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1.
On a bounded C
2-domain
we consider the singular boundary-value problem 1/2u=f(u) in D, u
D
=, where d3, f:(0,)(0,) is a locally Hölder continuous function such that f(u) as u0 at the rate u
–, for some (0,1), and is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in
. Such solutions are shown to satisfy a boundary Harnack principle. 相似文献
2.
Markku Kaikkonen 《Designs, Codes and Cryptography》1998,15(2):183-186
It is shown that A(22,10) 50, A(23,10) 76, A(25,10) 166, A(26,10) 270, A(29,10) 1460, and A(28,12) 178, where A(n,d) denotes the maximum cardinality of a binary code of length n and minimum Hamming distance d. The constructed codes are invariant under permutations of some affine (or closely related) permutation group and have been found using computer search. 相似文献
3.
Consider a classical cusp eigenform f=
n=1
a
n
(f)q
n
of weight k2 for 0(N) with a Dirichlet character mod N, and let L
f
(s,)=
n=1
(n)a
n
(f)n
-s
denote the L-function of f twisted with an arbitrary Dirichlet character . For a prime number p5, consider a family of cusp eigenforms f
(k) of weight k
, k
{f
(k)=
n=1
a
n
(f
(k))q
n
} containing f=f
(k), such that the Fourier coefficients a
n
(f
(k)) are given by certain p-adic analytic functions k
a
n
(f
(k)). The purpose of this paper is to construct a two variable p-adic L function attached to Colemans family {f
(k)} of cusp eigenforms of a fixed positive slope =v
p
(
p
)>0 where
p
=
p
(k
) is an eigenvalue (which depends on k
) of the Atkin operator U=U
p
. Our p-adic L-function interpolates the special values L
f(k)(s,) at points (s,k
) with s=1,2,...,k
-1. We give a construction using the Rankin-Selberg method and the theory of p-adic integration on a profinite group Y with values in an affinoid K-algebra A, where K is a fixed finite extension of Q
p
.
Our p-adic L-functions are p-adic Mellin transforms of certain A-valued measures. In their turn, such measures come from Eisenstein distributions with values in certain Banach A-modules M
=M
(N;A) of families of overconvergent forms over A. To Robert Alexander Rankin in memoriam 相似文献
4.
Based on the construction of infinite-dimensional balanced realizations,an alternative solution to the following inverse spectral problemis presented. Given a decreasing sequence of positive numbers(n)n>1 (i.e. 123...0), does there exist a Hankel operatorwhose sequance of singular values is (n)n>1? This paper isan extension of a previously published paper in which the sameapproach was taken in the case of a monotonically decreasingsequence(n)n>1. 相似文献
5.
Gratiane Ennadifi 《Extremes》1999,2(2):201-217
Let {Yn:n0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(t):t0} be a point process. In this paper, making use of strong invariance principles, we establish limit laws for the paced record process {X(t):t0} based on {Yn:n0} and {N(t):t0}. We consider as applications of our main results, the case of the classical and paced record models. We conclude by extensions of our theorems to non-homogeneous record processes. 相似文献
6.
In this paper, we prove the following theorems. (i) Let G bea graph of minimum degree 5. If G is embeddable in a surface and satisfies (5)|V(G)|+6()0, then G is edge reconstructible.(ii) Any graph of minimum degree 4 that triangulates a surfaceis edge reconstructible. (iii) Any graph which triangulatesa surface of characteristic 0 is edge reconstructible. 相似文献
7.
The conjecture stated in an earlier paper by the author thatthere is a constant (independent from both n and k) such that nd1 holds for everyn 2 and d 2, where is the length of the longest snake (cycle without chords) in the Cartesianproduct of d copies of thecomplete graph Kn, is proved. 相似文献
8.
Paola Biondi 《Geometriae Dedicata》1998,71(3):327-333
A property is given which characterizes the ovoids and the nonsingular ruled quadrics among the nonsingular Tallini sets in PG (d,n), d 2 and n 4. 相似文献
9.
For each n 4 there exists a finite 2-group Gn such that itsnth dimension subgroup does not coincide with its nth lowercentral subgroup. This settles the dimension subgroup conjecturenegatively for all n4. 相似文献
10.
The paper shows that any graph G with the maximum degree (G) 8, which is embeddable in a surface of Euler characteristic() 0, is totally ((G)+2)-colorable. In general, it is shownthat any graph G which is embeddable in a surface and satisfiesthe maximum degree (G) (20/9) (3())+1 is totally ((G)+2)-colorable. 相似文献
11.
