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本文引进了一类集值映射的积分,研究了这种积分的若干性质.在此基础上,讨论了这种积分与抽象函数的Riemann积分、Bochner积分和Petits积分的关系. 相似文献
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利用单积分计算重积分,是教材中的常见题型,而利用重积分计算单积分的题目确很少提及,作者例举了利用重积分计算单积分的例子,并阐明解题思路. 相似文献
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Zeng Yong Xie Yunsun 《大学数学》1998,(2)
本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分,并且用第一类曲线、曲面积分定义第二类曲线、曲面积分。 相似文献
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通过变量替换或分部积分可建立关于某些积分的方程,通过引入辅助积分可建立关于某些积分的方程组,解这些方程或方程组可得所求积分. 相似文献
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Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep
under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the
experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological
creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the
stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation
and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem
confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between
the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction
in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference
in their porosity.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.)
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000. 相似文献
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Peridynamics via finite element analysis 总被引:2,自引:0,他引:2
Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration. 相似文献
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V. P. Stavrov V. V. Stavrov N. V. Pankova K. Friedrich 《Mechanics of Composite Materials》2000,36(2):155-162
The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final
composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned
fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions
formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned
fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity
of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the
internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective
permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation.
Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000. 相似文献
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Classical approaches to location problems are based on the minimization of the average distance (the median concept) or the minimization of the maximum distance (the center concept) to the service facilities. The median solution concept is primarily concerned with the spatial efficiency while the center concept is focused on the spatial equity. The k-centrum model unifies both the concepts by minimization of the sum of the k largest distances. In this paper we investigate a solution concept of the conditional median which is a generalization of the k-centrum concept taking into account the portion of demand related to the largest distances. Namely, for a specified portion (quantile) of demand we take into account the entire group of the corresponding largest distances and we minimize their average. It is shown that such an objective, similar to the standard minimax, may be modeled with a number of simple linear inequalities. Equitable properties of the solution concept are examined. 相似文献
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Brian H. Gilding Mohammed Guedda 《Journal of Mathematical Analysis and Applications》2003,284(2):733-755
With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. 相似文献
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含有批处理机的三机流水作业加工总长问题在某些情形下的强NP困难性 总被引:2,自引:0,他引:2
本文研究含有批处理机的三台机器流水作业加工总长问题在某些情形下的计算复杂性。在批处理机上同时加工的工件组成一个工件批,一个工件批的所有工件同时开始、同时结束。当批处理机的容量有限时,我们证明了下列情形为强NP困难的:第一台机器是批处理机、其余两台机器是单机;第二台机器是单机、其余两台机器是批处理机;第三台机器是批处理机、其余两台机器是单机。 相似文献
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It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
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The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning
precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be
able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening
of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are
highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete.
The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The
effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross
section are analyzed. A simple iterative design method for the shear debonding is finally proposed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008. 相似文献
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Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors. 相似文献
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K. Petras 《Constructive Approximation》1998,14(2):231-245
We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain
complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented.
This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error
constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas
and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively
for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally
symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the
optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the
constant weight function and arguments outside the interval of integration.
September 7, 1995. Date revised: October 25, 1996. 相似文献