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1.
Rade T. Živaljević 《Discrete and Computational Geometry》2009,41(1):135-161
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature”, etc. in the context
of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type
invariant for cubical complexes, leading to a combinatorial “Theorema Egregium” for cubical complexes that are non-embeddable
into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson–Kozlov–Lovász graph coloring results to more general statements about
nondegenerate maps (colorings) of simplicial complexes and graphs.
The author was supported by grants 144014 and 144026 of the Serbian Ministry of Science and Technology. 相似文献
2.
We consider an operator of Bernstein for symmetric functions and give an explicit formula for its action on an arbitrary Schur
function. This formula is given in a remarkably simple form when written in terms of some notation based on the code of a
partition. As an application, we give a new and very simple proof of a classical result for the KP hierarchy, which involves
the Plücker relations for Schur function coefficients in a τ-function for the hierarchy. This proof is especially compact because we are able to restate the Plücker relations in a form
that is symmetrical in terms of partition code notation. 相似文献
3.
Toda (in SIAM J. Comput. 20(5):865–877, 1991) proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P
#P
, namely the class of languages that can be decided by a Turing machine in polynomial time given access to an oracle with
the power to compute a function in the counting complexity class #P. This result, which illustrates the power of counting, is considered to be a seminal result in computational complexity theory.
An analogous result in the complexity theory over the reals (in the sense of Blum–Shub–Smale real machines in Bull. Am. Math. Soc. (NS) 21(1): 1–46, 1989) has been missing so far. In this paper we formulate and prove a real analogue of Toda’s theorem. Unlike Toda’s proof in
the discrete case, which relied on sophisticated combinatorial arguments, our proof is topological in nature. As a consequence
of our techniques, we are also able to relate the computational hardness of two extremely well-studied problems in algorithmic
semi-algebraic geometry: the problem of deciding sentences in the first-order theory of the reals with a constant number of
quantifier alternations, and that of computing Betti numbers of semi-algebraic sets. We obtain a polynomial time reduction
of the compact version of the first problem to the second. This latter result may be of independent interest to researchers
in algorithmic semi-algebraic geometry. 相似文献
4.
The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or
without strong negation.
We would like to thank the referees for their valuable comments and suggestions. This research was supported by the Alexander
von Humboldt Foundation. The second author is grateful to
the Foundation for providing excellent working conditions and generous support of this research.
This work was also supported by the Japanese Ministry of Education, Culture, Sports, Science
and Technology, Grant-in-Aid for Young Scientists (B) 20700015, 2008. 相似文献
5.
For a small buffer queueing system fed by many flows of a large class of traffic processes we show the single server queue
and associated sample paths behave as if fed by marked Poisson traffic in a large deviations limit.
The timescale of events of interest tends to zero, so we study the log moment generating function as time tends to zero. The
associated rate function depends only on the mean arrival rate and the moment generating function of the arrivals. These results
are useful in estimating drop probabilities while studying the effect of small buffers on communication protocols.
Research supported by EPSRC Grant GR/S86266/01. 相似文献
6.
Andrea C. G. Mennucci 《Applied Mathematics and Optimization》2011,63(2):191-216
We formulate an Hamilton–Jacobi partial differential equation
H(x,Du(x))=0H(x,Du(x))=0 相似文献
7.
Nail H. Ibragimov 《Acta Appl Math》2009,105(2):157-187
The evolution equations of Maxwell’s equations has a Lagrangian written in terms of the electric E and magnetic H fields, but admit neither Lorentz nor conformal transformations. The additional equations ∇⋅E=0, ∇⋅H=0 guarantee the Lorentz and conformal invariance, but the resulting system is overdetermined, and hence does not have a Lagrangian.
The aim of the present paper is to attain a harmony between these two contradictory properties and provide a correspondence
between symmetries and conservation laws using the Lagrangian for the evolutionary part of Maxwell’s equations. 相似文献
8.
A suitable notion of hypercontractivity for a nonlinear semigroup {T
t
} is shown to imply Nash-type inequalities for its generator H, provided a subhomogeneity property holds for the energy functional (u,Hu). We use this fact to prove that, for semigroups generated by operators of p-Laplacian-type, hypercontractivity implies ultracontractivity. Then we introduce the notion of subordinated nonlinear semigroups
when the corresponding Bernstein function is f(x)=x
α
, and write an explicit formula for the associated generator. It is shown that hypercontractivity still holds for the subordinated
semigroup and, hence, that Nash-type inequalities hold as well for the subordinated generator. 相似文献
9.
