共查询到20条相似文献,搜索用时 359 毫秒
1.
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n x n matrices over R. Let (Jn(R)) be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let JJ = (Jn(R)) or Mn(R). We describe the additive preservers of idempotence from JJ to Mm(R) when 2 is a unit of R. Thereby, we also characterize the Jordan (respectively, ring and ring anti-) homomorphisms from Mn (R) to Mm (R) when 2 is a unit of R. 相似文献
2.
We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR
Nsuch that for everyr>0,h maps the Hilbert cube [−r, r]
N
precisely onto the “elliptic cube”
. This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR
N.The result is obtained by means of the Bing Shrinking Criterion.
Research supported in part by a grant from NSF-EPSCoR Alabama. 相似文献
3.
The review article of Crandall, Ishii, and Lions [Bull. AMS,27, No. 1, 1–67 (1992)] devoted to viscosity solutions of first- and second-order partial differential equations contains the
exact Lax formula
for a solution to the Hamilton-Jacobi nonlinear partial differential equation
where the Cauchy datav:R
n
→R are chosen as a function properly convex and semicontinuous from below, ‖·‖=<·,·> is the usual norm inR
n
,n ∉Z
+, andt ∉R
+ is a positive evolution parameter. The article also states that there is no exact proof of the Lax formula (1) based on general
properties of the Hamiltonian-Jacobi equation (2). This work presents precisely such an exact proof of the Lax formula (1).
Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv; Courant Institute
of Mathematical Sciences at NYU, New York. Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp.
20–25, 相似文献
((1)) |
((2)) |
4.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
5.
Michael Wolf 《Journal d'Analyse Mathématique》1996,68(1):107-120
We give a brief, elementary and analytic proof of the theorem of Hubbard and Masur [HM] (see also [K], [G]) that every class
of measured foliations on a compact Riemann surfaceR of genusg can be uniquely represented by the vertical measured foliation of a holomorphic quadratic differential onR. The theorem of Thurston [Th] that the space of classes of projective measured foliations is a 6g—7 dimensional sphere follows immediately by Riemann-Roch. Our argument involves relating each representative of a class of
measured foliations to an equivariant map from
to anR-tree, and then finding an energy minimizing such map by the direct method in the calculus of variations. The normalized Hopf
differential of this harmonic map is then the desired differential.
Partially supported by NSF grant DMS9300001; Alfred P. Sloan Research Fellow. 相似文献
6.
V. V. Makeev 《Journal of Mathematical Sciences》2007,140(4):558-563
Let ℝn be the n-dimensional Euclidean space, and let { · } be a norm in Rn. Two lines ℓ1 and ℓ2 in ℝn are said to be { · }-orthogonal if their { · }-unit direction vectors e
1 and e
2 satisfy {e
1 + e
2} = {e
1 − e
2}. It is proved that for any two norms { · } and { · }′ in ℝn there are n lines ℓ1, ..., ℓn that are { · }-and { · }′-orthogonal simultaneously. Let
be a continuous function on the unit sphere
with center O. It is proved that there exists an (n − 1)-cube C centered at O, inscribed in
, and such that all sums of values of f at the vertices of (n − 3)-faces of C are pairwise equal. If the function f is even,
then there exists an n-cube with the same properties. Furthermore, there exists an orthonormal basis e
1, ..., e
n such that for 1 ≤ i ≤ j ≤ n we have
. Bibliography: 8 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 107–117. 相似文献
7.
Feng WEI 《数学学报(英文版)》2005,21(4):823-832
Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф(Xi^△j) is a reduced generalized differential identity for an essential ideal of R, then ф(Zije(△j )) is a generalized polynomial identity for RF, where e(△j) are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф(Xi△j) is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф(Zij) is a generalized polynomial identity for [R, R]. Moreover, if ф(Xi△j) is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф(Zij) is a generalized polynomial identity for Q. 相似文献
8.
