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71.
One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact,
complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes
more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe
in constructive terms the Chern classes of a vector bundle.
Since deceased. 相似文献
72.
A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G. 相似文献
73.
Thallada Bhaskar Kazuya Murai Toshiki Matsui Mihai Adrian Brebu Md. Azhar Uddin Akinori Muto Yusaku Sakata Katsuhide Murata 《Journal of Analytical and Applied Pyrolysis》2003,70(2):369-381
The thermal degradation of acrylonitrile-butadiene-styrene copolymer (ABS-Br; 10 g) containing brominated flame retardant (Br: 9.59 wt.%) was carried out at 450 °C using a semi batch operation using two different temperature programs. The heating rate was found to affect the quality of the degradation oil and yield of products (liquid, gas and residue). Data on the effect of the temperature program on the accumulation of liquid products was presented. It was found that the majority of the bromine was concentrated in the carbon residue and while majority of the nitrogen accumulates in the liquid products irrespective of degradation mode. The use of a one step constant heating rate process (I) produced a higher liquid yield (39%), than a two step process (29%). Differences were also noted in the Br and N contained in the liquids produced by the two processes. 相似文献
74.
Mihai Tibăr 《Israel Journal of Mathematics》2007,157(1):309-322
We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general
linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles.
For one-dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy
via monodromies of nearby sections. Our standpoint allows one to find, in certain cases, the structure of the Milnor fibre
up to the homotopy type. 相似文献
75.
José Seade Mihai Tibăr Alberto Verjovsky 《Bulletin of the Brazilian Mathematical Society》2005,36(2):275-283
Using a geometric approach, we determine the relations between the local Euler obstruction Euf of a holomorphic function f and several generalizations of the Milnor number for functions on singular spaces.
*This work was partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially
supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401. 相似文献
76.
AP
*-geometric linear complementarity problem (P
*GP) as a generalization of the monotone geometric linear complementarity problem is introduced. In particular, it contains
the monotone standard linear complementarity problem and the horizontal linear complementarity problem. Linear and quadratic
programming problems can be expressed in a “natural” way (i.e., without any change of variables) asP
*GP. It is shown that the algorithm of Mizunoet al. [6] can be extended to solve theP
*GP. The extended algorithm is globally convergent and its computational complexity depends on the quality of the starting
points. The algorithm is quadratically convergent for problems having a strictly complementary solution.
The work of F. A. Potra was supported in part by NSF Grant DMS 9305760 相似文献
77.
In real semialgebraic geometry it is common to represent a polynomial q which is positive on a region R as a weighted sum of squares. Serious obstructions arise when q is not strictly positive on the region R. Here we are concerned with noncommutative polynomials and obtaining a representation for them which is valid even when strict
positivity fails.
Specifically, we treat a ``symmetric' polynomial q(x, h) in noncommuting variables, {x1, . . . , } and {h1, . . . , } for which q(X,H) is positive semidefinite whenever
are tuples of selfadjoint matrices with ||Xj|| ≤ 1 but Hj unconstrained. The representation we obtain is a Gram representation in the variables h
where Pq is a symmetric matrix whose entries are noncommutative polynomials only in x and V is a ``vector' whose entries are polynomials in both x and h. We show that one can choose Pq such that the matrix Pq(X) is positive semidefinite for all ||Xj|| ≤ 1. The representation covers sum of square results ([Am. Math. (to appear); Linear Algebra Appl. 326 (2001), 193–203; Non commutative Sums of Squares, preprint]) when gx = 0. Also it allows for arbitrary degree in h, rather than degree two, in the main result of [Matrix Inequalities: A Symbolic Procedure to Determine Convexity Automatically
to appear IOET July 2003] when restricted to x-domains of the type ||Xj|| ≤ 1.
Partially supported by NSF, DARPA and Ford Motor Co.
Partially supported by NSF grant DMS-0140112
Partially supported by NSF grant DMS-0100367 相似文献
78.
This work addresses the computation of free-energy differences between protein conformations by using morphing (i.e., transformation)
of a source conformation into a target conformation. To enhance the morphing procedure, we employ permutations of atoms: we
seek to find the permutation σ that minimizes the mean-square distance traveled by the atoms. Instead of performing this combinatorial
search in the space of permutations, we show that the best permutation can be found by solving a linear assignment problem.
We demonstrate that the use of such optimal permutations significantly improves the efficiency of the free-energy computation. 相似文献
79.
In this paper we discuss the problem of verifying and computing optimal controls of systems whose dynamics is governed by
differential systems with a discontinuous right-hand side. In our work, we are motivated by optimal control of mechanical
systems with Coulomb friction, which exhibit such a right-hand side. Notwithstanding the impressive development of nonsmooth
and set-valued analysis, these systems have not been closely studied either computationally or analytically. We show that
even when the solution crosses and does not stay on the discontinuity, differentiating the results of a simulation gives gradients
that have errors of a size independent of the stepsize. This means that the strategy of “optimize the discretization” will
usually fail for problems of this kind. We approximate the discontinuous right-hand side for the differential equations or
inclusions by a smooth right-hand side. For these smoothed approximations, we show that the resulting gradients approach the
true gradients provided that the start and end points of the trajectory do not lie on the discontinuity and that Euler’s method
is used where the step size is “sufficiently small” in comparison with the smoothing parameter. Numerical results are presented
for a crude model of car racing that involves Coulomb friction and slip showing that this approach is practical and can handle
problems of moderate complexity. 相似文献
80.
Mihai Mihăilescu Gheorghe Moroşanu 《Nonlinear Analysis: Real World Applications》2013,14(3):1466-1476
This paper investigates a nonlinear and non-homogeneous system of partial differential equations. The motivation comes from the fact that in a particular case the problem discussed here can be used in modeling the behavior of nonlinear Hencky-type materials. The main result of the paper establishes the existence of a nontrivial solution in an adequate functional space of Orlicz–Sobolev type by using Schauder’s fixed point theorem combined with adequate variational techniques. 相似文献