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1.
Yasutsugu Fujita 《Periodica Mathematica Hungarica》2009,59(1):81-98
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k
2, k
2 + 1, 4k
2 + 1, d} is a D(−k
2)-quadruple, then d = 1, and that if {k
2 − 1, k
2, 4k
2 − 1, d} is a D(k
2)-quadruple, then d = 8k
2(2k
2 − 1). 相似文献
2.
Antonio Cossidente 《Designs, Codes and Cryptography》2010,54(1):1-9
We will show that associated with the classical 1-system of the elliptic quadric Q
−(7, q) are certain infinite families of two-character sets with respect to hyperplanes, and partial ovoids of Q
+(15, q). 相似文献
3.
The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G has a unique nonabelian composition factor isomorphic to F
4(q). We also show that if G is a finite group satisfying |G| = |F
4(q)| and Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G @ F4(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F
4(q) where q = 2
n
> 2. 相似文献
4.
We prove that if a symmetric submarkovian semigroup (T
t
)
t>0
satisfies an estimate of the form
where ϕ is an increasing C
1
-diffeomorphism of [0,+∞) with subexponential growth, then a suitable function of its infinitesimal generator is bounded from
L
p
(M) to L
q
(M) for 1<p<q<+∞, and that a weak converse holds true if p=2. In the special case where ϕ(t)=Ct
μ
for small t and ϕ(t)=C′ exp(ct
ν
) for large t, μ>0, c>0, 0<ν<1, one obtains a sharp and explicit result, which applies for instance to sublaplacians on solvable unimodular Lie
groups with exponential growth.
Received: 29 June 2001 /
Published online: 1 April 2003
Mathematics Subject Classifications (2000): 47D06, 58J35, 43A80
Research supported by the Italian M.U.R.S.T., fondi 60%, the Italian GNAFA, and the European Commission (European TMR Network
``Harmonic Analysis' 1998–2001, Contract ERBFMRX-CT97-0159). 相似文献
5.
Alexander A. Davydov Stefano Marcugini Fernanda Pambianco 《Designs, Codes and Cryptography》2009,50(3):359-372
An infinite family of complete (q
2 + q + 8)/2-caps is constructed in PG(3, q) where q is an odd prime ≡ 2 (mod 3), q ≥ 11. This yields a new lower bound on the second largest size of complete caps. A variant of our construction also produces
one of the two previously known complete 20-caps in PG(3, 5). The associated code weight distribution and other combinatorial properties of the new (q
2 + q + 8)/2-caps and the 20-cap in PG(3, 5) are investigated. The updated table of the known sizes of the complete caps in PG(3, q) is given. As a byproduct, we have found that the unique complete 14-arc in PG(2, 17) contains 10 points on a conic. Actually, this shows that an earlier general result dating back to the Seventies fails
for q = 17.
相似文献
6.
Maks A. Akivis Vladislav V. Goldberg Valentin V. Lychagin 《Selecta Mathematica, New Series》2004,10(4):431-451
We find d – 2 relative differential invariants for a d-web, d 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g4(x, y),..., gd(x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g4, and d – 4 PDEs of the second order with respect to f and g4,..., gd. For d = 4, this result confirms Blaschkes conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage. 相似文献
7.
Giuseppe Borrelli 《manuscripta mathematica》2009,130(4):523-531
We prove that if the bicanonical map of a minimal surface of general type S with p
g
= q = 1 and KS2=8{K_{S}^2=8} is nonbirational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification
of minimal surfaces of general type with pg=q=1, KS2=8{p_{g}=q=1, K_{S}^2=8} and nonbirational bicanonical map. 相似文献
8.
Carlos Rito 《Geometriae Dedicata》2012,157(1):319-330
We study surfaces of general type S with p
g
= 0 and K
2 = 3 having an involution i such that the bicanonical map of S is not composed with i. It is shown that, if S/i is not rational, then S/i is birational to an Enriques surface or it has Kodaira dimension 1 and the possibilities for the ramification divisor of
the covering map S → S/i are described. We also show that these two cases do occur, providing an example. In this example S has a hyperelliptic fibration of genus 3 and the bicanonical map of S is of degree 2 onto a rational surface. 相似文献
9.
William D. Banks 《Monatshefte für Mathematik》2012,75(1):157-163
Let φ be the Euler function. Fix , and let be an arbitrary set of primes of positive lower natural density. Using a variant of the Alford–Granville–Pomerance construction, we show that there are infinitely many Carmichael numbers N with a totient of the form , where and is a nonempty product of primes from the set . In particular, for any fixed natural number n, there are infinitely many Carmichael numbers N such that φ(N) = a 2 + nb 2 for some positive integers a and b. 相似文献
10.
Romain Tessera 《Monatshefte für Mathematik》2011,61(4):115-118
The Schur algebra is the algebra of operators which are bounded on ℓ
1 and on ℓ
∞. In this note, we exhibit an element of the group algebra of the free group with two generators, which, as a convolution
operator, is invertible in ℓ
2, and whose inverse is not bounded on ℓ
1 nor on ℓ
∞. In particular, this shows that the Schur algebra is not inverse-closed. 相似文献
11.
