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1.
The paper outlines why the spectrum of maximal ideals Spec ? A of a countable-dimensional differential ?-algebra A of transcendence degree 1 without zero divisors is locally analytic, which means that for any ?-homomorphism ψ M: A → ? (MSpec ? A) and any aA the Taylor series \(\widetilde {{\psi _M}}{\left( a \right)^{\underline{\underline {def}} }}\sum\limits_{m = 0}^\infty {\psi M\left( {{a^{\left( m \right)}}} \right)} \frac{{{z^m}}}{{m!}}\) has nonzero radius of convergence depending on the element aA.  相似文献   

2.
Forq an odd prime power, and 1<n<q, the Desarguesian planePG(2,q) does not contain an(nq–q+n,n)-arc.Supported by Italian M.U.R.S.T. (Research Group onStrutture geometriche, combinatoria, loro applicazioni) and G.N.S.A.G.A. of C.N.R.  相似文献   

3.

It was once conjectured that if is a uniform algebra on its maximal ideal space and if each point of is a peak point for , then . This peak point conjecture was disproved by Brian Cole in 1968. However, it was recently shown by Anderson and Izzo that the peak point conjecture does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. Although the corresponding assertion for smooth three-manifolds is false, we establish a peak point theorem for real-analytic three-manifolds with boundary.

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4.
We construct a monomorphism from the differential algebra k{x}/[x m ] to a Grassmann algebra endowed with a structure of differential algebra. Using this monomorphism, we prove the primality of k{x}/[x m ] and its algebra of differential polynomials, solve one of so-called Ritt problems related to this algebra, and give a new proof of the integrality of ideal [x m ].  相似文献   

5.
Of the five abelian groups of order 81, three are known not to contain a (81, 16, 3) difference set. We prove that the remaining two groups behave similarly. Consequently, two of the missing entries in Lander's table can be filled with a negative response.  相似文献   

6.
The existence of an almost nilpotent variety of linear algebras with noninteger exponent is proved. Examples of almost nilpotent varieties with integer exponents were only known so far.  相似文献   

7.
In the paper, we give the almost sure limiting behaviour of the increments of partial sums of a-mixing sequence when the moment generating functions do not exist. The results obtained are close to those for an independent sequence provided that the mixing coefficients tend to zero rapidly enough.The Project Supported by National Natural Science Foundation of China.  相似文献   

8.
Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds   总被引:3,自引:0,他引:3  
We completely classify three-dimensional homogeneous Lorentzian manifolds, equipped with Einstein-like metrics. Similarly to the Riemannian case (E. Abbena et al., Simon Stevin Quart J Pure Appl Math 66:173–182, 1992), if (M, g) is a three-dimensional homogeneous Lorentzian manifold, the Ricci tensor of (M, g) being cyclic-parallel (respectively, a Codazzi tensor) is related to natural reductivity (respectively, symmetry) of (M, g). However, some exceptional examples arise. The author is supported by funds of MURST, GNSAGA and the University of Lecce.  相似文献   

9.
This article deals with the activity of example generation as a special case of problem solving. We asked university students in the scientific-technological area to produce examples (which may exist or not) of mathematical objects fulfilling given requirements. For the analysis of students’ performances, we have developed a model that attempts to grasp the nature of the different stages in the solving process. The discussion of the findings allows us to outline specificities and educational potentialities of example generation activities.  相似文献   

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In this paper, we prove the three-dimensional C P E $CPE$ conjecture with nonnegative Ricci curvature. Moreover, we establish rigidity theorems for three-dimensional compact, oriented, connected V-static metrics with nonnegative Ricci curvature. Finally, we obtain classification results on three-dimensional vacuum static space and Miao–Tam critical metric with nonnegative Ricci curvature.  相似文献   

13.
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 4, pp. 93–101, July–August, 1990.  相似文献   

14.
The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least three admitting a conformal essential action of a Lie group locally isomorphic to \({{\mathrm{PSL}}}(2,\mathbf {R})\). It is established by using a general result on local isometries of real-analytic rigid geometric structures. As corollary, we deduce the same conclusion for conformal essential actions of connected semi-simple Lie groups on real-analytic compact Lorentz manifolds. This work is a contribution to the understanding of the Lorentzian version of a question asked by A. Lichnerowicz.  相似文献   

15.
The number α, 0≦α≦1, is a jump forr if for any positive ε and any integerm,mr, anyr-uniform hypergraph withn>n o (ε,m) vertices and at least (α+ε) \(\left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)\) edges contains a subgraph withm vertices and at least (α+c) \(\left( {\begin{array}{*{20}c} m \\ r \\ \end{array} } \right)\) edges, wherec=c(α) does not depend on ε andm. It follows from a theorem of Erdös, Stone and Simonovits that forr=2 every α is a jump. Erdös asked whether the same is true forr≧3. He offered $ 1000 for answering this question. In this paper we give a negative answer by showing that \(1 - \frac{1}{{l^{r - 1} }}\) is not a jump ifr≧3,l>2r.  相似文献   

16.
Suppose that a strongly regular graph Γ with parameters (v, k, λ, μ) has eigenvalues k, r, and s. If the graphs Γ and \(\bar \Gamma \) are connected, then the following inequalities, known as Krein’s conditions, hold: (i) (r + 1)(k + r + 2rs) ≤ (k + r)(s + 1)2 and (ii) (s + 1)(k + s + 2rs) ≤ (k + s)(r + 1)2. We say that Γ is a Krein graph if one of Krein’s conditions (i) and (ii) is an equality for this graph. A triangle-free Krein graph has parameters ((r 2 + 3r)2, r 3 + 3r 2 + r, 0, r 2 + r). We denote such a graph by Kre(r). It is known that, in the cases r = 1 and r = 2, the graphs Kre(r) exist and are unique; these are the Clebsch and Higman–Sims graphs, respectively. The latter was constructed in 1968 together with the Higman–Sims sporadic simple group. A.L. Gavrilyuk and A.A. Makhnev have proved that the graph Kre(3) does not exist. In this paper, it is proved that the graph Kre(4) (a strongly regular graph with parameters (784, 116, 0, 20)) does not exist either.  相似文献   

17.
Let C(X) be the algebra of all real-valued continuous functions on a completely regular Hausdorff space X, and C*(X) the subalgebra of bounded functions. We prove that for any intermediate algebra A between C*(X) and C(X), other than C*(X), there exists a smaller intermediate algebra with the same real maximal ideals as in A. The space X is called A-compact if any real maximal ideal in A corresponds to a point in X. It follows that, for a noncompact space X, there does not exist any minimal intermediate algebra A for which A is A-compact. This completes the answer to a question raised by Redlin and Watson in 1987.  相似文献   

18.
We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on simplicial trees. This implies that their Gromov boundaries, defined at density less than \frac12{\frac{1}{2}} , are Menger curves.  相似文献   

19.
This paper presents an investigation of convex surfaces with definite metrics in E3in(2;1) and of the question of imbedding definite metrics in the form of convex surfaces.Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 8, pp. 257–277, 1977.The author profoundly thanks É. G. Poznyak and I. Kh. Sabitov for help.  相似文献   

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