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1.
Amiram Braun 《Israel Journal of Mathematics》1986,55(3):345-349
An example is given of a ringR (with 1) satisfying the standard identityS
6[x
1, ...,x
6] butM
2(R), the 2 × 2 matrix ring overR, does not satisfyS
12[x
1, ...,x
12]. This is in contrast to the caseR=M
n (F),F a field, where by the Amitsur-Levitzki theoremR satisfiesS
2n [x
1, ...,x
2n] andM
2(R) satisfiesS
4n
[x
1, ...,x
n].
Part of this work was done while the author enjoyed the hospitality of the University of California at San Diego, the University
of Texas at Austin and the University of Washington at Seattle. 相似文献
2.
Els Bergen Esther Ramakers Luc Vrancken 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):139-157
In this paper we prove the Magid-Ryan conjecture for 4-dimensional affine hyperspheres in R5. This conjecture states that every affine hypersphere with non-zero Pick invariant and constant sectional curvature is affinely
equivalent with either (x
1
2
±x
2
2
)(x
3
2
±x
4
2
...(x
2m−1
2
±x
2m
2
) = 1 or (x
1
2
±x
2
2
(x
3
2
±x
4
2
)...(x
2m−1
2
±x
2m
2
)x
2m+1 = 1 where the dimensionn satisfiesn = 2m orn =2m + 1. This conjecture was proved in [11] in case the metric is positive definite and in [2] in case the metric is Lorentzian. 相似文献
3.
If X is a geodesic metric space and x
1,x
2,x
3 ∈ X, a geodesic triangle
T = {x
1,x
2,x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. $\delta(X)=\inf\{\delta\ge 0: \, X \, \text{ is $\delta(X)=\inf\{\delta\ge 0: \, X \, \text{ is In this paper we relate the hyperbolicity constant of a graph with some known parameters of the graph, as its independence
number, its maximum and minimum degree and its domination number. Furthermore, we compute explicitly the hyperbolicity constant
of some class of product graphs. 相似文献
4.
Zhensheng Lin Jianqing Chen Xiuli Tang 《Mathematical Methods in the Applied Sciences》2020,43(10):6200-6222
We consider some p-Laplacian type equations with sum of nonlocal term and subcritical nonlinearities. We prove the existence of the ground states, which are positive. Because of including p=2, these results extend the results of Li, Ma and Zhang [Nonlinear Analysis: Real World Application 45(2019) 1-25]. When p=2, N=3, by a variant variational identity and a constraint set, we can prove the existence of a non-radially symmetric solution. Moreover, this solution u(x1, x2, x3) is radially symmetric with respect to (x1, x2) and odd with respect to x3. 相似文献
5.
Stephanos Venakides 《纯数学与应用数学通讯》1985,38(2):125-155
The inverse scattering method is used to determine the distribution limit as ? → 0 of the solution u(x, t, ?) of the initial value problem. Ut ? 6uux + ?2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ? 0 has been solved by Peter D. Lax and C. David Levermore [8], [9], [10]. The computation of the distribution limit of u(x, t, ?) as ? → 0 is reduced to a quadratic maximization problem, which is then solved. 相似文献
6.
John F. Gately 《代数通讯》2013,41(7):3137-3153
Let R k[x 1,x 2,x 3] be a 3-dimensional polynomial ring over a field k.We show that no non-trivial relations exist among *-products of complete one-fibered (x 1,x 2,x 3)-primary monomial ideals. This is connected with questions about how Zariski's work on the unique factorization of complete ideals in regular local rings of dimension two might be generalized to higher dimensions. 相似文献
7.
Let f be an arithmetical function and S={x 1,x 2,…,xn } a set of distinct positive integers. Denote by [f(xi ,xj }] the n×n matrix having f evaluated at the greatest common divisor (xi ,xj ) of xi , and xj as its i j-entry. We will determine conditions on f that will guarantee the matrix [f(xi ,xj )] is positive definite and, in fact, has properties similar to the greatest common divisor (GCD) matrix [(xi ,xj )] where f is the identity function. The set S is gcd-closed if (xi ,xj )∈S for 1≤ i j ≤ n. If S is gcd-closed, we calculate the determinant and (if it is invertible) the inverse of the matrix [f(xi ,xj )]. Among the examples of determinants of this kind are H. J. S. Smith's determinant det[(i,j)]. 相似文献
8.
