共查询到20条相似文献，搜索用时 15 毫秒
1.
Simon Raulot 《Mathematische Zeitschrift》2009,261(2):321-349
Let M be an n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric g, a spin structure σ and a chirality operator Γ. We define and study some properties of a spin conformal invariant given by:
where is the smallest eigenvalue of the Dirac operator under the chiral bag boundary condition . More precisely, we show that if n ≥ 2 then:
相似文献
2.
One of the classical problem in computational biology is the character compatibility problem or perfect phylogeny problem. A standard formulation of this problem in terms of two closely related questions is the following. Given a data set consisting
of a finite set X and a set
of partitions induced on X by a set of characters. Is
compatible, that is, does there exist an evolutionary tree that represents (in a well-defined sense) the data? If this is the case,
is this tree unique? A fundamental result in phylogenetics states that the answer to the former of the two questions is yes
precisely if the partition intersection graph
associated to
can be made chordal by obeying a certain rule.
The main insight from this paper is that the relation graph
associated to a set
of partitions may provide a key for deciding whether such a chordalization of
exists. To prove our results, we introduce an extension of the concept of the partition intersection graph associated to
using
.
Received August 27, 2004 相似文献
3.
We study the q-Clifford algebras
, called FRT–Clifford algebras, introduced by Faddeev, Reshetikhin and Takhtajan. It is shown that
acts on the q-exterior algebra
. Moreover, explicit formulas for the embedding of
into
and its relation to the vector and spin representations of
are given and proved. 相似文献
4.
E. M. El-Kholy El-Said R. Lashin Salama N. Daoud 《Proceedings Mathematical Sciences》2007,117(3):293-300
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds.
We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case
of equi-Gaussian curvature foldings, f: M → P
n
, of an orientable surface M onto a polygon P
n
we prove that
and we generalize (iii) for #nT
2. 相似文献
| ((i)) |
| ((ii)) |
| ((iii)) |
5.
6.
Antonio Cañada Juan A. Montero Salvador Villegas 《Mediterranean Journal of Mathematics》2006,3(2):177-187
Let us consider the linear boundary value problem
where
and
is defined by
Classical Lyapunov inequality states that
for any function
where
The constant 4/L is optimal. Let us note that Lyapunov inequality is given in terms of
the usual norm in the space L1(0, L). In this paper we review some recent results on Lp Lyapunovtype inequalities,
, for ordinary and partial differential equations on a bounded and regular domain in
In the last case, it is showed that the relation between the quantities p and N/2 plays a crucial role, pointing out a deep difference with respect to the ordinary case. In the proof, the best constants
are obtained by using a related variational problem and Lagrange multiplier theorem. Finally, the linear results are combined
with Schauder fixed point theorem in the study of resonant nonlinear problems.
The authors have been supported by the Ministry of Science and Technology of Spain MTM2005- 01331 and by Junta de Andalucia
(FQM116). 相似文献
| ((0.1)) |
7.
We establish a new bound for the exponential sum
where λ is an element of the residue ring modulo a large prime number
and
are arbitrary subsets of the residue ring modulo p − 1 and γ (n) are any complex numbers with | γ (n)| ≦ 1.
Received: 15 June 2005 相似文献
8.
Horst Alzer 《Mediterranean Journal of Mathematics》2008,5(4):395-413
We present several sharp inequalities for the volume of the unit ball in ,
. One of our theorems states that the double-inequality
holds for all n ≥ 2 with the best possible constants
This refines and complements a result of Klain and Rota.
相似文献
9.
Yong-Zhuo Chen 《Positivity》2008,12(4):643-652
Let A and H be two operators defined in an ordered Banach space such that
, and
, where . This paper discusses the conditions which will guarantee the existence of an asymptotically attractive fixed point for T = A + H.
相似文献
10.
Steven D. Taliaferro 《Mathematische Annalen》2007,338(3):555-586
We study C
2,1 nonnegative solutions u(x,t) of the nonlinear parabolic inequalities
in a punctured neighborhood of the origin in , when and . We show that a necessary and sufficient condition on λ for such solutions u to satisfy an a priori bound near the origin is , and in this case, the a priori bound on u is
This a priori bound for u can be improved by imposing an upper bound on the initial condition of u. 相似文献
11.
