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951.
An unsteady flow of viscous incompressible fluid past a sphere is investigated. The values of the inertial and unsteady terms in the Navier-Stokes equations are characterized by translational (R) and vibrational (Rk) Reynolds numbers, which are assumed small. The solution is constructed in the form of an expansion with respect to max(R, R
k
1/2
) by the method of matched asymptotic expansions. A correction to the Stokes force, correct to o[max(R, R
k
1/2
)], is calculated. It is shown that the result depends strongly on the ratio R/R
k
1/2
and goes over into the well-known equations for the cases R 0, Rk 0.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 11–16, January–February, 1988. 相似文献
952.
953.
The free in-plane vibrations of circular rings with wheel-plates as generalised elastic foundations are studied using analytical methods and numerical simulations. The three-parameter Winkler elastic layer is proposed as a mathematical model of the foundation. The effects of rotary inertia and shear deformation are included in the analytical model of the system. The motion equations of systems are derived on the basis of the thin ring theory and Timoshenko?s theory. The separation of variables method is used to find general solutions to the free vibrations. Elaborated analytical models are used to determine the natural frequencies and the natural mode shapes of vibrations of an arbitrarily chosen set of simplified models of aviation gears and railway wheels. The eigenvalue problem is formulated and solved by using a finite element representation for each simplified model. The results for these models are discussed and compared. The proposed solutions are verified by experimental investigation. It is important to note that the solutions proposed here could be useful to engineers dealing with the dynamics of aviation gears, railway wheels and other circular ring systems. 相似文献
954.
A high-accuracy Runge-Kutta/WENO method of up to fourth order with respect to time and fifth order with respect to space is developed for the numerical modeling of small-amplitude wave propagation in a steady fluid-saturated elastic porous medium. A system of governing equations is derived from a general thermodynamically consistent model of a compressible fluid flow through a saturated elastic porous medium, which is described by a hyperbolic system of conservation laws with allowance for finite deformations of the medium. The results of numerical solution of one- and two-dimensional wave fields demonstrate the efficiency of the method. 相似文献
955.
Roman Vershynin 《Random Structures and Algorithms》2014,44(2):135-182
We study symmetric random matrices H, possibly discrete, with iid above‐diagonal entries. We show that H is singular with probability at most , and . Furthermore, the spectrum of H is delocalized on the optimal scale . These results improve upon a polynomial singularity bound due to Costello, Tao and Vu, and they generalize, up to constant factors, results of Tao and Vu, and Erdös, Schlein and Yau.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 135‐182, 2014 相似文献
956.
We report the heteroepitaxial growth of SrTiO3 thin films on Si(001) by hybrid molecular beam epitaxy (hMBE). Here, elemental strontium and the metal‐organic precursor titanium tetraisopropoxide (TTIP) were co‐supplied in the absence of additional oxygen. The carbonization of pristine Si surfaces during native oxide removal was avoided by freshly evaporating Sr into the hMBE reactor prior to loading samples. Nucleation, growth and crystallization behavior as well a structural properties and film surfaces were characterized for a series of 46‐nm‐thick SrTiO3 films grown with varying Sr to TTIP fluxes to study the effect of non‐stoichiometric growth conditions on film lattice parameter and surface morphology. High quality SrTiO3 thin films with epitaxial relationship (001)SrTiO3 || (001)Si and [110]SrTiO3 || [100]Si were demonstrated with an amorphous layer of around 4 nm thickness formed at the SrTiO3/Si interface. The successful growth of high quality SrTiO3 thin films with atomically smooth surfaces using a thin film technique with scalable growth rates provides a promising route towards heterogeneous integration of functional oxides on Si. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim) 相似文献
957.
We present a new method called UTAGMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMS–INT is a general additive value function augmented by two types of components corresponding to “bonus” or “penalty” values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTAGMS–INT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTAGMS–INT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral. 相似文献
958.
We show that, for any prime power $n$ and any convex body $K$ (i.e., a compact convex set with interior) in $\mathbb{R }^d$ , there exists a partition of $K$ into $n$ convex sets with equal volumes and equal surface areas. Similar results regarding equipartitions with respect to continuous functionals and absolutely continuous measures on convex bodies are also proven. These include a generalization of the ham-sandwich theorem to arbitrary number of convex pieces confirming a conjecture of Kaneko and Kano, a similar generalization of perfect partitions of a cake and its icing, and a generalization of the Gromov–Borsuk–Ulam theorem for convex sets in the model spaces of constant curvature. 相似文献
959.
Roman Frič 《Mathematica Slovaca》2014,64(3):545-554
D-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized. We present a classification of D-posets leading to a hierarchy of distinguished subcategories of D-posets related to probability and study their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory. In particular, we describe the transition from the Boolean cogenerator {0, 1} to the fuzzy cogenerator [0, 1] and prove that the generated ?ukasiewicz tribes form an epireflective subcategory of the bold algebras. 相似文献
960.
Roman Tomaschitz 《Mathematical Methods in the Applied Sciences》2014,37(9):1249-1272
Weber integrals and Beltrami integrals are studied, which arise in the multipole expansions of spherical random fields. These integrals define spectral averages of squared spherical Bessel functions with Gaussian or exponentially cut power‐law densities. Finite series representations of the integrals are derived for integer power‐law index μ, which admit high‐precision evaluation at low and moderate Bessel index n. At high n, numerically tractable uniform asymptotic approximations are obtained on the basis of the Debye expansion of modified spherical Bessel functions in the case of Weber integrals. The high‐n approximation of Beltrami integrals can be reduced to Legendre asymptotics. The Airy approximation of Weber and Beltrami integrals is derived as well, and numerical tests are performed over a wide range of Bessel indices by comparing the exact finite series expansions of the integrals with their high‐index asymptotics. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献