Following I. Volichenko we study varieties of Lie algebras over a field of characteristic zero, satisfying the identity [[x 1,x 2,x 3], [x 4 x 5 x 6]] = 0. We prove that the exponential growth of any proper subvariety is a positive integer and any positive integer can be so realized. 相似文献
9.
In this paper we study the set of x ∈ [0, 1] for which the inequality |x − x
n
| < z
n
holds for infinitely many n = 1, 2, .... Here x
n
∈ [0, 1) and z
n
s> 0, z
n
→ 0, are sequences. In the first part of the paper we summarize known results. In the second part, using the theory of distribution
functions of sequences, we find the asymptotic density of n for which |x − x
n
| < z
n
, where x is a discontinuity point of some distribution function of x
n
. Generally, we also prove, for an arbitrary sequence x
n
, that there exists z
n
such that the density of n = 1, 2, ..., x
n
→ x, is the same as the density of n = 1, 2, ..., |x − x
n
| < z
n
, for x ∈ [0, 1]. Finally we prove, using the longest gap d
n
in the finite sequence x
1, x
2, ..., x
n
, that if d
n
≤ z
n
for all n, z
n
→ 0, and z
n
is non-increasing, then |x − x
n
| < z
n
holds for infinitely many n and for almost all x ∈ [0, 1]. 相似文献
10.
Mi Hee Park 《代数通讯》2013,41(10):4464-4480
Let T be an integral domain with a maximal ideal M, ?: T → K: = T/M the natural surjection, and R the pullback ??1(D), where D is a proper subring of K. We give necessary and sufficient conditions for the mixed extensions R[x 1]]…[x n ]] to be catenarian, where each [x i ]] is fixed as either [x i ] or [[x i ]]. We also give a complete answer to the question of determining the field extensions k ? K such that the contraction map Spec(K[x 1]]…[x n ]]) → Spec(k[x 1]]…[x n ]]) is a homeomorphism. As an application, we characterize the globalized pseudo-valuation domains R such that R[x 1]]…[x n ]] is catenarian. 相似文献
11.
P. M. Prenter 《Numerische Mathematik》1971,18(3):243-253
Leta=x
0<x
1<...<x
N
=b be a partition of the interval [a, b] and letL be a normalm-th order linear differential operator. The purpose of this note is to point out that spline functions in one variable need not be excluded to piecewise fits of functions belonging to the null spaceN(L
*
L) on each closed subinterval [x
i,x
i+1], 0in-1 but may be extended to piecewise fits of functions belonging toN(L
i
*
L
i) on each subinterval [x
i,x
i+1] provided theL
i's are selected from a uniformly bounded family of normal linear differential operators. Furthermore when theL
i's are so selected one obtains the usual integral relations and error estimates obtained for splines [2, 8 and 9] including the extended error estimates obtained by Swartz and Varga [10]. 相似文献
12.
In TheE(2,A) sections of SL(2,A) (Ann. of Math. 134 (1991), 159–188), we locate the E(A) normalized subgroups of SL(2,A) in central sections of SL(2,A) for all subrings of Q and all commutative rings satisfying SR
2
In solving this problem we introduced the notion of radix (see (1.1)) and the group C(Px) = [E(2,A),E(2,A;Px)] = [SL(2,A), SL(2,A;Px)] for the rings considered here.The purpose of this paper is to determine SL(2,A;PxC(Px) for SR
2 rings and number rings with infinitely many units.In Section 2, Mennicke symbols for Jordan ideals are defined. They are determined for number rings and shown to be connected to power residue symbols in a delicate way. This extends the work of Bass, Milnor and Serre.In Section 3, an explicit homomorphism from E(2,Al;Px) into an additive section of A is given for all commutative rings A. If A satisfiesSR
2 the kernel of this map is C(Px.The main problem for number rings is solved by giving an explicit homomorphism on SL(2,A;Px) whose kernel is C(Px). 相似文献
13.
Gustaf Söderlind 《BIT Numerical Mathematics》1984,24(3):391-393
We derive an error bound for fixed-point iterationsx
n+1=f(x
n
) by using monotonicity in the sense of [2]. The new bound is preferable to the classical one which bounds the error in terms of the Lipschitz constant off. 相似文献
14.
