderw
±(m+n)
, based only on knowledge of the Laurent series coefficients off up to terms inw
±(m+n)
. This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent
series ofP
m
matches that ofQ
n
f up to terms of orderw
±(m+n
), but based on knowledge of the series coefficients off up to terms inw
±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and
corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of
the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations
are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably
similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the
use of either. 相似文献
19.
Let G be a group, R an integral domain, and V
G
the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1
G
of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications,
In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique
de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen theorem [Duistermaat J.J., van der Kallen W., Constant terms
in powers of a Laurent polynomial, Indag. Math., 1998, 9(2), 221–231], and also by recent studies on the notion of Mathieu
subspaces, we show that for finite groups G, V
G
also forms a Mathieu subspace of the group algebra R[G] when certain conditions on the base ring R are met. We also show that for the free abelian groups G = ℤ
n
, n ≥ 1, and any integral domain R of positive characteristic, V
G
fails to be a Mathieu subspace of R[G], which is equivalent to saying that the Duistermaat-van der Kallen theorem cannot be generalized to any field or integral
domain of positive characteristic. 相似文献
20.
In this paper, we shall give an integral equality by applying the operator □ introduced by S.Y. Cheng and S.T. Yau [7] to
compact spacelike hypersurfaces which are immersed in de Sitter spaceS
1
n+1
(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvaturen(n−1)r is isometric to a sphere ifr<c.
Research partially Supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and
Culture. 相似文献