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1.
Yu. V. Nesterenko 《Moscow University Mathematics Bulletin》2009,64(4):165-171
An elementary proof of the irrationality of ζ(3) is presented. The proof is based on a two times more dense sequence of Diophantine
approximations to this number than the sequence in the original proof of Apery. 相似文献
2.
Federico Bartolozzi 《Annali di Matematica Pura ed Applicata》1974,100(1):307-325
Sunto Un piano proiettivo ordinato π è M-piano se e solo se esistono un suo punto x ed una sua retta X, x ∉ X, tali che:
1) π è (p, P)-transitivo, p ε P, quando e solo quando p ε X e P = p ∪ x;
2) π è (p, P)-semitransitivo se p ε X, p ∉ P, x ε P.
Un epimorfismo f: π → π′ è un M-epimorfismo se e solo se f(x) ∉ f(X). In questo lavoro si caratterizzano i piani π′ che si
ottengono da un M-piano π mediante un M-epimorfismo; si perviene alla caratterizzazione usufruendo, tra l'altro, della nozione
di posto di un sistema cartesiano e della classificazione degli M-piani dovuta aJ. André.
Entrata in Redazione il 1o agosto 1973.
Lavoro eseguito con contributo del C.N.R. nell'ambito del ? Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni ?. 相似文献
Summary An M-plane π is an ordered projective plane containing a point x and a line X with x ∉ X such that: (i) π is (p, P)-transitive, p ε P, p ε X and P = p ∪ x; (ii) π is (p, P)-semitransitive for every p ε X with p ∉ P and x ε P. An M-epimorphism is an epimorphism f: π → π′ such that f(x) ∉ f(X). We determine the planes π′ that are M-epimorphic images of a given M-plane π; our results are obtained using, among other things, the concept of a place of a cartesian group, and the classification of M-planes given byJ. André.
Entrata in Redazione il 1o agosto 1973.
Lavoro eseguito con contributo del C.N.R. nell'ambito del ? Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni ?. 相似文献
3.
A classical theorem of Wiener (Ann Math 33:1–100, 1932) on the form of a doubly invariant subspace of the shift operator in L
2 over (-π, π] is generalized in three directions: The interval (-π, π] is replaced by a locally compact abelian group, L
2 is replaced by La, a ? (0, ¥){L^{\alpha}, \alpha \in (0, \infty)}, and the measure as well as the functions of L
α
may be operator-valued. 相似文献
4.
Joginder S Dhiman 《Proceedings Mathematical Sciences》2000,110(3):335-345
Recently discovered hydrodynamic instability [1], in a simple Bénard configuration in the parameter regime
under the action of a nonadverse temperature gradient, is shown to be suppressed by the simultaneous action of a uniform
rotation and a uniform magnetic field both acting parallel to gravity for oscillatory perturbations whenever (Qσ
1/π2 + J/π4) > 1 and the effective Rayleigh numberR(1 -T
0α2) is dominated by either 27π4(1 + l/σ1/4 or 27π4/2 according as σ1 ≥1 or σ1
≤ 1 respectively. HereT
0is the temperature of the lower boundary while α2 is the coefficient of specific heat at constant volume due to temperature variation and σ1,R,Q andJ respectively denote the magnetic Prandtl number, the Rayleigh number, the Chandrasekhar number and the Taylor number. 相似文献
5.
J. I. Abdullaev 《Theoretical and Mathematical Physics》2005,145(2):1551-1558
We consider the two-particle Schrodinger operator H(k) on the one-dimensional lattice ℤ. The operator H(π) has infinitely
many eigenvalues zm(π) = v(m), m ∈ ℤ+. If the potential v increases on ℤ+, then only the eigenvalue z0(π) is simple, and all the other eigenvalues are of multiplicity two. We prove that for each of the doubly degenerate eigenvalues
zm(π), m ∈ ℕ, the operator H(π) splits into two nondegenerate eigenvalues z
m
−
(k) and z
m
+
(k) under small variations of k ∈ (π − δ, π). We show that z
m
−
(k) < z
m
+
(k) and obtain an estimate for z
m
+
(k) − z
m
−
(k) for k ∈ (π − δ, π). The eigenvalues z0(k) and z
1
−
(k) increase on [π − δ, π]. If (Δv)(m) > 0, then z
m
±
(k) for m ≥ 2 also has this property.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 212–220, November, 2005. 相似文献
6.
We continue the study of specialized block-colourings of Steiner triple systems initiated in [2] in which the triples through
any element are coloured according to a given partition π of the replication number. Such colourings are equitable if π is
an equitable partition (i.e., the difference between any two parts of π is at most one). Our main results deal with colourings
according to equitable partitions into two, and three parts, respectively. 相似文献
7.
