共查询到20条相似文献,搜索用时 15 毫秒
1.
Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient
variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering family on a submanifold Y with ample normal bundle in X, the main results relate, under suitable conditions, the associated rational connected fiber structures on X and on Y. Applications of these results include an extension theorem for Mori contractions of fiber type and a classification theorem
in the case Y has a structure of projective bundle or quadric fibration.
All authors acknowledge support by MIUR National Research Project “Geometry on Algebraic Varieties” (Cofin 2004). The research
of the second author was partially supported by NSF grants DMS 0111298 and DMS 0548325. The third author acknowledges partial
support by the University of Milan (FIRST 2003). 相似文献
2.
Mohab Safey El Din 《Mathematics in Computer Science》2007,1(1):177-207
Let f be a polynomial in of degree D. We focus on testing the emptiness and computing at least one point in each connected component of the semi-algebraic set
defined by f > 0 (or f < 0 or f ≠ 0). To this end, the problem is reduced to computing at least one point in each connected component of a hypersurface
defined by f − e = 0 for
positive and small enough. We provide an algorithm allowing us to determine a positive rational number e which is small enough in this sense. This is based on the efficient computation of the set of generalized critical values of the mapping which is the union of the classical set of critical values of the mapping f and the set of asymptotic critical values of the mapping f. Then, we show how to use the computation of generalized critical values in order to obtain an efficient algorithm deciding
the emptiness of a semi-algebraic set defined by a single inequality or a single inequation. At last, we show how to apply
our contribution to determining if a hypersurface contains real regular points. We provide complexity estimates for probabilistic
versions of the latter algorithms which are within arithmetic operations in . The paper ends with practical experiments showing the efficiency of our approach on real-life applications.
相似文献
3.
M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
4.
We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations
in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain
conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions
on the norms for perturbations). Based on established evaluations we derive further information about decaying properties
of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations
corresponding to Jacobi type operators.
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5.
We start by introducing a Čech homology with compact supports which we then use in order to construct an infinite-dimensional
homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for
a semilinear Schr?dinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical
group, defined in terms of the infinite-dimensional homology mentioned above. Finally, we employ this fact in order to construct
solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory,
we also include some new results.
Dedicated to Felix Browder on the occasion of his 80th birthday 相似文献
6.
Nong Gu Daniel Lazard Fabrice Rouillier Yong Xiang 《Mathematics in Computer Science》2007,1(2):291-304
The basic objective of blind signal separation is to recover a set of source signals from a set of observations that are mixtures
of the sources with no, or very limited knowledge about the mixture structure and source signals. To extract the original
sources, many algorithms have been proposed; among them, the cross-correlation and constant modulus algorithm (CC-CMA) appears
to be the algorithm of choice due to its computational simplicity.
An important issue in CC-CMA algorithm is the global convergence analysis, because the cost function is not quadratic nor
convex and contains undesirable stationary points. If these undesirable points are local minimums, the convergence of the
algorithm may not be guaranteed and the CC-CMA would fail to separate source signals.
The main result of this paper is to complete the classification of these stationary points and to prove that they are not
local minimums unless if the mixing parameter is equal to 1.
This is obtained by using the theory of discriminant varieties to determine the stationnary points as a function of the parameter
and then to show that the Hessian matrix of the cost function is not positive semidefinite at these stationnay points, unless
if the mixing parameter is 1.
相似文献
7.
Hamidreza Rahmati 《Archiv der Mathematik》2009,92(1):26-34
A finite module M over a noetherian local ring R is said to be Gorenstein if Exti(k, M) = 0 for all i ≠ dim R. An endomorphism φ: R → R of rings is called contracting if for some i ≥ 1. Letting φR denote the R-module R with action induced by φ, we prove: A finite R-module M is Gorenstein if and only if HomR(φR, M) ≅ M and ExtiR(φR, M) = 0 for 1 ≤ i ≤ depth R.
Received: 7 December 2007 相似文献
8.
Minoru Itoh 《Selecta Mathematica, New Series》2009,14(2):247-274
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as
a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies some interesting
expansion formulas, in which there is a curious duality. Moreover, this class includes examples which are useful to describe
the eigenvalues of Capelli type central elements of the universal enveloping algebras of classical Lie algebras.
相似文献
9.
The method of singular sequences is used to provide a simple and, in some respects, a more general proof of a known spectral
result for leaky wires. The method introduces a new concept of asymptotic straightness.
Received: 4 October 2007 相似文献
10.
Hirofumi Tsumura 《Archiv der Mathematik》2007,88(1):42-51
In this paper, we study certain polylogarithmic double series
where p, q, r are nonnegative integers and x is any complex number with
. First we give certain polylogarithmic interpolation formulas of the results of Mordell, Subbarao-Sitaramachandrarao and
Zagier. By specializing to x = 1, we can obtain their results. Secondly we calculate some special values of these polylogarithmic double series.
