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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.
Zhang Xiao-Dong 《Indagationes Mathematicae》1996,7(4):559
Extension properties of compact positive operators on Banach lattices are investigated. The following results are obtained:
1.
(1) Any compact positive operator (any compact lattice homomorphism, resp.) from a majorizing sublattice G of a Banach lattice E into another Banach lattice F can be extended to a compact positive operator (a compact lattice homomorphism, resp.) from E into F; 2.
(2) Any compact positive operator defined on a closed majorizing sublattice G of a Banach lattice E has a compact positive extension on E that preserves the spectrum (a necessary modification is needed).
3.
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.
4.
Let G be a 2-edge-connected simple graph with girth g, independence number α(G), and if one of the following two conditions holds
then G is upper embeddable and the lower bound v − 3g + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α(G) is also obtained.
Huang Yuanqiu: Partially supported by National Science Foundation of China (No. 10771062) and Program for New Century Excellent
Talents in University (No. NCET-07-0276). 相似文献
(1) | α(G) ≤ 2; | |
(2) | α(G) ≥ 3, and for any three nonadjacent vertices v
i
(i = 1,2,3), it has
|
5.
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 .
6.
Ahmed Ainouche 《Graphs and Combinatorics》2009,25(2):129-137
Let G = (V, E) be a any simple, undirected graph on n ≥ 3 vertices with the degree sequence . We consider the class of graphs satisfying the condition where , is a positive integer. It is known that is hamiltonian if θ ≤ δ. In this paper,
相似文献
(i) | we give a necessary and sufficient condition, easy to check, ensuring that is nonhamiltonian and we characterize all the exceptional sub-classes. |
(ii) | we prove that is either bipartite or contains cycles of all lengths from 3 to c(G), the length of a longest cycle in G. |
7.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
(1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
(2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
(3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
(4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
8.
Ulrich Kohlenbach 《Archive for Mathematical Logic》1992,31(5):305-317
LetA
H be the Herbrand normal form ofA andA
H,D a Herbrand realization ofA
H. We show
(i) | There is an example of an (open) theory + with function parameters such that for someA not containing function parameters | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
(ii) | Similar for first order theories + if the index functions used in definingA H are permitted to occur in instances of non-logical axiom schemata of , i.e. for suitable ,A | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
(iii) | In fact, in (1) we can take for + the fragment ( 1 0 -IA)+ of second order arithmetic with induction restricted to 1 0 -formulas, and in (2) we can take for the fragment ( 1 0,b -IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
(iv) |
On the other hand,
|