共查询到20条相似文献,搜索用时 353 毫秒
1.
Robert Kaufman Jeremy T. Tyson Jang-Mei Wu 《Publications Mathématiques de L'IHéS》2005,101(1):209-241
According to a theorem of Martio, Rickman and Väisälä, all nonconstant Cn/(n-2)-smooth quasiregular maps in Rn, n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in R3. We prove that the order of smoothness is sharp in R4. For each n≥5 we construct a C1+ε(n)-smooth quasiregular map in Rn with nonempty branch set. 相似文献
2.
《代数通讯》2013,41(7):3311-3326
Abstract Let R be a prime ring and 𝒰(R) its group of units. We prove that if 𝒰(R) satisfies a group identity and 𝒰(R) generates R,then either R is a domain or R is isomorphic to the algebra of n × n matrices over a finite field of order d. Moreover the integers n and d depend only on the group identity satisfed by 𝒰(R). This result has been recently proved by C. H. Liu and T. K. Lee (Liu,C. H.; Lee,T. K. Group identities and prime rings generated by units. Comm. Algebra (to appear)) and here we present a new different proof. 相似文献
3.
Let R be a prime ring with involution * and d be a nonzero derivation on R such that d(x *) = -d(x)* for all x ∈ R. Suppose that n ≥ 1 is a fixed integer. Then (I) if d(s) n = 0 for all s = s *, then R is either a commutative domain or an order in a 4-dimensional central simple algebra; (II) if d(s) n ∈Z, the center of R for all s = s *, then R is either a commutative domain or an order in a simple algebra of dimension 4 or 16 over its center. 相似文献
4.
《代数通讯》2013,41(9):4273-4290
Abstract The 𝒥-radical of a lattice-ordered ring Ris the ?-ring analogue of the Jacobson radical of a ring. It is shown that if the matrix ring R n has the usual lattice order, then 𝒥(R n ) = 𝒥(R) n . The connection between an element abeing right ?-quasi-regular and the inequality a ○ x ≤ 0 is also investigated. For squares in an f-ring the connection is an equivalence. In general it is still an equivalence provided xis the sum of elements from a larger f-ring whose absolute values lie in R. It is also shown that the vanishing of annihilators in an f-ring is inherited by enough totally ordered homomorphic images to give a subdirect product decomposition. 相似文献
5.
For given two graphs G dan H, the Ramsey number R(G,H) is the smallest positive integer n such that every graph F of order n must contain G or the complement of F must contain H. In [12], the Ramsey numbers for the combination between a star S
n
and a wheel W
m
for m=4,5 were shown, namely, R(S
n
,W
4)=2n−1 for odd n and n≥3, otherwise R(S
n
,W
4)=2n+1, and R(S
n
,W
5)=3n−2 for n≥3. In this paper, we shall study the Ramsey number R(G,W
m
) for G any tree T
n
. We show that if T
n
is not a star then the Ramsey number R(T
n
,W
4)=2n−1 for n≥4 and R(T
n
,W
5)=3n−2 for n≥3. We also list some open problems.
Received: October, 2001 Final version received: July 11, 2002
RID="*"
ID="*" This work was supported by the QUE Project, Department of Mathematics ITB Indonesia
Acknowledgments. We would like to thank the referees for several helpful comments. 相似文献
6.
On an n-dimensional vector space, equipped with a scalar product, we prescribe (0, 4) -, (0, 5)-, … type tensors R(0), R(1), …, satisfying the well-known conditions for a curvature tensor and its derivatives and furthermore certain inequalities for the absolute values of the components of R(k). Then there is an analytic Riemannian metric g on an open ball of the Cartesian space Rn[u1, …, un] for which u1, …, un are normal coordinates and (▽(k)R)0 = R(k) (k = 0, 1, 2, …) hold under an identification of the tangent space T0Rn at the origin with the vector space; ▽(k)R denote the curvature tensor and its covariant derivatives with respect to the Levi-Civita connection ▽ of g, respectively. 相似文献
7.
8.
Second Homology Groups and Universal Coverings of Steinberg Leibniz Algebras of Small Characteristic
It is known that the second Leibniz homology group HL 2 (𝔰𝔱𝔩 n (R)) of the Steinberg Leibniz algebra 𝔰𝔱𝔩 n (R) is trivial for n ≥ 5. In this article, we determine HL 2(𝔰𝔱𝔩 n (R)) explicitly (which are shown to be not necessarily trivial) for n = 3, 4 without any assumption on the base ring. 相似文献
9.
10.
A. K. Varma 《Israel Journal of Mathematics》1972,12(4):337-341
Letx
kn=2θk/n,k=0,1 …n−1 (n odd positive integer). LetR
n(x) be the unique trigonometric polynomial of order 2n satisfying the interpolatory conditions:R
n(xkn)=f(xkn),R
n
(j)(xkn)=0,j=1,2,4,k=0,1…,n−1. We setw
2(t,f) as the second modulus of continuity off(x). Then we prove that |R
n(x)-f(x)|=0(nw2(1/nf)). We also examine the question of lower estimate of ‖R
n-f‖. This generalizes an earlier work of the author. 相似文献
11.
A method is put forward to establish the lower bounds for somen-color classical Ramsey numbers
. With this method six new explicit lower boundsR
4(4) ≥458,R
3(5) ≥ 242,R
3(6)≥1070,R
3(7) ≥ 1214,R
3(8) ≥2834 andR
3(9) ≥ 5282 are obtained using a computer.
Project supported by Guangxi Natural Science Foundation 相似文献
12.