Received: 21 November 2005; Revised: 8 May 2006 相似文献
11.
Microarrays offer unprecedented possibilities for the so-called omic, e.g., genomic and proteomic, research. However, they
are also quite challenging data to analyze. The aim of this paper is to provide a short tutorial on the most common approaches
used for pattern discovery and cluster analysis as they are currently used for microarrays, in the hope to bring the attention
of the Algorithmic Community on novel aspects of classification and data analysis that deserve attention and have potential
for high reward.
R. Giancarlo is partially supported by Italian MIUR grants PRIN “Metodi Combinatori ed Algoritmici per la Scoperta di Patterns
in Biosequenze” and FIRB “Bioinformatica per la Genomica e la Proteomica” and Italy-Israel FIRB Project “Pattern Discovery
Algorithms in Discrete Structures, with Applications to Bioinformatics”. D. Scaturro is supported by a MIUR Fellowship in
the Italy-Israel FIRB Project “Pattern Discovery Algorithms in Discrete Structures, with Applications to Bioinformatics”. 相似文献
12.
Let R be a real closed field. The Pierce–Birkhoff conjecture says that any piecewise polynomial function f on R
n
can be obtained from the polynomial ring R[x
1,..., x
n
] by iterating the operations of maximum and minimum. The purpose of this paper is threefold. First, we state a new conjecture,
called the Connectedness conjecture, which asserts, for every pair of points , the existence of connected sets in the real spectrum of R[x
1,..., x
n
], satisfying certain conditions. We prove that the Connectedness conjecture implies the Pierce–Birkhoff conjecture. Secondly,
we construct a class of connected sets in the real spectrum which, though not in itself enough for the proof of the Pierce–Birkhoff
conjecture, is the first and simplest example of the sort of connected sets we really need, and which constitutes the first
step in our program for a proof of the Pierce–Birkhoff conjecture in dimension greater than 2. Thirdly, we apply these ideas
to give two proofs that the Connectedness conjecture (and hence also the Pierce–Birkhoff conjecture in the abstract formulation)
holds locally at any pair of points , one of which is monomial. One of the proofs is elementary while the other consists in deducing this result as an immediate
corollary of the main connectedness theorem of this paper. 相似文献
13.
Hernán R. Henríquez 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(5):797-822
We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded
functional differential equations with infinite delay.
Research supported in part by FONDECYT, grant 1050314. 相似文献
14.
Let G be a p-adic algebraic group of polynomial growth and H be a closed subgroup of G. We prove the growth conjecture for the homogeneous space G/H, that is, G/H supports a recurrent random walk if and only if G/H has polynomial growth of degree atmost two.
Received: 23 November 2007 相似文献
15.
We compute some algebraic invariants (e.g. depth, Castelnuovo-Mumford regularity) for a special class of monomial ideals,
namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.
Received: 25 October 2007 相似文献
16.
This note studies the structure of the divisorial fixed part of for a 1-connected curve D on a smooth surface S. It is shown that if the divisorial fixed part F of is non empty then it has arithmetic genus ≤ 0 and each component of F is a smooth rational curve. The structure of curves D, with non empty divisorial fixed part F for , is also described.
Received: 16 August 2007 相似文献
17.
Using microlocalization, the positive and the negative parts for a class of second order formally self-adjoint pseudodifferential
operators are constructed.
相似文献
18.
In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are isomorphic. This last result uses the Fourier-Mukai transform of coherent systems introduced by Hernández Ruipérez and Tejero Prieto. 相似文献
19.
Wilhelm Plesken 《Archiv der Mathematik》2009,92(2):111-118
Both the Gauss-Bruhat decomposition and the LU-decomposition of the general linear group over a field are examples of a Thomas
decomposition of systems of polynomial equations and inequations into disjoint triangular systems, a recently rediscovered
method of the nineteen-thirties, applied to the inequation det (A) ≠ 0 for an n × n-matrix of indeterminants. More specifically it is shown that the cells of the two decompositions can be described by determinantal
equations and inequations yielding simple systems in the sense of Thomas of a rather special type, which are called split
and allow counting solutions over any finite field.
Received: 17 March 2008, Revised: 12 August 2008 相似文献
20.
Singleton attractor (also called fixed point) detection is known to be NP-hard even for AND/OR Boolean networks (AND/OR BNs
in short, i.e., BNs consisting of AND/OR nodes), where BN is a mathematical model of genetic networks and singleton attractors
correspond to steady states. In our recent paper, we developed an O(1.787n) time algorithm for detecting a singleton attractor of a given AND/OR BN where n is the number of nodes. In this paper, we present an O(1.757n) time algorithm with which we succeeded in improving the above algorithm. We also show that this problem can be solved in
time, which is less than O((1 + ∈)n) for any positive constant ∈, when a BN is planar.
A preliminary version of this paper has appeared in Proc. 3rd International Conference on Algebraic Biology (AB2008) [27]. 相似文献