Jérôme Droniou Juan-Luis Vázquez 《Calculus of Variations and Partial Differential Equations》2009,34(4):413-434
We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation
posed in a bounded domain , with pure Neumann boundary conditions
Under the assumption that with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution if ∫Ω
f
dx = 0, and also that the kernel is generated by a function , unique up to a multiplicative constant, which satisfies a.e. on Ω. We also prove that the equation
has a unique solution for all ν > 0 and the map is an isomorphism of the respective spaces. The study is made in parallel with the dual problem, with equation
The dependence on the data is also examined, and we give applications to solutions of nonlinear elliptic PDE with measure
data and to parabolic problems. 相似文献
12.
Sandro Zagatti 《Calculus of Variations and Partial Differential Equations》2008,31(4):511-519
We consider a class of non convex scalar functionals of the form
under standard assumptions of regularity of the solutions of the associated relaxed problem and of local affinity of the bipolar
f
** of f on the set {f
** < f}. We provide an existence theorem, which extends known results to lagrangians depending explicitly on the three variables,
by the introduction of integro-extremal minimizers of the relaxed functional which solve the equation
or the opposite one, almost everywhere and in viscosity sense. 相似文献
13.
We consider the following Liouville equation in
For each fixed and a
j
> 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior:
相似文献
14.
J.-P. Allouche 《The Ramanujan Journal》2007,14(1):39-42
We answer a question of Berndt and Bowman, asking whether it is possible to deduce the value of the Ramanujan integral I from the value of the Ramanujan integral J, where
and
We also show that the second integral can be deduced from a classical expression of the ψ function due to Dirichlet and from
the classical equality
which is a simple consequence of Frullani-Cauchy’s theorem.
2000 Mathematics Subject ClassificationPrimary—33B15
Partially supported by MENESR, ACI NIM 154 Numération. 相似文献
15.
16.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
, wheref∈L
1
loc(ℝ) is the unknown function andg,T
1, andT
2 are given functions satisfying the conditions
.
Most attention is paid to the nontrivial solvability of the homogeneous equation
.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
17.
Daniel Wilczak 《Foundations of Computational Mathematics》2006,6(4):495-535
In this paper we present a new topological tool which allows us to prove the existence of Shilnikov homoclinic or heteroclinic
solutions. We present an application of this method to the Michelson system
[16]. We prove that there exists a countable set of parameter values
for which a pair of the Shilnikov homoclinic orbits to the equilibrium points
appear. This result was conjectured by Michelson [16]. We also show that there exists a countable set of parameter values
for which there exists a heteroclinic orbit connecting the equilibrium
possessing a one-dimensional unstable manifold with the equilibrium
possessing a one-dimensional stable manifold. The method used in the proof can be applied to other reversible systems. To
verify the assumptions of the main topological theorem for the Michelson system, we use rigorous computations based on interval
arithmetic. 相似文献
18.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
19.
Let K, D be n-dimensional convex bodes. Define the distance between K and D as
where the infimum is taken over all
and all invertible linear operators T. Assume that 0 is an interior point of K and define
where is the uniform measure on the sphere. We use the difference body estimate to prove that K can be embedded into
so that
for some absolute constants C and
. We apply this result to show that the distance between two n-dimensional convex bodies does not exceed
up to a logarithmic factor. 相似文献
20.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
. There is a celebrated sum formula [6, 10] among multiple zeta values as
,
where range over all positive integers with in the summation.
In this paper, we shall prove the so called restricted sum formula [4]. Namely, for all positive integers m and q with m ≥ q and a nonnegative integer p, that
. We prove the assertion by new expressions of multiple zeta values in terms of Drinfeld integrals.
This work was supported by the Department of Mathematics, National Chung Cheng University and by the National Science Council
of Taiwan, Republic of China. 相似文献