An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed
convex proper cone inR
n and −Γ′ be the antipodes of the dual cone of Γ. Let
be a partial differential operator with constant coefficients inR
n, whereQ(ζ)≠0 onR
n−iΓ′ andP
i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R
n−iΓ′;P
j(ζ)=0, gradP
j(ζ)≠0} contains some real point on which gradP
j≠0 and gradP
j∉Γ∪(−Γ). LetC be an open cone inR
n−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in
{ξ∈R
n;P(ξ)=0}. Ifu∈ℒ′∩L
loc
2
(R
n−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition
implies that the support ofu is contained in Γ. 相似文献
9.
Hans G. Kellerer 《Probability Theory and Related Fields》1987,76(1):71-80
Summary A point process
on R
+ can be represented by the associated counting process (ξ
t
;t∈
R
+) or by the associated sequence of jump times (τ
n
;n∈
Z
+) and in accordance may possess two types of Markov property. The present paper first clarifies their mutual dependence, leading
in particular to the notion of “weak multiplicativity” for the joint distribution of two consecutive jump times. Then, by
means of results from a previous paper, a uniquely determined “Markov variant”
is assigned to
without changing the one-dimensional marginals. This provides in particular a new characterization of the Poisson process
by these marginals and the adequate Markov property. Further applications concern the explicit construction of the compensator
and certain transition probabilities of
. 相似文献
10.
Nakao HAYASHI Pavel I. NAUMKIN 《数学学报(英文版)》2006,22(5):1441-1456
We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut+uux-uxx+uxxx=0,x∈R,t〉0. We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that if the initial data u0 ∈H^s (R)∩L^1 (R), where s 〉 -1/2, then there exists a unique solution u (t, x) ∈C^∞ ((0,∞);H^∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u(t)=t^-1/2fM((·)t^-1/2)+0(t^-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L^1 (R), then the asymptotics are true u(t)=t^-1/2fM((·)t^-1/2)+O(t^-1/2-γ) where γ ∈ (0, 1/2). 相似文献
11.
Suppose λ is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal functionL
λ(x)
x∈R, satisfying the interpolatory conditionsL
k = δ0k,k∈Z
. One objective of this paper is to derive several additional properties ofL
λ. For example, it is shown thatL
λ possesses the signregularity property sgn[L
λ(x)]=sgn[sin(πx)/(πx)],x∈R, and that |L
λ (x)|≤2e
8 min {(⌊|x|⌋+1)-1,exp(-λ⌊|x|⌋)},x∈R. The analysis is based on a simple representation formula forL
λ and employs some methods from classical function theory. A second consideration in the paper is the Gaussian cardinal-interpolation
operatorL
λ, defined by the equation (L
λy)(x):=
,x∈R, y=(yk)k∈Z. On account of the exponential decay of the cardinal functionL
λ,L
λ is a well-defined linear map froml
∞ (Z) intoL
∞ (R). Its associated operatornorm ‖L
λ‖ is called the Lebesgue constant ofL
λ. The latter half of the paper establishes the following estimates for the Lebesgue constant: ‖L
λ‖≍1, λ→∞, and ║Lλ║≍log(1/λ), λ→0+. Suitable multidimensional analogues of these results are also given.
For Carl de Boor, on the occasion of his sixtieth birthday 相似文献
12.
Alexander Brudnyi 《Arkiv f?r Matematik》2004,42(1):31-59
LetM be a non-compact connected Riemann surface of a finite type, andR⋐M be a relatively compact domain such thatH
1(M,Z)=H
1(R,Z). Let
be a covering. We study the algebraH
∞(U) of bounded holomorphic functions defined in certain subdomains
. Our main result is a Forelli type theorem on projections inH
∞(D).
Research supported in part by NSERC. 相似文献
13.