Rao’s flag-transitive plane π of order 49 and π
t
, the plane obtained by transposing matrices of a representative set of π, has been studied. It is shown that π
t
is flag-transitive, π
t
is not isomorphic to π, and π
t
is obtained from π by replacement of a net of degree 25. Further, (1) the flag-transitive planes associated with 1-spread sets S
2b
and S
2a
in the classified list of translation planes of order 49 enumerated by Mathon et al, are respectively isomorphic to π and π
t
(2) The flag-transitive planes associated with the 1-spread sets of 0an* in the classified list of translation planes of
order 49 enumerated by Charnes et al are isomorphic to π and π
t
in some order. 相似文献
8.
Anthony Manning 《Proceedings Mathematical Sciences》1995,105(3):269-271
A givenn ×n matrix of rational numbers acts onC
π and onQ
π. We assume that its characteristic polynomial is irreducible and compare a basis of eigenvectors forC
π with the standard basis forQ
π. Subject to a hypothesis on the Galois group we prove that vectors from these two bases are as independent of each other
as possible. 相似文献
9.
We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr,r,n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. π has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined. 相似文献
10.
Franc Forstnerič 《Journal of Geometric Analysis》2003,13(1):77-94
Let S be a closed connected real surface and π: S→X a smooth embedding or immersion of S into a complex surface X. We denote
by I(π) (resp. by I±(π) if S is oriented) the number of complex points of π (S)∪X counted with algebraic multiplicities. Assuming that I(π)≤0
(resp. I±(π)≤0 if S is oriented) we prove that π can be C0 approximated by an isotopic immersion π1: S→X whose image has a basis of open Stein neighborhood in X which are homotopy equivalents to π1 (S). We obtain precise results for surfaces in
and find an immersed symplectic sphere in
with a Stein neighborhood. 相似文献
11.
Marcello Lucia 《Calculus of Variations and Partial Differential Equations》2006,26(3):313-330
We consider the equation
If Ω is of class C
2, we show that this problem has a non-trivial solution u
λ for each λ ∊ (8 π, λ*). The value λ* depends on the domain and is bounded from below by 2 j
0
2 π, where j
0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j
0
2 π > 8 π). Moreover, the family of solution u
λ blows-up as λ → 8 π. 相似文献
12.
Baohua Fu 《Inventiones Mathematicae》2003,151(1):167-186
In this paper, firstly we calculate Picard groups of a nilpotent orbit 𝒪 in a classical complex simple Lie algebra and discuss
the properties of being ℚ-factorial and factorial for the normalization 𝒪tilde; of the closure of 𝒪. Then we consider the
problem of symplectic resolutions for 𝒪tilde;. Our main theorem says that for any nilpotent orbit 𝒪 in a semi-simple complex
Lie algebra, equipped with the Kostant-Kirillov symplectic form ω, if for a resolution π:Z𝒪tilde;, the 2-form π*(ω) defined on π−1(𝒪) extends to a symplectic 2-form on Z, then Z is isomorphic to the cotangent bundle T
*(G/P) of a projective homogeneous space, and π is the collapsing of the zero section. It proves a conjecture of Cho-Miyaoka-Shepherd-Barron
in this special case. Using this theorem, we determine all varieties 𝒪tilde; which admit such a resolution.
Oblatum 6-V-2002 & 7-VIII-2002?Published online: 10 October 2002 相似文献
13.
Let Ω be a domain with piecewise smooth boundary. In general, it is impossible to obtain a generalized solution u ∈ W
2
2
(Ω) of the equation Δ
x
2
u = f with the boundary conditions u = Δxu = 0 by solving iteratively a system of two Poisson equations under homogeneous Dirichlet conditions. Such a system is obtained
by setting v = −Δu. In the two-dimensional case, this fact is known as the Sapongyan paradox in the theory of simply supported
polygonal plates. In the present paper, the three-dimensional problem is investigated for a domain with a smooth edge Γ. If
the variable opening angle α ∈ C∞(Γ) is less than π everywhere on the edge, then the boundary-value problem for the biharmonic equation is equivalent to the
iterated Dirichlet problem, and its solution u inherits the positivity preserving property from these problems. In the case
α ∈ (π 2π), the procedure of solving the two Dirichlet problems must be modified by permitting infinite-dimensional kernel
and co-kernel of the operators and determining the solution u ∈ W
2
2
(Ω) by inverting a certain integral operator on the contour Γ. If α(s) ∈ (3π/2,2π) for a point s ∈ Γ, then there exists a
nonnegative function f ∈ L2(Ω) for which the solution u changes sign inside the domain Ω. In the case of crack (α = 2π everywhere on Γ), one needs to
introduce a special scale of weighted function spaces. In this case, the positivity preserving property fails. In some geometrical
situations, the problems on well-posedness for the boundary-value problem for the biharmonic equation and the positivity property
remain open. Bibliography: 46 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 336, 2006, pp. 153–198. 相似文献
14.
