共查询到20条相似文献,搜索用时 46 毫秒
1.
Marcello Lucia 《Calculus of Variations and Partial Differential Equations》2006,26(3):313-330
We consider the equation
If Ω is of class C
2, we show that this problem has a non-trivial solution u
λ for each λ ∊ (8 π, λ*). The value λ* depends on the domain and is bounded from below by 2 j
0
2 π, where j
0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j
0
2 π > 8 π). Moreover, the family of solution u
λ blows-up as λ → 8 π. 相似文献
2.
Feng-Yu Wang 《Potential Analysis》2008,28(4):321-334
For μ: = e
V(x)dx a probability measure on a complete connected Riemannian manifold, we establish a correspondence between the Entropy-Information
inequality and the transportation-cost inequality for μ(f
2) = 1, where Φ and Ψ are increasing functions. Moreover, under the curvature–dimension condition, a Sobolev type HWI (entropy-cost-information)
inequality is established. As applications, explicit estimates are obtained for the Sobolev constant and the diameter of a
compact manifold, which either extend or improve some corresponding known results.
Supported in part by NNSFC(10721091) and the 973-project in China. 相似文献
3.
C.-S. Lin 《Proceedings of the American Mathematical Society》2001,129(3):855-859
Two of the most useful inequality formulas for bounded linear operators on a Hilbert space are the Löwner-Heinz and Reid's inequalities. The first inequality was generalized by Furuta (so called the Furuta inequality in the literature). We shall generalize the second one and obtain its related results. It is shown that these two generalized fundamental inequalities are all equivalent to one another.
4.
Jian Wang 《数学学报(英文版)》2012,28(2):357-370
Criteria for the super-Poincaré inequality and the weak-Poincaré inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p. 15) of Prof. Mu-Fa Chen's book "Eigenvalues, Inequalities and Ergodic Theory" (Springer, London, 2005). As a byproduct, we conclude that only ergodic birth-death processes on finite state space satisfy the Nash inequality with index 0 ν≤ 2. 相似文献
5.
LetP be the convex hull of perfect matchings of a graphG=(V, E). The dominant ofP is {y∈R
E
∶y≥x for somex∈P}. A theorem of Fulkerson implies that, ifG is bipartite, then the dominant ofP can be described by linear inequalities having {0, 1}-valued coefficients. However, this is far from true in general. Here
it is proved that, for every positive integern, there exists a graph for which the dominant has an essential valid inequality whose coefficient-set includes the firstn positive integers. A similar result holds for the submissive ofP, {y∈R
E
∶0≤y≤x for somex∈P}.
Research partially supported by a grant from NSERC of Canada. 相似文献
6.
Charles J. Colbourn 《Mathematica Slovaca》2009,59(1):77-108
It has been shown that the number of occurrences of any ℓ-line configuration in a Steiner triple system can be written as
a linear combination of the numbers of full m-line configurations for 1 ≤ m ≤ ℓ; full means that every point has degree at least two. More precisely, the coefficients of the linear combination are
ratios of polynomials in v, the order of the Steiner triple system. Moreover, the counts of full configurations, together with v, form a linear basis for all of the configuration counts when ℓ ≤ 7. By relaxing the linear integer equalities to fractional
inequalities, a configuration polytope is defined that captures all feasible assignments of counts to the full configurations.
An effective procedure for determining this polytope is developed and applied when ℓ = 6. Using this, minimum and maximum
counts of each configuration are examined, and consequences for the simultaneous avoidance of sets of configurations explored.
To Alex Rosa on the Occasion of his Seventieth Birthday 相似文献
7.
William D. Banks Derrick N. Hart Pieter Moree C. Wesley Nevans 《Monatshefte für Mathematik》2009,157(4):303-322
In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality σ(n) < e
γ
n log log n holds for every integer n > 5040, where σ(n) is the sum of divisors function, and γ is the Euler–Mascheroni constant. We exhibit a broad class of subsets of the natural numbers such that the Robin inequality holds for all but finitely many . As a special case, we determine the finitely many numbers of the form n = a
2 + b
2 that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality n/φ(n) < e
γ
log log n; since σ(n)/n < n/φ(n) for n > 1 our results for the Robin inequality follow at once.
相似文献
8.
In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis
Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective
function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the
unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate
and illustrate the steps of the resolution process of the problem. 相似文献
9.
