共查询到20条相似文献,搜索用时 46 毫秒
1.
Loïc Foissy 《Advances in Mathematics》2011,226(6):4702
We consider systems of combinatorial Dyson–Schwinger equations in the Connes–Kreimer Hopf algebra HI of rooted trees decorated by a set I. Let H(S) be the subalgebra of HI generated by the homogeneous components of the unique solution of this system. If it is a Hopf subalgebra, we describe it as the dual of the enveloping algebra of a Lie algebra g(S) of one of the following types:
1.
g(S) is an associative algebra of paths associated to a certain oriented graph. 2.
Or g(S) is an iterated extension of the Faà di Bruno Lie algebra. 3.
Or g(S) is an iterated extension of an infinite-dimensional abelian Lie algebra.
2.
In this paper we consider a stochastic R&D decision model for a single firm operating in a competitive environment. The study focuses on the firm's optimal policy which maximizes the expected discounted net return from the project. The firm's policy is composed of two ingredients: a stopping time which determines when the developed technology should be introduced and protected by a patent, and an investment strategy which specifies the expenditure rate throughout the R&D program. The main findings of the study are:
(a)
Under a constant expenditure rate strategy, the optimal stopping time of the project is a control limit policy of the following form: stop whenever the project's state exceeds a fixed critical value, or when a similar technology is introduced and protected by one of the firm's rivals, whichever occurs first. (b)
For a R&D race model in which the winner-takes-all competition and the loser's return is zero, we show that the firm's optimal expenditure rate throughout the R&D program increases monotonically as a function of the project's state.
3.
Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A|≥k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b:V(G)?A with ∑v∈V(G)b(v)=0, there always exists a map f:E(G)?A−{0}, such that at each v∈V(G), in A, then G is A-connected. Let Z3 denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is Z3-connected. In this paper, we proved the following.
(i)
Every 5-edge-connected graph is Z3-connected if and only if every 5-edge-connected line graph is Z3-connected. (ii)
Every 6-edge-connected triangular line graph is Z3-connected. (iii)
Every 7-edge-connected triangular claw-free graph is Z3-connected.
4.
Fredrik Kuivinen 《Discrete Optimization》2011,8(3):459-477
Let (L;?,?) be a finite lattice and let n be a positive integer. A function f:Ln→R is said to be submodular if for all . In this article we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding such that as efficiently as possible. We establish
•
a min–max theorem, which states that the minimum of the submodular function is equal to the maximum of a certain function defined over a certain polyhedron; and •
a good characterisation of the minimisation problem, i.e., we show that given an oracle for computing a submodular f:Ln→Z and an integer m such that , there is a proof of this fact which can be verified in time polynomial in n and ; and •
a pseudopolynomial-time algorithm for the minimisation problem, i.e., given an oracle for computing a submodular f:Ln→Z one can find in time bounded by a polynomial in n and .
5.
6.
7.
8.
9.
10.
11.
A closed, convex and bounded setP in a Banach spaceE is called a polytope if every finite-dimensional section ofP is a polytope. A Banach spaceE is called polyhedral ifE has an equivalent norm such that its unit ball is a polytope. We prove here:
We deduce from these two results that in a polyhedral Banach space (for instance in c0(ℕ) or inC(K) forK countable compact), every equivalent norm can be approximated by norms which are analytic onE/{0}. 相似文献
(1) | LetW be an arbitrary closed, convex and bounded body in a separable polyhedral Banach spaceE and let ε>0. Then there exists a tangential ε-approximating polytopeP for the bodyW. |
(2) | LetP be a polytope in a separable Banach spaceE. Then, for every ε>0,P can be ε-approximated by an analytic, closed, convex and bounded bodyV. |
12.
13.
14.
We prove that the solution operators et (f, y){\cal e}_t (\phi , \psi ) for the nonlinear wave equations with supercritical nonlinearities are not Lipschitz mappings from a subset of the finite-energy space ([(H)\dot]1 ?Lr+1) ×L2(\dot {H}^1 \cap L_{\rho +1}) \times L_2 to [(H)\dot]sq¢\dot {H}^s_{q'} for t 1 0t\neq 0, and 0 £ s £ 1,0\leq s\leq 1, (n+1)/(1/2-1/q¢) = 1(n+1)/(1/2-1/q')= 1. This is in contrast to the subcritical case, where the corresponding operators are Lipschitz mappings ([3], [6]). Here et(f, y)=u(·, t){\cal e}_t(\phi , \psi )=u(\cdot , t), where u is a solution of {