H. Martini K. J. Swanepoel P. Oloff de Wet 《Journal of Optimization Theory and Applications》2009,143(1):149-157
We give a new proof that a star {op
i
:i=1,…,k} in a normed plane is a Steiner minimal tree of vertices {o,p
1,…,p
k
} if and only if all angles formed by the edges at o are absorbing (Swanepoel in Networks 36: 104–113, 2000). The proof is simpler and yet more conceptual than the original one.
We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular,
a star {op
i
:i=1,…,k} in any CL-space is a Steiner minimal tree of vertices {o,p
1,…,p
k
} if and only if all angles are absorbing, which in turn holds if and only if all distances between the normalizations
\frac1||pi||pi\frac{1}{\Vert p_{i}\Vert}p_{i}
equal 2. CL-spaces include the mixed ℓ
1 and ℓ
∞ sum of finitely many copies of ℝ. 相似文献
10.
Alysson M. Costa Jean-François Cordeau Bernard Gendron 《Computational Optimization and Applications》2009,42(3):371-392
Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like
relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities
that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated
to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays
to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities.
We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments
show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities. 相似文献
11.
We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability
problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we
also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling
of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse
anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary
solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers
and potentially for future applications in nano- and molecular wires. 相似文献
12.
13.
In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition.
We establish a blow up result for large initial data and a decay result for small enough initial data. 相似文献
14.
Murali K. Srinivasan 《Journal of Algebraic Combinatorics》2011,34(2):301-322
The de Bruijn–Tengbergen–Kruyswijk (BTK) construction is a simple algorithm that produces an explicit symmetric chain decomposition
of a product of chains. We linearize the BTK algorithm and show that it produces an explicit symmetric Jordan basis (SJB).
In the special case of a Boolean algebra, the resulting SJB is orthogonal with respect to the standard inner product and,
moreover, we can write down an explicit formula for the ratio of the lengths of the successive vectors in these chains (i.e.,
the singular values). This yields a new constructive proof of the explicit block diagonalization of the Terwilliger algebra
of the binary Hamming scheme. We also give a representation theoretic characterization of this basis that explains its orthogonality,
namely, that it is the canonically defined (up to scalars) symmetric Gelfand–Tsetlin basis. 相似文献
15.
We show that any family of sets uniformly definable in an o-minimal structure has an extended compression scheme of size equal
to the number of parameters in the defining formula. 相似文献
16.
We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This
perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version,
sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly
constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality
condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in
addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity
condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic
convergence under the same assumptions as above, which also gives a new result. 相似文献
17.
G. van der Laan A. J. J. Talman Z. Yang 《Journal of Optimization Theory and Applications》2010,144(2):391-407
Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set
{±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits
a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite
set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some
mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1}
n
+q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations
under certain natural conditions. An economic application is provided. 相似文献
18.
Andrzej Derdzinski 《Journal of Geometric Analysis》2009,19(2):301-357
The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general,
locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics,
raised by Díaz-Ramos, García-Río and Vázquez-Lorenzo (J. Geom. Anal. 16, 39–52, 2006).
Work begun during the author’s visit to the University of Santiago de Compostela, supported by Grant MTM2006-01432 (Spain). 相似文献
19.
We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication,
and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift equations), for computing sequence terms and power series coefficients, and for guessing recurrence equations given
initial terms of a sequence.
C. Koutschan partially supported by the Austrian Science Foundation (FWF) grants SFB F1305. 相似文献
20.
Jeffrey B. Vancouver Charles A. Scherbaum 《Computational & Mathematical Organization Theory》2008,14(1):1-22
Self-regulation theories in applied psychology disagree about whether action or perceptions are the focus of regulation. Computational
models based on the two conceptualizations were constructed and simulated. In one scenario, they performed identically and
in conjunction with participants in a study of the goal-level effect (Vancouver et al., Organ Res Methods 8:100–127, 2005). In another scenario they created differentiating predictions and only the computational model based on the self-regulation
of perceptions matched the data of participants. Implications for research and practice are discussed.
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