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1.
Extremals for constrained minimization problems, min F, are classified according to the growth properties of the linear functionalF() restricted to . Various singular and nonsingular extremal types are investigated in detail for the special case where = {measurableu(·): [0, 1] U},U = a bounded polyhedral convex set in m , andF is understood in Fréchet's sense relative to anL p norm withp [1, ). The analysis yields newL p minimization corollaries of recently developed general convergence rate theories for conditional and projected gradient methods, and a Newton method for constrained minimization. These results help to explain trends in the behavior of computational procedures for certain large scale structured nonlinear programs in k ask increases to , with particular application to a large class of optimal control problems with linearly constrained inputs; control problems with bang-bang solutions are considered at some length.Investigation supported by NSF Research Grants ECS-8005958 and ENG 78-03385.  相似文献   

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3.
LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.  相似文献   

4.
Let (,A,P) denote some probability space and some sub--algebra ofA. It is shown that there exists a semiregular versionQ (A),A, , of the conditional distributionP(A|), AA, i.e., Q (A), (AA fixed) is andAQ (A),AA ( fixed), is a probability charge satisfyingQ (N)=0, , for allP-zero setsN, if and only ifL 1(,P|) has a lifting, which exists for any sub--algebra ofA ifL 1(,A P) is separable. Separability ofL 1(,A,P) implies also the existence of a strongly semiregular versionQ (A),A, , ofP(A|), A , i.e., Q (A), (AA fixed), is -measurable andAQ (A),A ( fixed), is a probability charge. Furthermore,P can be written as P 1+(1–)P 2, 01, whereP 1 are probability measures onA such thatP 1(A|),AA, has a semiregular version vanishing for anyP-zero setN andP 2 is singular with respect to any probability measure onA of the type ofP 1. In the case 0<<1 the probability measuresP j ,j=1, 2, are uniquely determined. The decomposition can be carried over to the case, where the additional condition thatQ (N)=0 for all and anyP-zero setN is valid, is omitted respectively semiregularity is replaced by (i) strong semiregularity, or (ii) classical regularity. In the last mentioned case (ii) the decomposition is multiplicative.  相似文献   

5.
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc (k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying for fixed , contains at leastc convex independent points. We determine the exact asymptotic behavior ofc (k), proving that there are two positive constants=(), such thatk 1/3c (k)k 1/3. To establish the upper bound ofc (k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying . The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties.  相似文献   

6.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K 1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K 1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism.  相似文献   

7.
Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))2. LetH(x) be an arbitrary primitive of 1/h –1(x). Note that the functionH –1 x is positive and increasing on (–, +),H –1 0 asx– andH –1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000.  相似文献   

8.
We prove that the Hessian matrix of the real period function () associated with the real versal deformation f (x)=±x 4+2 x 2+1 x+0 of a singularity of type A 3, is nondegenerate, provided that 3 does not belong to the discriminant set of the singularity. We explain the relation between this result and the perturbations of the spherical pendulum.  相似文献   

9.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in p , n , respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in n . The function c: p+n is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in n . Computational experiments show that the resulting algorithms work well for problems with smalln.  相似文献   

10.
We obtain the analytic expression for the total cross section of the reaction e e +l l + (l=,) taking possible quasianapole interaction effects into account. We find numerical restrictions on the interaction parameter value from data for the reaction e e ++ in the energy domain below the Z 0 peak.  相似文献   

11.
On the distribution of square-full and cube-full integers   总被引:1,自引:0,他引:1  
LetN r (x) be the number ofr-full integers x and let r (x) be the error term in the asymptotic formula forN r (x). Under Riemann's hypothesis, we prove the estimates 2(x)x1/7+, 3(x)x97/804+(>0), which improve those of Cao and Nowak. We also investigate the distribution ofr-full andl-free numbers in short intervals (r=2,3). Our results sharpen Krätzel's estimates.  相似文献   

12.
Summary The following Artin type characterization of : + + is proved: Assume thatf: + + satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on [l/p, 1 + ] for some > 0 and lim x 0 xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation.  相似文献   

