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71.
Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms,
and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is
given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object
and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples
are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is
to give full details of the foregoing. 相似文献
72.
Elena Larraz Carlos Elvira Julio San Romn 《Journal of polymer science. Part A, Polymer chemistry》2003,41(11):1641-1649
This article explores the synthesis of a novel methacrylic macromonomer with an amphiphilic character derived from poly(ethylene glycol) tert‐octylphenyl ether (MT) and its respective homopolymer. To know their reactivity in radical copolymerization reactions with methyl methacrylate (MMA), a model monomer (MTm) was synthesized to determine the reactivity ratios and compare them with the low molar fractions of copolymers of MT with MMA because they were difficult to isolate. They were rMTm = 0.97 and rMMA = 0.95. The compositional diagrams when representing the weight fraction of MT and MTm in the feed and the copolymer suggested that a clear correlation exists between the experimental points of the model monomer MTm and the macromonomer MT ones, suggesting that the length of the side poly(ethylene oxide) chain does not affect the reactivity of the methacrylic double bond in the prepared monomers for this type of polymerization reaction. The reactivity ratios of the copolymers have a tendency for the formation of random or Bernoullian copolymers. The glass‐transition temperatures (Tg's) of the prepared copolymers were determined by differential scanning calorimetry, deviated from the Fox equation, and discussed on the basis of treatments that consider the influence of the monomeric units along the copolymer chains, determining the Tg of the corresponding alternating dyads. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1641–1649, 2003 相似文献
73.
María G. Armentano Ricardo G. Durn 《Numerical Methods for Partial Differential Equations》2003,19(5):653-664
In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003 相似文献
74.
Gabriela Jeronimo Teresa Krick Juan Sabia Martín Sombra 《Foundations of Computational Mathematics》2004,4(1):41-117
We present a bounded probability algorithm for the computation of the
Chowforms of the equidimensional components of an algebraic variety. In particular,
this gives an alternative procedure for the effective equidimensional decomposition
of the variety, since each equidimensional component is characterized by its Chow
form.
The expected complexity of the algorithm is polynomial in the size and the geometric
degree of the input equation system defining the variety. Hence it improves (or
meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects,
which constitutes a further contribution of the paper.
The algorithm is based on elimination theory techniques, in line with the geometric
resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators.
In fact, ours can be considered as an extension of their algorithm for zero-dimensional
systems to the case of positive-dimensional varieties. The key element for dealing
with positive-dimensional varieties is a new Poisson-type product formula. This
formula allows us to compute the Chow form of an equidimensional variety from a
suitable zero-dimensional fiber.
As an application, we obtain an algorithm to compute a subclass of sparse resultants,
whose complexity is polynomial in the dimension and the volume of the input
set of exponents. As another application, we derive an algorithm for the computation
of the (unique) solution of a generic overdetermined polynomial equation system. 相似文献
75.
Günter Graumann Prof. Dr. 《ZDM》2005,37(3):190-198
Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”. 相似文献
76.
Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.
77.
78.
Hai Huyen Dam Hans-Jürgen Zepernick Sven Nordholm Jörgen Nordberg 《Annals of Operations Research》2005,133(1-4):249-264
The performance of a code division multiple access system depends on the correlation properties of the employed spreading
code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to
improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses
intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this
paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic
auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach
is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between
various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences. 相似文献
79.
A method based on a single test is proposed to characterize the elasticity of an isotropic homogeneous material in the shape of a cylinder of any slenderness (length-diameter) ratio. Firstly, the Rayleigh-Ritz method is used to determine the natural frequencies of the cylinders vibrating axisymmetrically. The study is focused on cylindrical samples with diameter and length of similar magnitude so that the shear modulus and the Poisson ratio can be calculated simultaneously. Subsequently, the theoretical results for cylinders of slenderness ratio between 0.1 and 3 are analyzed in order to obtain the data required to determine the elastic constants from one of the two lowest measured natural frequencies and their quotient. The analysis of the results demonstrates that any slenderness ratio is useful in the calculation of the elastic constants, although in some cases the third natural frequency should be used. Furthermore, the influence of the length-diameter quotient on the sensitivity of the method is analyzed by evaluating the systematic uncertainties for both dynamic elastic constants. Finally, the method is experimentally tested by characterizing two steel cylinders with slenderness ratios 0.1 and 1, respectively. The results demonstrate that uncertainties for both Poisson ratio and the shear modulus are smaller when the slenderness ratio is 1. 相似文献
80.
E. García-Matres N. Stüßer M. Hofmann M. Reehuis 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,32(1):35-42
The magnetic structures of Mn1-xFexWO4 with x
= 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase
diagram could be completed in the coexistence range of different magnetic structures up to x
= 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector
= (±1/4, 1/2, 1/2) was found for x
⩽ 0.22 while the magnetic spins order with
= (1/2, 0, 0) for x
≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with
= (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x
= 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽
x
⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed
to a spin arrangement with
= (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed
Mn2+- and Fe2+-ions in the coexistence range 0.12 ⩽
x
⩽ 0.29 of different magnetic structures related to those of pure MnWO4 and FeWO4.
Received 9 October 2002 Published online 14 March 2003 相似文献