R. Kh. Sadikova 《Mathematical Notes》1997,62(4):469-479
We prove a discrete and an integral version of an inequality for sourcewise representable functions and use them to derive
the Wirtinger inequality and its generalizations.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 564–576, October, 1997.
Translated by M. A. Shishkova 相似文献
10.
Liming Xiong 《Graphs and Combinatorics》2001,17(4):775-784
It is proved that the hamiltonian index of a connected graph other than a path is less than its diameter which improves the
results of P. A. Catlin etc. [J. Graph Theory 14 (1990) 347–364] and M. L. Sarazin [Discrete Math. 134(1994)85–91]. Nordhaus-Gaddum's
inequalities for the hamiltonian index of a graph are also established.
Received: July 17, 1998 Final version received: September 13, 1999 相似文献
11.
Consider Hardy’s inequalities with general weight ϕ for functions nonzero on the boundary. By an integral identity in C
1(
), define Hilbert spaces H
k
1
(Ω, ϕ) called Sobolev-Hardy spaces with weight ϕ. As a corollary of this identity, Hardy’s inequalities with weight ϕ in C
1 (
) follow. At last, by Hardy’s inequalities with weight ϕ = 1, discuss the eigenvalue problem of the Laplace-Hardy operator with critical parameter (N − 2)2/4 in H
1
1 (Ω).
相似文献
12.
Csirmaz László 《Periodica Mathematica Hungarica》2007,54(1):31-49
A convex set is inscribed into a rectangle with sides a and 1/a so that the convex set has points on all four sides of the rectangle. By “rounding” we mean the composition of two orthogonal
linear transformations parallel to the edges of the rectangle, which makes a unit square out of the rectangle. The transformation
is also applied to the convex set, which now has the same area, and is inscribed into a square. One would expect this transformation
to decrease the perimeter of the convex set as well. Interestingly, this is not always the case. For each a we determine the largest and smallest possible increase of the perimeter.
相似文献
13.
Denote by B
2σ,p
(1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [−σ, σ]. It is shown that a function in B
2σ,p
can be reconstructed in L
p(ℝ) by its sampling sequences {f (κπ / σ)}
κ∈ℤ and {f’ (κπ / σ)}
κ∈ℤ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L
p
r
(ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.
Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education under grant number
KM 200410009010 and by the Natural Science Foundation of China under grant number 10071006 相似文献
14.
Jing Hai Shao 《数学学报(英文版)》2011,27(6):1195-1204
In this paper, the dimensional-free Harnack inequalities are established on infinite-dimensional spaces. More precisely, we
establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract
Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important
quantities in one inequality, the relative entropy “H”, Wasserstein distance “W”, and Fisher information “I”. 相似文献
15.
Bicheng Yang 《Acta Mathematica Hungarica》2004,104(4):291-299
By introducing three parameters A, B and α, and estimating the weight coefficient, we give a new extension of Hilbert's inequality with a best constant factor involving
the β function. As applications, we consider the equivalent form and some particular results.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
GAOYI 《高校应用数学学报(英文版)》1998,13(2):150-158
Some modified Levitin-Polyak projection methods are proposed in this paper for solving monotone linear variational inequality x∈Ω,(x′-x)^T(Hx c)≤0,for any x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality. 相似文献
17.
YoungHoKIM 《数学学报(英文版)》2004,20(1):57-62
In this paper,some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved.The results of this paper reduce to those of Pachpatte(1998,J.Math.Anal.Appl.226,166-179)and Zhan and Debnath(2001,J.Math.Anal.Appl.262,411-418). 相似文献
18.
Sheng Jun Fan 《数学学报(英文版)》2009,25(10):1681-1692
Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen's inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang's results, under the same assumptions as Jiang's, we investigate the necessary and sufficient condition on g under which Jensen's inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen's inequality for BSDEs. 相似文献
19.
J. Popenda 《Proceedings Mathematical Sciences》1992,102(1):73-81
Gronwall’s inequality has many extensions and analogues among them the discrete one. In this paper we present theorems which
look like Gronwall’s lemma in the classical propositional calculus. 相似文献
20.
George A. Anastassiou 《Journal of Mathematical Analysis and Applications》2008,337(2):962-968
The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to functions on general domains using the L∞ norm of its nth partial derivatives. For radial functions on balls the inequality is sharp. 相似文献