X. J. Long 《Journal of Optimization Theory and Applications》2011,148(1):197-208
The purpose of this paper is to consider a class of nondifferentiable multiobjective fractional programming problems in which
every component of the objective function contains a term involving the support function of a compact convex set. Based on
the (C,α,ρ,d)-convexity, sufficient optimality conditions and duality results for weakly efficient solutions of the nondifferentiable
multiobjective fractional programming problem are established. The results extend and improve the corresponding results in
the literature. 相似文献
12.
V. Yu. Gubarev 《Siberian Mathematical Journal》2009,50(3):395-404
We take the exterior power ℝ4 ∧ ℝ4 of the space ℝ4, its mth symmetric power V = S
m
(∧2ℝ4) = (ℝ4 ∧ ℝ4) ∨ (ℝ4 ∧ ℝ4) ∨ ... ∨(ℝ4 ∧ ℝ4), and put V
0 = L((x ∧ y)∨ ... ∨(x ∧ y): x, y ∈ ℝ4). We find the dimension of V
0 and an algorithm for distinguishing a basis for V
0 efficiently. This problem arose in vector tomography for the purpose of reconstructing the solenoidal part of a symmetric
tensor field.
Original Russian Text Copyright ? 2009 Gubarev V. Yu.
The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant
NSh-344.2008.1).
__________
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 3, pp. 503–514, May–June, 2009. 相似文献
13.
Jeff Edmonds 《Discrete and Computational Geometry》2008,39(4):747-765
We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair
within a set of n points) into ℝ2 Cartesian space preserving their l
∞ (or l
1) metric distances. Its expected time is
(i.e., within a poly-log of the size of the input) beating the previous
algorithm. In contrast, we prove that detecting l
∞3 embeddings is NP-complete. The problem is also NP-complete within l
12 or l
∞2 with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are
curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded
in l
∞3; however, it can be embedded if any single point is removed.
This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper. 相似文献
14.
设U≥0表示一个固定单李代数的半量子群,给出了U≥0的性质和表示. 证明了Hopf代数U≥0不是拟余交换的,因此左U≥0模范畴不是辫子monoidal范畴. 在权模范畴W中,给出了所有单对象和投射对象. 最后描述了所有单的Yetter-Drinfel'd U≥0权模. 相似文献
15.
本文研究亚纯函数的值分布问题.利用值分布理论,获得了一个带精简密指量的模分布的不等式,改进了Xu和Yang等人的结果. 相似文献
16.
Jimmy Petean 《Geometriae Dedicata》2009,143(1):37-48
We study isoperimetric regions on Riemannian manifolds of the form (M
n
× (0, π), sin2(t)g + dt
2) where g is a metric of positive Ricci curvature ≥ n − 1. When g is an Einstein metric we use this to compute the Yamabe constant of
(M ×\mathbbR, g+ dt2 ){(M \times \mathbb{R}, g+ dt^2 )} and so to obtain lower bounds for the Yamabe invariant of M × S
1. 相似文献
17.
B. de Malafosse 《Acta Mathematica Hungarica》2009,122(3):217-230
We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between
s
h,l
(λ, μ) = s
α
0((Δ − λI)
h
) + s
β
(c)((Δ − μI)
l
) and s
γ
. Among other things the aim of this paper is to reduce the set (s
h,l
(λ, μ), s
γ
to a set of the form S
τ,γ
.
相似文献
18.
Samuel A. Ilori 《K-Theory》1989,2(5):623-624
We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO
–i
groups of G
3(
n
), n odd, are related to the known torsion of the KO
–i
groups of G2(
n
). 相似文献
19.
M. H. M. Rashid 《Ukrainian Mathematical Journal》2012,63(8):1256-1267
If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum
of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations
by finite-rank operators. 相似文献
20.
We consider the projective line over the finite quotient ring R⋄ ≡ GF(2)[x]/〈x
3 − x〉. The line is endowed with 18 points, spanning the neighborhoods of three pairwise distant points. Because R⋄ is not a local ring, the neighbor (or parallel) relation is not an equivalence relation, and the sets of neighbors for two
distant points hence overlap. There are nine neighbors of any point on the line, forming three disjoint families under the
reduction modulo either of the two maximal ideals of the ring. Two of the families contain four points each, and they swap
their roles when switching from one ideal to the other, the points in one family merging with (the image of) the point in
question and the points in the other family passing in pairs into the remaining two points of the associated ordinary projective
line of order two. The single point in the remaining family passes to the reference point under both maps, and its existence
stems from a nontrivial character of the Jacobson radical
of the ring. The quotient ring
is isomorphic to GF(2) ⊗ GF(2). The projective line over
features nine points, each of them surrounded by four neighbors and four distant points, and any two distant points share
two neighbors. We surmise that these remarkable ring geometries are relevant for modeling entangled qubit states, which we
will discuss in detail in Part II of this paper.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 44–53, April, 2007. 相似文献