In this article, we study holomorphic vector fields transverseto the boundary of a polydisc in n, n 3. We prove that, undera suitable hypothesis of transversality with the boundary ofthe polydisc, the foliation is the pull-back of a linear hyperbolicfoliation via a locally injective holomorphic map. This is then 3 version for one-dimensional foliations of a previous resultproved for n = 2 by Brunella and Sad and for codimension-onefoliations by Ito and Scárdua. 相似文献
12.
Mohammed-Larbi Labbi 《Annals of Global Analysis and Geometry》1997,15(4):299-312
We establish the stability of the class of manifolds with positive p-curvature under surgeries in codimension p + 3. As a consequence of this result, we first obtain the classification of compact 2-connected manifolds of dimension 7 with positive Einstein tensor; and secondly the existence of metrics with positive Einstein tensor on any compact, simply connected, non-spin manifold of dimension 7 whose second homotopy group is isomorphic to Z2. 相似文献
13.
14.
We show that the direct product conjecture for n(G; ), whereG is the direct product of two groups of type FPn, holds forn = 3 and give counterexamples for n 4. Previously, counter-exampleswere known only for a related conjecture involving the homotopical-invariants, where the conjecture already fails for n 3. 相似文献
15.
There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues 12
n
if and only if, 1 +
n
0, 2 +
n-10,...,
m
+
n - m + 10,
m + 10,...,
n - m
0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph 相似文献
16.
Noboru Hamada 《Graphs and Combinatorics》1989,5(1):63-81
In this paper, we shall characterize all {(q + 1) + 2, 1;t, q}-min · hypers and all {2(q + 1) + 2, 2; 2,q}-min · hypers for any integert 2 and any prime powerq 3. In the next paper [8], we shall characterize all {2(q + 1) + 2, 2;t, q}-min · hypers for any integert 3 and any prime powerq 5 using the results in this paper. 相似文献
17.
André Raspaud 《Discrete Mathematics》2009,309(18):5678-1005
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number of the graph G is the smallest number of colors in a linear coloring of G. In this paper we prove that every planar graph G with girth g and maximum degree Δ has if G satisfies one of the following four conditions: (1) g≥13 and Δ≥3; (2) g≥11 and Δ≥5; (3) g≥9 and Δ≥7; (4) g≥7 and Δ≥13. Moreover, we give better upper bounds of linear chromatic number for planar graphs with girth 5 or 6. 相似文献
18.
The binding number of a graph and its triangle 总被引:2,自引:0,他引:2
Shi Ronghua 《应用数学学报(英文版)》1985,2(1):79-86
In this paper we prove the following conjecture of Woodall[1]: if bind (G)3/2, thenG contains a triangle. Moreover we also prove that if bind (G)3/2, then each vertex is contained in a 4-cycle, each edge is contained in a 5-cycle whenV(G)11, and there exists a 6-cycle inG. 相似文献
19.
A famous Diophantine equation is given by yk=(x+1)(x+2)...(x+m). (1) For integers k2 and m2, this equation only has the solutionsx = j (j = 1, ..., m), y = 0 by a remarkable result ofErds and Selfridge [9] in 1975. This put an end to the old questionof whether the product of consecutive positive integers couldever be a perfect power (except for the obviously trivial cases).In a letter to D. Bernoulli in 1724, Goldbach (see [7, p. 679])showed that (1) has no solution with x0 in the case k = 2 andm = 3. In 1857, Liouville [18] derived from Bertrand's postulatethat for general k2 and m2, there is no solution with x0 ifone of the factors on the right-hand side of (1) is prime. Byuse of the ThueSiegel theorem, Erds and Siegel [10] provedin 1940 that (1) has only trivial solutions for all sufficientlylarge kk0 and all m. This was closely related to Siegel's earlierresult [30] from 1929 that the superelliptic equation yk=f(x) has at most finitely many integer solutions x, y under appropriateconditions on the polynomial f(x). The ineffectiveness of k0was overcome by Baker's method [1] in 1969 (see also [2]). In 1955, Erds [8] managed to re-prove the result jointly obtainedwith Siegel by elementary methods. A refinement of Erds' ideasfinally led to the above-mentioned theorem as follows. 相似文献
20.
On the Compactness and Approximation Numbers of Hardy-Type Integral Operators in Lorentz Spaces 总被引:1,自引:0,他引:1
We characterize the mapping properties such as the boundedness,compactness and measure of noncompactness for those real weightfunctions , , u0, v0, for which the Hardy-type integral operatorof the form
acts from to , when the parameters are restricted to the range 1 < max (r,s) min (p, q) < and the kernel k(x, y) 0 satisfies theOinarov condition (see (2) below). For the case k(x, y) = 1,we obtain lower and upper estimates of the approximation numbers,extending the result of [5]. 相似文献