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1.
We prove that on a closed, smooth, convex surface of revolution , whose poles are not flattening points, there exists only a countable set of parallels n. Each of these parallels cuts surface into two parts so that one of the parts, , admits nontrivial, infinitesimal bendings in the process of which all the points of its boundary n are displaced on a preassigned, conic sleeve K that is coaxial with the surface. The sequence of such parallels n converges to parallel *, which has the following properties: 1) the tangent cone to surface along * is orthogonal to sleeve K; 2) surface , cut off from surface by parallel *, has rigidity of first order in the indicated class of bendings.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 3–8, 1990.  相似文献   

2.
Let R(r, m) be the rth order Reed-Muller code of length 2 m , and let (r, m) be its covering radius. We prove that if 2 k m - r - 1, then (r + k, m + k) (r, m + 2(k - 1). We also prove that if m - r 4, 2 k m - r - 1, and R(r, m) has a coset with minimal weight (r, m) which does not contain any vector of weight (r, m) + 2, then (r + k, m + k) (r, m) + 2k(. These inequalities improve repeated use of the known result (r + 1, m + 1) (r, m).This work was supported by a grant from the Research Council of Wright State University.  相似文献   

3.
We obtain a bound for the error in the numerical integration of the quasilinear equation ut+((u))x=0 by a finite difference method in the case when (u)0.Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 207–215, February, 1973.  相似文献   

4.
5.
Let G denote a semisimple group, a discrete subgroup, B=G/P the Poisson boundary. Regarding invariants of discrete subgroups we prove, in particular, the following:(1) For any -quasi-invariant measure on B, and any probablity measure on , the norm of the operator () on L 2(B,) is equal to (), where is the unitary representation in L 2(X,), and is the regular representation of .(2) In particular this estimate holds when is Lebesgue measure on B, a Patterson–Sullivan measure, or a -stationary measure, and implies explicit lower bounds for the displacement and Margulis number of (w.r.t. a finite generating set), the dimension of the conformal density, the -entropy of the measure, and Lyapunov exponents of .(3) In particular, when G=PSL2() and is free, the new lower bound of the displacement is somewhat smaller than the Culler–Shalen bound (which requires an additional assumption) and is greater than the standard ball-packing bound.We also prove that ()=G() for any amenable action of G and L 1(G), and conversely, give a spectral criterion for amenability of an action of G under certain natural dynamical conditions. In addition, we establish a uniform lower bound for the -entropy of any measure quasi-invariant under the action of a group with property T, and use this fact to construct an interesting class of actions of such groups, related to 'virtual' maximal parabolic subgroups. Most of the results hold in fact in greater generality, and apply for instance when G is any semi-simple algebraic group, or when is any word-hyperbolic group, acting on their Poisson boundary, for example.  相似文献   

6.
Let {T1, ..., TN} be a finite set of linear contraction mappings of a Hilbert space H into itself, and let r be a mapping from the natural numbers N to {1, ..., N}. One can form Sn=Tr(n)...Tr(1) which could be described as a random product of the Ti's. Roughly, the Sn converge strongly in the mean, but additional side conditions are necessary to ensure uniform, strong or weak convergence. We examine contractions with three such conditions. (W): xn1, Txn1 implies (I-T)xn0 weakly, (S): xn1, Txn1 implies (I-T)xn0 strongly, and (K): there exists a constant K>0 such that for all x, (I-T)x2K(x2–Tx2).We have three main results in the event that the Ti's are compact contractions. First, if r assumes each value infinitely often, then Sn converges uniformly to the projection Q on the subspace i= 1 N [x|Tix=x]. Secondly we prove that for such compact contractions, the three conditions (W), (S), and (K) are equivalent. Finally if S=S(T1, ..., TN) denotes the algebraic semigroup generated by the Ti's, then there exists a fixed positive constant K such that each element in S satisfies (K) with that K.  相似文献   

7.
Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in 2n+1. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions.  相似文献   

8.
9.
Given a ratio , >>0, and a triangle ABC, on the sides and , using ratios , and , three circles of Apollonius are denned. In this paper, we will show that the three centers are collinear, the circles are coaxal and develop a necessary and sufficient condition that these circles intersect. J. A. Hoskins, W. D. Hoskins and R. G. Stanton obtained these results in a recent paper using algebraic computation. Our aim is to establish all these results using only results from elementary Euclidean geometry and thereby uncovering more geometric insights and avoid lengthy calculations.  相似文献   

10.
, ( ) . , : , , .

This research was partially supported by National Science Foundation under grant INT-8400708.  相似文献   

11.
( ) . .