Yonglin Cao 《Semigroup Forum》2011,83(2):190-204
Let R be a finite commutative chain ring, n a positive integer and R
n
the free R-module of rank n consisting of column vectors over R. The generalized affine transformation monoid Gaff
n
(R) of R
n
is introduced, then Schützenberger groups of -classes, principal factors and group -classes of the monoid Gaff
n
(R) are investigated. As corollaries, basic numerical information of Gaff
n
(R) is given. 相似文献
13.
Li Fuan 《数学学报(英文版)》1987,3(3):247-255
LetR be an arbitrary commutative ring, andn be an integer ≥3. It is proved for any idealJ ofR thatESp
2n(R,J)=[ESp
2n(R),ESp
2n(J)]=[ESp
2n(R),ESp
2n(R,J)] =[ESp
2n(R),GSp
2n(R,J)]=[Sp
2n(R),ESp
2n(R,J)]. Furthermore, the problem of normal subgroups ofSp
2n(R) has an affirmative solution if and only ifaR=a
2R+2aR for eacha inR. This covers the relevant results of [4], [8], [10], [12] and [13].
Project Supported by the Science Fund of the Chinese Academy of Sciences 相似文献
14.
The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. This paper deduces some properties of R-sets of connected graphs. It is shown that for a connected graph G of order n and diameter 2 the number of R-sets equal to V(G) is bounded above by ?n2/4?{\lfloor n^{2}/4\rfloor} . It is conjectured that this bound holds for every connected graph of order n. A lower bound for the metric dimension dim(G) of G is proposed in terms of a family of R-sets of G having the property that every subfamily containing at least r ≥ 2 members has an empty intersection. Three sufficient conditions, which guarantee that a family F=(Gn)n 3 1{\mathcal{F}=(G_{n})_{n\geq 1}} of graphs with unbounded order has unbounded metric dimension, are also proposed. 相似文献
15.
16.
Juncheol Han 《代数通讯》2013,41(2):872-879
Let R be a ring with identity, X(R) the set of all nonzero non-units of R and G(R) the group of all units of R. By considering left and right regular actions of G(R) on X(R), the following are investigated: (1) For a local ring R such that X(R) is a union of n distinct orbits under the left (or right) regular action of G(R) on X(R), if J n ≠ 0 = J n+1 where J is the Jacobson radical of R, then the set of all the distinct ideals of R is exactly {R, J, J 2,…, J n , 0}, and each orbit under the left regular action is equal to the one under the right regular action. (2) Such a ring R is left (and right) duo ring. (3) For the full matrix ring S of n × n matrices over a commutative ring R, the number of orbits under left regular action of G(S) on X(S) is equal to the number of orbits under right regular action of G(S) on X(S); the result also holds for the ring of n × n upper triangular matrices over R. 相似文献
17.
We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group BQ(k,E(n)) of E(n) that are isomorphic. For any triangular structure R on E(n) we prove that the subgroup BM(k,E(n),R) of BQ(k,E(n)) arising from R is isomorphic to a direct product of BW(k), the Brauer-Wall group of the ground field k, and Symn(k), the group of n × n symmetric matrices under addition. For a general quasi-triangular structure R on E(n) we construct a split short exact sequence having BM(k,E(n),R) as a middle term and as kernel a central extension of the group of symmetric matrices of order r < n (r depending on R). We finally describe how the image of the Hopf automorphism group inside BQ(k,E(n)) acts on Symn (k). 相似文献
18.
The minimal cardinality of a q-ary code of length n and covering radius at most R is denoted by Kq(n, R); if we have the additional requirement that the minimum distance be at least d, it is denoted by Kq(n, R, d). Obviously, Kq(n, R, d) Kq(n, R). In this paper, we study instances for which Kq(n,1,2) > Kq(n, 1) and, in particular, determine K4(4,1,2)=28 > 24=K4(4,1).Supported in part by the Academy of Finland under grant 100500. 相似文献
19.
A distribution function F on the nonnegative real line is called subexponential if limx(1-F
*n
(x)/(1 - F(x)) = n for all n 2, where F
*n
denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its density analogue. Among others we discuss the asymptotic behavior of the remainder term R
n
(x) defined by R
n
(x) = 1 - F*n(x) - n(1 - F(x)) and of its density analogue rn (x) = -(Rn (x))'. Our results complement and complete those obtained by several authors. In an earlier paper, we obtained results of the form n(x) = O(1)f(x)R(x), where f is the density of F and R(x) =
0
x
(1-F(y))dy. In this paper, among others we obtain asymptotic expressions of the form R
n(x)=
2
n
R2(x) + O(1)(-f'(x))R2(x) where f' is the derivative of f. 相似文献
20.
Eric Todd Quinto 《Journal of Mathematical Analysis and Applications》1982,90(2):408-420
Let R be the classical Radon transform that integrates a function over hyperplanes in Rn and let SM be the transform that integrates a function over spheres containing the origin in Rn. We prove continuity results for both transforms and explicitly give the null space of R for a class of square integrable functions on the exterior of a ball in Rn as well as the null space of SM for square integrable functions on a ball. We show SM: L2(Rn) → L2(Rn) is one-one, and we characterize the range of SM on classes of smooth functions and square integrable functions by certain moment conditions. If g(x) is a Schwartz function on Rn that is zero to infinite order at x = 0, we prove moment conditions sufficient for g to be in the range of SM(C∞(Rn)). We apply our results on SM to existence and uniqueness theorems for solutions to a characteristic initial value problem for the Darboux partial differential equation. 相似文献