Junior Michel José M. Rodríguez José M. Sigarreta María Villeta 《Proceedings Mathematical Sciences》2010,120(5):593-609
If X is a geodesic metric space and x
1, x
2, x
3 ∈ X, a geodesic triangle T = {x
1, x
2, x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X) = inf{δ ≥ 0: X is δ-hyperbolic}. In this paper we characterize the product graphs G
1 × G
2 which are hyperbolic, in terms of G
1 and G
2: the product graph G
1 × G
2 is hyperbolic if and only if G
1 is hyperbolic and G
2 is bounded or G
2 is hyperbolic and G
1 is bounded. We also prove some sharp relations between the hyperbolicity constant of G
1 × G
2, δ(G
1), δ(G
2) and the diameters of G
1 and G
2 (and we find families of graphs for which the inequalities are attained). Furthermore, we obtain the precise value of the
hyperbolicity constant for many product graphs. 相似文献
15.
This paper calculates the Hochschild homology of fatpoints—rings of the formk[x
1,x
2,…,x
d
]/m
a
wherek is a field of characteristic zero and m=(x
1
x
2,…,x
d
). The calculation includes the multiplicative structure induced by the shuffle product. The answer is given in terms of the
homology of tori relative to theira-diagonal. Since the rings in question are monoidal, this calculation also determines their topological Hochschild homology.
By a theorem of Goodwillie, the dimensions of the cyclic homology groups of these rings are determined as well. 相似文献
16.
Domingo Pestana José M. Rodríguez José M. Sigarreta María Villeta 《Central European Journal of Mathematics》2012,10(3):1141-1151
If X is a geodesic metric space and x
1; x
2; x
3 ∈ X, a geodesic triangle T = {x
1; x
2; x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of
degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs. 相似文献
17.
V. A. Roman’kov 《Siberian Mathematical Journal》2011,52(2):348-351
We solve Problems 17.82 and 17.86(b) posed by Mikhailov in the Kourovka Notebook [1]. Namely, we construct: (1) an example
of a finitely presented group H in which the intersection H
(ω) of all terms of the derived series is distinct from its commutant; (2) an example of a balanced presentation 〈x
1, x
2, x
3|r
1, r
2, r
3〉 of the trivial group for which F(x
1, x
2, x
3)/[R
1,R
2] is not a residually soluble group (here R
i
(i = 1, 2) denotes the normal closure of r
i
in F(x
1, x
2, x
3)). The construction of the second example is related to some approach to the Whitehead asphericity conjecture. 相似文献
18.
O. E. Lev 《Journal of Optimization Theory and Applications》1977,22(1):31-34
A decomposition method, used in least-weight plastic design, is extended to solve problems with nonlinearity arising from variable structure geometry. The problem considered is that of finding vectorsx
1,x
2, andq that minimize [l max{|x
1|, |x
2|}], subject toAx
1=b
1 andAx
2=b
2, where both the vectorl and the matrixA are nonlinear functions ofq. 相似文献
19.
Andrés del Junco 《Israel Journal of Mathematics》1983,44(2):160-188
LetT
α be the translationx↦x+α (mod 1) of [0, 1), α irrational. LetT be the Lebesgue measure-preserving automorphism ofX=[0, 3/2) defined byTx = x + 1 forx∈[0, 1/2),Tx=T
α(x−1) forx∈[1,3/2) andTx = T
α
x forx∈[1/2, 1), i.e.T isT
α with a tower of height one built over [0, 1/2). If α is poorly approximable by rationals (there does not exist {p
n
/q
n
} with |α−p
n
/q
n
|=o(q
n
−2)) and λ is a measure onX
k
all of whose one-dimensional marginals are Lebesgue and which is ⊗
i − 1
k
T
1 invariant and ergodic (l>0) then λ is a product of off-diagonal measures. This property suffices for many purposes of counterexample construction.
A connection is established with the POD (proximal orbit dense) condition in topological dynamics.
Research supported in part by NSF contract MCS-8003038. 相似文献
20.
For systems of second-order nonlinear ordinary differential equations with the Dirichlet boundary conditions, we develop generalized
three-point difference schemes of high-order accuracy on a nonuniform grid. The construction of the suggested schemes requires
solving four auxiliary Cauchy problems (two problems for systems of nonlinear ordinary differential equations and two problems
for matrix linear ordinary differential equations) on the intervals [x
j−1, x
j
] (forward) and [x
j
, x
j+1] (backward) at each grid point; this is done at each step by any single-step method of accuracy order $
\bar m
$
\bar m
= 2[(m+1)/2]. (Here m is a given positive integer, and [·] is the integer part of a number.) We prove that such three-point difference schemes
have the accuracy order $
\bar m
$
\bar m
for the approximation to both the solution u of the boundary value problem and the flux K(x)d
u/dx at the grid points. 相似文献