P. C. Allaart 《Acta Mathematica Hungarica》2008,121(3):243-275
This paper concerns the maximum value and the set of maximum points of a random version of Takagi’s continuous, nowhere differentiable
function. Let F(x):=∑
n=1∞
ε
n
ϕ(2
n−1
x), x ∈ R, where ɛ
1, ɛ
2, ... are independent, identically distributed random variables taking values in {−1, 1}, and ϕ is the “tent map” defined by ϕ(x) = 2 dist (x, Z). Let p:= P (ɛ
1 = 1), M:= max {F(x): x ∈ R}, and := {x ∈ [0, 1): F(x) = M}. An explicit expression for M is given in terms of the sequence {ɛ
n
}, and it is shown that the probability distribution μ of M is purely atomic if p < , and is singular continuous if p ≧ . In the latter case, the Hausdorff dimension and the multifractal spectrum of μ are determined. It is shown further that the set is finite almost surely if p < , and is topologically equivalent to a Cantor set almost surely if p ≧ . The distribution of the cardinality of is determined in the first case, and the almost-sure Hausdorff dimension of is shown to be (2p − 1)/2p in the second case. The distribution of the leftmost point of is also given. Finally, some of the results are extended to the more general functions Σa
n − 1
ɛ
n
ϕ(2
n − 1
x), where 0 < a < 1.
相似文献
14.
Given a semi-convex functionu: ω⊂R
n→R and an integerk≡[0,1,n], we show that the set ∑k defined by
相似文献
15.
刘斌 《高校应用数学学报(英文版)》2002,17(2):135-144
§ 1 IntroductionWe are interested in the existence ofthree-solutions ofthe following second-order dif-ferential equations with nonlinear boundary value conditionsx″=f( t,x,x′) , t∈ [a,b] ,( 1 .1 )g1 ( x( a) ,x′( a) ) =0 , g2 ( x( b) ,x′( b) ) =0 ,( 1 .2 )where f:[a,b]×R1 ×R1 →R1 ,gi:R1 ×R1 →R1 ( i=1 ,2 ) are continuous functions.The study ofthe existence of three-solutions ofboundary value prolems forsecond or-der differential equations was initiated by Amann[1 ] .In[1 … 相似文献
16.
H. E. A. Campbell I. Hughes F. Pappalardi P. S. Selick 《Commentarii Mathematici Helvetici》1991,66(1):322-331
In [1] the first and last authors studied a decomposition ofH
*(R
P
∞×…×R
P
∞;F
2) into modules over the Steenrod algebra obtained from an action of the cyclic group
. Here a minimal set of generators for the ring of invariants is characterized and counted by analyzing the associated ring
of Laurent polynomials. A structure theorem for the ring of invariant Laurent polynomials is given and a ‘destabilisation
cancels localisation’ theorem is obtained.
The authors gratefully acknowledge the support of NSERC. 1980 Mathematics Subject classification, 13F20, 55. Keywords: Invariant
theory, Steenrod algebra. 相似文献
17.
Alexandru Zaharescu 《The Ramanujan Journal》2006,11(1):95-102
We provide asymptotic formulas for sums over arithmetic progressions of coefficients of products of the form
18.
In his PhD thesis, Arnon [1] builds a completion of the Dickson algebras which contains a “free root” algebraD
fin on the top Dickson classes. Hu’ng [5] has shown that this algebra is in fact isomorphic to a similar completion (A
μ)* of the dual of the Steenrod algebraA*. Arnon also completed the Steenrod algebraA with respect to its halving homomorphism to obtainA
μ. Here we study an analogous completion of the Dyer-Lashof algebraR to obtainR
μ with canonical subcoalgebrasR
μ[n]. Unlike the Steenrod algebra, we may further completeR
μ with respect to length to obtain
. It turns out, somewhat surprisingly, that the dual (
) contains (A
μ)* as a dense subalgebra.
This research is supported in part by the Natural Sciences and Engineering Research Council of Canada. 相似文献
19.
We prove the following theorem. Assume f ∈ L
∞(R
2) with bounded support. If f is continuous at some point (x
1,x
2) ∈ R
2, then the double Fourier integral of f is strongly q-Cesàro summable at (x
1,x
2) to the function value f(x
1,x
2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset
of R
2, then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on
.
Research partially supported by the Australian Research Council and the Hungarian National Foundation for Scientific Research
under Grant T 046 192. 相似文献
20.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
|