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1.
LiQiongXU WeiMinXUE 《数学学报(英文版)》2003,19(1):141-146
Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n
4 elements and these rings have five (2p+4) isomorphic classes for p = 2 (p ≠ 2).
This research is supported by the National Natural Science Foundation of China, and the Scientific Research Foundation for
“Bai-Qian-Wan” Project, Fujian Province of China 相似文献
2.
By the method of synthetic geometry, we define a seemingly new transformation of a three-dimensional projective space where
the corresponding points lie on the rays of the first order, nth class congruence C
n
1 and are conjugate with respect to a proper quadric Ψ. We prove that this transformation maps a straight line onto an n + 2 order space curve and a plane onto an n + 2 order surface which contains an n-ple (i.e. n-multiple) straight line. It is shown that in the Euclidean space the pedal surfaces of the congruences C
n
1 can be obtained by this transformation. The analytical approach enables new visualizations of the resulting curves and surfaces
with the program Mathematica. They are shown in four examples.
相似文献
3.
In this paper, we get W
1,p
(R
n
)-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and
Tananka’s results.
Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural
Science Foundation of China. 相似文献
4.
We obtain a generalization of the Pontryagin-Van Campen theorem to the case of locally compact topological n-groups. We also consider the convolutions of measures and the Fourier transform on locally compact topological n-groups. 相似文献
5.
In this paper we use the real differential geometric definition of a metric (a unimodular oriented metric) tt*-bundle of Cortés and the author (Topological-anti-topological fusion equations, pluriharmonic maps and special Kähler manifolds) to define a map Φ from the space of metric (unimodular oriented metric) tt*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to {GL}(r)/O(p,q) (respectively {SL}(r)/SO(p,q)), where (p,q) is the signature of the metric. In the sequel the image of the map Φ is characterized. It follows, that in signature (r,0) the image of Φ is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin (Comm. Math. Phys. 152 (1992; S539–S564). 相似文献
6.
V. K. Leont’ev 《Computational Mathematics and Mathematical Physics》2008,48(6):1063-1075
The structure of the faces of an n-dimensional cube is studied. Some combinatorial results describing the mutual arrangement and the metric characteristics of this structure are obtained. 相似文献
7.
This is a continuation of the paper [14]. It is shown that any finite subdirect product of exchange rings satisfying the n-stable range condition is still an exchange ring satisfying the n-stable range condition. Furthermore, we give necessary and sufficient conditions on matrices over an exchange ring R, under which R satisfies the n-stable range condition. This generalizes the corresponding results for unit-regular rings and the stable range one condition.2000 Mathematics Subject Classification: 19B10, 16E50This work was supported by the National Natural Science Foundation of China (Grant No. 19801012) and the Ministry of Education of China. 相似文献
8.
In this paper we extend the notion of n-weak amenability of a Banach algebra
when n ∈ ℕ. Technical calculations show that when
is Arens regular or an ideal in
**, then
* is an
(2n)-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ∕. 相似文献
9.
Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μ
s
is the unique Borel probability measure with support in A that minimizes
over all such probability measures. If A is strongly -rectifiable, then μ
s
converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below.
This research was supported, in part, by the U. S. National Science Foundation under grants DMS-0505756 and DMS-0808093. 相似文献
10.
Let F be a graph of order at most k. We prove that for any integer g there is a graph G of girth at least g and of maximum degree at most 5k13 such that G admits a surjective homomorphism c to F, and moreover, for any F-pointed graph H with at most k vertices, and for any homomorphism h from G to H there is a unique homomorphism f from F to H such that h=fc. As a consequence, we prove that if H is a projective graph of order k, then for any finite family of prescribed mappings from a set X to V(H) (with ||=t), there is a graph G of arbitrary large girth and of maximum degree at most 5k26mt (where m=|X|) such that and up to an automorphism of H, there are exactly t homomorphisms from G to H, each of which is an extension of an f.Supported in part by the National Science Council under grant NSC89-2115-M-110-012Final version received: June 9, 2003 相似文献
11.
