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1.
With a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables
defined by the orders of a function on irreducible components of the curve. The Poincaré series of this filtration turns out
to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding
to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula
for the Poincaré series of the corresponding multi-index filtration similar to the one associated with plane germs. Here we
show that the Poincaré series of a set of divisorial valuations on the ring of germs of functions of two variables defines
“the topology of the set of the divisors” in the sense that it defines the minimal resolution of this set up to combinatorial
equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which
shows that the Alexander polynomial is equivalent to the embedded topology. 相似文献
2.
This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with
light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results
about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the
asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions.
In the above studies, some differences and relations between the results on a distribution and its corresponding density can
be discovered.
相似文献
3.
Angelo Miele 《Journal of Optimization Theory and Applications》2010,147(3):483-490
On the occasion of the 50th anniversary of the theorem of the image trajectories in the Earth-Moon space, the author revisits
the theorem and clarifies the relation between the class of image trajectories and the class of symmetric free-return trajectories,
which were employed in the Apollo program. In a nutshell, the symmetric free-return trajectories are those image trajectories
that intersect the Earth-Moon axis orthogonally at some point above the far side of the Moon. Optimization implications are
pointed out. 相似文献
4.
A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control
the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads
to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then,
the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class
of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then
approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution
of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into
a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness
of this idea is that the method is not iterative and it does not need any initial guess of the solution.
相似文献
5.
In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation
of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence
relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation
allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed
orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed.
Finally, a Markov’s type theorem is presented. 相似文献
6.
Let M be a generic CR manifold in
\BbbCm+d\Bbb{C}^{m+d} of codimension d, locally given as the common zero set of real-valued functions r
1,…,r
d
. Given an integer δ=1,…,d, we find a necessary and sufficient condition for M to contain a real submanifold of codimension δ with the same CR structure. We also find a necessary and sufficient condition and several sufficient conditions for M to admit a complex submanifold of complex dimension n, for any n=1,…,m. We use the method of prolongation of an exterior differential system. The conditions are systems of partial differential
equations on r
1,…,r
d
of third order. 相似文献
7.
How to get the timing right. A computational model of the effects of the timing of contacts on team cohesion in demographically diverse teams 总被引:1,自引:0,他引:1
Lau and Murnighan’s faultline theory explains negative effects of demographic diversity on team performance as consequence of strong demographic faultlines. If demographic differences between group members are correlated across various dimensions, the team is likely to show a “subgroup split” that inhibits communication and effective collaboration between team members. Our paper proposes a rigorous formal and computational reconstruction of the theory. Our model integrates four elementary mechanisms of social interaction, homophily, heterophobia, social influence and rejection into a computational representation of the dynamics of both opinions and social relations in the team. Computational experiments demonstrate that the central claims of faultline theory are consistent with the model. We show furthermore that the model highlights a new structural condition that may give managers a handle to temper the negative effects of strong demographic faultlines. We call this condition the timing of contacts. Computational analyses reveal that negative effects of strong faultlines critically depend on who is when brought in contact with whom in the process of social interactions in the team. More specifically, we demonstrate that faultlines have hardly negative effects when teams are initially split into demographically homogeneous subteams that are merged only when a local consensus has developed. 相似文献
8.
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems
of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider
8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift–Hohenberg equation. We prove that a formal
solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution
of the pattern-forming partial differential equation (PDE) up to an exponentially small error. 相似文献
9.
We consider the Erlang loss system, characterized by N servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of N. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates. 相似文献
10.
The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB)
equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function
computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other
initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum.
Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered. 相似文献
11.
In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional
Euclidean space. As a consequence, we prove that an parallelepiped with relation
for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter. 相似文献
12.
James East 《Semigroup Forum》2010,81(2):357-379
The (full) transformation semigroup Tn\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group Sn í Tn{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of Tn\mathcal{T}_{n}. The complement Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of Tn\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of Tn\mathcal{T}_{n}. 相似文献
13.
Pseudo-differential and Fourier series operators on the torus
\mathbbTn=(\BbbR/2p\BbbZ)n{{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}
are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal
symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is
established. Periodization of operators and hyperbolic partial differential equations is discussed. Fourier series operators,
which are analogues of Fourier integral operators on the torus, are introduced, and formulae for their compositions with pseudo-differential
operators are derived. It is shown that pseudo-differential and Fourier series operators are bounded on L
2 under certain conditions on their phases and amplitudes. 相似文献
14.
Given a set of vectors F={f
1,…,f
m
} in a Hilbert space H\mathcal {H}, and given a family C\mathcal {C} of closed subspaces of H\mathcal {H}, the subspace clustering problem consists in finding a union of subspaces in C\mathcal {C} that best approximates (is nearest to) the data F. This problem has applications to and connections with many areas of mathematics, computer science and engineering, such
as Generalized Principal Component Analysis (GPCA), learning theory, compressed sensing, and sampling with finite rate of
innovation. In this paper, we characterize families of subspaces C\mathcal {C} for which such a best approximation exists. In finite dimensions the characterization is in terms of the convex hull of an
augmented set C+\mathcal {C}^{+}. In infinite dimensions, however, the characterization is in terms of a new but related notion; that of contact half-spaces.
As an application, the existence of best approximations from π(G)-invariant families C\mathcal {C} of unitary representations of Abelian groups is derived. 相似文献
15.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
16.
We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under the quincunx dilation matrix is presented. 相似文献
17.
18.
In this paper we consider approximations of the occupation measure of the Fractional Brownian motion by means of some functionals
defined on regularizations of the paths. In a previous article Berzin and León proved a cylindrical convergence to a Wiener
process of conveniently rescaled functionals. Here we show the tightness of the approximation in the space of continuous functions
endowed with the topology of uniform convergence on compact sets. This allows us to simplify the identification of the limit. 相似文献
19.
Jean-Christophe Breton 《Journal of Theoretical Probability》2010,23(1):21-38
We investigate the regularity of shot noise series and of Poisson integrals. We give conditions for the absolute continuity
of their law with respect to the Lebesgue measure and for their continuity in total-variation norm. In particular, the case
of truncated series in addressed. Our method relies on a disintegration of the probability space based on a mere conditioning
by the first jumps of the underlying Poisson process. 相似文献
20.
Andreas Philipp 《Semigroup Forum》2010,81(3):424-434
The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature.
For finitely generated monoids, S.T. Chapman and P. García-Sánchez, together with several co-authors, derived a method to
calculate the catenary and tame degree from the monoid of relations, and they applied this method successfully in the case
of numerical monoids. In this paper, we investigate the algebraic structure of this approach. Thereby, we dispense with the
restriction to finitely generated monoids and give applications to other invariants of non-unique factorizations, such as
the elasticity and the set of distances. 相似文献