Summary Let e be continuous and 2π-periodic, h continuous and bounded, and n>0 an integer. Sufficient conditions for the existence of 2π-periodic solutions of x″+n2x+h(x)= =e(t) are given. The proofs are based on a modification of Cesari's method and the Schauder fixed point theorem.
Author is partially supported by N. S. F. under Grant 7447.
Entrata in Redazione il 26 agosto 1968. 相似文献
15.
In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted byB
π, p
(R
n
), 1≤p<∞, i.e., for 1<p<∞,B
π, p
(R
n
) is isomorphic tol
p
(Z
n
), and forp=1,B
π, 1
(R
n
) is isomorphic to the discrete Hardy space with several variables, which is denoted byH(Z
n
).
This project is supported by the National Natural Science Foundation of China (19671012) and Doctoral Programme Institution
of Higher Education Foundation of Chinese Educational Committee and supported by Youth Foundation of Sichuan. 相似文献
16.
Jun Li 《manuscripta mathematica》1993,78(1):223-243
In this note we prove that the number of irreducible components of Hom (π,G) is the same as π1(G), where π is a surface group andG is complex semisimple. This is established by studying the flat bundles on Riemann surfaces.
The present work is partially supported by NSF grant DMS89-04922 相似文献
17.
Normal approximations for descents and inversions of permutations of the set {1,2,…,n} are well known. We consider the number of inversions of a permutation π(1),π(2),…,π(n) of a multiset with n elements, which is the number of pairs (i,j) with 1≤i<j≤n and π(i)>π(j). The number of descents is the number of i in the range 1≤i<n such that π(i)>π(i+1). We prove that, appropriately normalized, the distribution of both inversions and descents of a random permutation of
the multiset approaches the normal distribution as n→∞, provided that the permutation is equally likely to be any possible permutation of the multiset and no element occurs more
than α
n times in the multiset for a fixed α with 0<α<1. Both normal approximation theorems are proved using the size bias version of Stein’s method of auxiliary randomization
and are accompanied by error bounds.
This work was supported by a research fellowship from the Sloan Foundation. 相似文献
18.
Given a connected spaceX, we consider the effect of Quillen’s plus construction on the homotopy groups ofX in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequenceAX→X→X
+, we explain the contribution of π
n
X to π
n
X
+, π
n+1
X
+ and π
n
AX, π
n+1
AX explicitly in terms of the low dimensional homology of π
n
X regarded as a module over π1
X. Key ingredients developed here for this purpose are universal II-central fibrations and a theory of universal central extensions
of modules, analogous to universal central extensions of perfect groups.
Research partially supported by NSERC of Canada. 相似文献
19.
A. A. Panov 《Mathematical Notes》1977,21(1):22-28
The number Kp,q, i.e., the number of (p, q) corridors of closed domains which are convex in the vertical direction, consist of elementary
squares of the integral lattice, are situated within a rectangle of the size q × p, and completely cover the side of length
p of this rectangle under projection is computed. The asymptotic (Kp,q/q2)1/p → λ, as p, q → ∞, where λ = 0.3644255… is the maximum root of the equation1F1(-1/2 − 1/(16λ), 1/2, 1/(4λ)) = 0,1F1 being the confluence hypergeometric function, is established. These results allow us to compute the ε entropy of the space
of continuous functions with the Hausdorff metric.
Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 39–50, January, 1977. 相似文献
20.
The instability of a hot horizontal layer of ferromagnetic fluid rotating about a vertical axis has been investigated when
the Prandtl numberP < 1. Earlier it was shown that forP > 1 the overstability cannot occur. In this paper the convective and overstable marginal states have been investigated separately
forP < 1 and it is found that though convective marginal state is possible for alla, the non-dimensional wave number, and N the Taylor number, the overstability is possible only ifN > (1 +P)π
4/(1 −P) and in case the condition is satisfied, overstability is possible for all those values ofa which satisfya
2 < [N(1 −P)π
2/(1 +P)]
1/3 − π2. IfR
c
(con)
andR
c
(o.s)
are the critical values of the convective and the overstable marginal states respectively, then it is also found thatR
c
(con)
<R
c
(o.s)
providedN is not sufficiently large. 相似文献