Dedicated to Professor K. Tandori on his seventieth birthday

This research was supported in part by Grant # K41 100 of the Joint Fund of the Government of Ukraine and the International Science Foundation.  相似文献   

12.
13.
(r k ) - , +1 –1 1/2. =( i ) , 0< 1 p ... n ... . (a i )M. (a i ) . , [2], .  相似文献   

14.
Let be a ball in N, centered at zero, and letu be a minimizer of the nonconvex functional over one of the classesC M := {w W loc 1, () 0 w(x) M in,w concave} orE M := {w W loc 1,2 () 0 w(x) M in,w 0 inL()}of admissible functions. Thenu is not radial and not unique. Therefore one can further reduce the resistance of Newton's rotational body of minimal resistance through symmetry breaking.  相似文献   

15.
We give a new2 index theorem for the basic example of Toeplitz operators on the circle. The joint torsion, a non zero complex valued analytic index, of a pair of Fredholm Toeplitz operatorsT andT withH symbols is computed by residues in the disk, and is determined by a monodromy integral which specifies the isomorphism class of a flat line bundle on the circle. When the symbols and are rational a product of joint torsions identifies the isomorphism class of the bundle inH 1 (S 1,C *), and the identification extends by rational approximation to the case of smooth symbols defined on the circle.Partially supported by National Science Foundation grants to both authors.  相似文献   

16.
Summary In this paper we give necessary and sufficient conditions for the superposition operator Fx(s)=f(s, x(s)) to satisfy a Lipschitz condition Fx1 - Fx2kx1 - x2 or a Darbo condition (FN)k(N) in ideal spaces of measurable functions, where is the Hausdorff measure of noncompactness. Moreover, we characterize a large class of spaces in which the above mentioned two conditions are equivalent.
Sunto In questo lavoro diamo delle condizioni necessarie e sufficienti perchè l'operatore di sovrapposizione Fx(s)=f (s, x(s)) soddisfi alla condizione di Lipschitz Fx1–Fx2 kx1–x2 o quella di Darbo (FN)k(N) in spazi ideali di funzioni misurabili, ove è la misura di non compattezza di Hausdorff. Inoltre, caratterizziamo un'ampia classe di spazi in cui le suddette due condizioni sono equivalenti.
  相似文献   

17.
The main result is the following theorem. Let be a commutative Banach algebra with radical R, where the factor algebra is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rn1 /n 0 as n uniformly for r R, rl, then the algebra is strongly decomposable, i.e., there exists a closed subalgebra B isomorphic to such that =BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed . There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967.  相似文献   

18.
19.
Summary This paper is concerned with the rate of convergence to zero of theL pmetrics np1p, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that the np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1p, p, np/np is universally bounded away from zero and infinity asn.  相似文献   

20.
The effect of the relaxation time spectrum on the critical, i.e., limiting, conditions of stable shear flow of viscoelastic liquids at small Reynolds numbers was investigated. The approach developed in [1] was generalized to the Zimm, Rouse, Spriggs, and Ferry-Landel-Williams (FLW) viscoelastic relaxation time spectra. The FLW spectrum depicts the plateau of the viscoelasticity of high-molecular-weight polymer melts. The problem of the frequency dependence of the components of the complex shear modulus at different steady-state flow rates for the case of periodic shear directed both parallel to steady-state flow and orthogonal to it was solved for all of the listed models. The results of the experiment on superposition of periodic shear on the steady-state flow of a moderately concentrated solution of polyisobutylene were compared with the results of calculating the effect of steady-state flow on the frequency viscoelastic functions for liquids whose viscoelasticity is approximated by a Spriggs relaxation time spectrum. The calculation showed that in flow of liquids approximated by Rouse, Zimm, or Spriggs spectra, only parallel and orthogonal elastic losses of stability occur and dissipative loss of stability does not. Three types of instability (two elastic — parallel and orthogonal - and one dissipative — parallel) predict the prospects for use of the FLW spectrum. For this model, like the models using the Rouse and Zimm spectra, the shear rate at which instability is generated, especially dissipative instability, is a function of the number of relaxation times considered in the calculation. It was found that the predicted generation of dissipative instability begins for shear rates qD* greater than the critical rates of generation of elastic parallel qE* and elastic orthogonal qE* instabilities, in contrast to the ZFD model which predicts that qE*<qD*<qE*. The critical shear rates are correlated with the appearance of supermolecular viscoelastic structures caused by shear flow, called elastic-dissipative by analogy with dissipative structures.For communication 1 see [1].Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 119–135, January–February, 1997.  相似文献   

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