Recently the first author presented exact formulas for the number of 2
n
-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity
and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2
n
-periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization
of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the
1-error linear complexity for p
n
-periodic sequences over prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p
n
-periodic sequences over .
相似文献
12.
Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ?Q, then p=∞. Denote by DGL n np , n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL n np . In this work we intend to answer the following two questions: Given an object (L(V), ?) in DGL n 3n+2 and denote by S(L(V), ?) the class of objects homotopy equivalent to (L(V), ?). How we can characterize a free dgl to belong to S(L(V), ?)? Fix an object (L(V), ?) in DGL n 3n+2 . How many homotopy equivalence classes of objects (L(W), δ) in DGL n 3n+2 such that H * (W, d′)?H * (V, d) are there? Note that DGL n 3n+2 is a subcategory of DGL n np when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl. 相似文献
13.
In this paper we study the L
p
-discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which
is also known as Roth net) with N points has L
p
-discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has L
p
-discrepancy (p an even integer) of order
which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L
2-discrepancy of digitally shifted Hammersley point sets which show that the value of the L
2-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position
of these.
This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305. 相似文献
14.
The j-function j(z) = q−1+ 744 + 196884q + ⋅s plays an important role in many problems. In [7], Zagier, presented an interesting series of functions obtained from the
j-function: jm(ζ) = (j(ζ) – 744)∨T0(m), where T0(m) is the usual m′th normalized weight 0 Hecke operator. In [3], Bruinier et al. show how this series of functions can be used to describe
all meromorphic modular forms on SL2(ℤ). In this note we use these functions and basic notions about modular forms to determine previously unidentified congruence
relations between the coefficients of Eisenstein series and the j-function.
2000 Mathematics Subject Classification: Primary–11B50, 11F03, 11F30
The author thanks the National Science Foundation for their generous support. 相似文献
15.
We determine the L
p
discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the L
p
discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound
on L
p
discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the
Hammersley point set and show that there always exist permutations such that the L
p
discrepancy of the generalized Hammersley point set is of best possible order. For the L
2 discrepancy such permutations are given explicitly.
F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research
Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献
16.
Alexander V. Isaev 《Geometric And Functional Analysis》2007,17(1):192-219
We obtain a complete classification of complex Kobayashihyperbolic manifolds of dimension n ≥ 2, for which the dimension of the group of holomorphic automorphisms is equal to n2.
Received: May 2005 Accepted: November 2005 相似文献
17.
By using hyperbolic virtual unit of Clifford algebra, the concept of n-dimensional space-time unit spheres is introduced. It is used as n-dimensional Minkowski space-time and Lorentz transformation. 相似文献
18.
Yin-Zhu Gao 《Czechoslovak Mathematical Journal》2007,57(4):1223-1237
In this paper LJ-spaces are introduced and studied. They are a common generalization of Lindelöf spaces and J-spaces researched by E. Michael. A space X is called an LJ-space if, whenever {A, B} is a closed cover of X with A ∩ B compact, then A or B is Lindelöf. Semi-strong LJ-spaces and strong LJ-spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors. 相似文献
19.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
20.
In this work we generalize the case of scalar curvature zero the results of Simmons (Ann. Math. 88 (1968), 62–105) for minimal cones in Rn+1. If Mn−1 is a compact hypersurface of the sphere Sn(1) we represent by C(M)ε the truncated cone based on M with center at the origin. It is easy to see that M has zero scalar curvature if and only if the cone base on M also has zero scalar curvature. Hounie and Leite (J. Differential Geom. 41 (1995), 247–258) recently gave the conditions for the ellipticity of the partial differential equation of the scalar curvature.
To show that, we have to assume n ⩾ 4 and the three-curvature of M to be different from zero. For such cones, we prove that, for n ≤slant 7 there is an ε for which the truncate cone C(M)ε is not stable. We also show that for n ⩾ 8 there exist compact, orientable hypersurfaces Mn−1 of the sphere with zero scalar curvature and S3 different from zero, for which all truncated cones based on M are stable.
Mathematics Subject Classifications (2000): 53C42, 53C40, 49F10, 57R70. 相似文献