13.
We will investigate the properties of series of functions which are unconditionally convergent almost everywhere on [0, 1]. We will establish the following theorem: If the series k=1 f k(x) converges unconditionally almost everywhere, then there exists a sequence {k} 1 ,k , such that if k k , k=1, 2,..., the series k=1 k/k(x) converges unconditionally almost every-where.Translated from Mate matte heskie Zametki, Vol. 14, No. 5, pp. 645–654, November, 1973.The author wishes to thank Professor P. L. Ul'yanov for his help.  相似文献   

14.
IfA andB are two bounded domains in n and (A), (B) are the lowest eigenvalues of – with Dirichlet boundary conditions then there is some translate,B x, ofB such that (AB x)<(A)+(B). A similar inequality holds for .There are two corollaries of this theorem: (i) A lower bound for sup x {volume (AB x)} in terms of (A), whenB is a ball; (ii) A compactness lemma for certain sequences inW 1,p ( n ).Work partially supported by U.S. National Science Foundation grant PHY-8116101 A01. AMS(MOS) Classification: 35P15  相似文献   

15.
We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in n . We first estimate the kinematic formula for the total scalar curvature D 0gD 1 Rdv of then–2 dimensional intersection submanifold D 0gD 1. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in n (4). Forn=4, we directly obtain another sufficient condition in 4.  相似文献   

16.
Analysis is presented for the heat transfer performance of square ducts with internal fins from each wall in the case of combined free and forced convection by fully developed laminar flow. Numerical results are obtained for the Nusselt number and the pressure drop parameter for various values of finlengths and heat source parameter. For various values of Rayleigh numbers, the Nusselt number increases with the increase in finlength and decreases with the increase in heat source parameter.
Zusammenfassung Es wird eine Analyse für den Wärmeaustausch von quadratischen Rohren mit inneren Rippen an jeder Wand im Falle einer Kombination von freier und erzwungener Konvektion bei voll entwickelter laminarer Strömung gegeben. Numerische Resultate für die Nusselt-Zahl und den Druckabfall-Koeffizienten für verschiedene Rippenbreiten und Parameter der Wärmequelle werden erhalten. Für einige Werte der Rayleighzahl wächst die Nusselt-Zahl mit der Rippenbreite und fällt mit wachsendem Parameter der Wärmequelle.

Nomenclature A cross sectional area of the duct - B 2k Bernoulli numbers - c p specific heat at constant pressure - D h hydraulic diameter of finless duct - E n complex constants (20) - F heat source parameter,Q/c p - F n () defined by Equation (14) - G(, , , ) Green's function (15, 16) - g gravitational acceleration - H() Heaviside function - h() defined by Equation (22) - i imaginary unit,i 2=–1 - ImW imaginary part ofW - K(,t) kernel of the integral equation, defined by (25) - k thermal conductivity - L pressure drop parameter, –D h 2 (p/x+ w )/ - l fin length of each fin, Figure (1) - N u Nusselt number, Equation (32) - p pressure - Q heat generation rate - R() defined by Equation (26) - R A Rayleigh number, w gc p D h 4 /k - ReW real part ofW - T dimensionless temperature, (tt w )/(c p D h 2 /k) - T mx dimensionless mixed mean temperature, Equation (33) - t fluid temperature - t 0 reference temperature atx=0 - u local axial velocity - mean axial velocity - V u/ - W complex function defined by Equation (6) - w suffix denoting wall conditions - W 0 defined by Equation (9) - W 1 WW 0, Equation (18) - x axial coordinate along the length of the duct - y, z cross-sectional coordinates - constant temperature gradient, t/x - coefficient of thermal expansion of the fluid - fluid density - n - dynamic viscosity - () Dirac delta function - 2 Laplacian operator, 2/y 2/2/z 2 - , y/D h ,z/D h   相似文献   

17.
For any finite groupG we construct examples of an AF algebraA and an action byG onA such that the fixed point algebra is not AF. The construction ofA is done by successive foldings and cuttings of the interval in a way originally suggested by Blackadar and, in a different context, by Connes in his talk in Oslo in 1978.  相似文献   

18.
19.
Summary Let P be a Markov operator on L (X, , m). Theorem 1: (i) P is weakly mixing (ii) For every fL there is a sequence {nt} of density 1 such that all w *-cluster points of are constants (iii) For every fL there is a {kj} with w *-convergent to a constant. Theorem 2: If P is induced by a non-singular transformation , P is weakly mixing For every A, { –n(A)} has a remotely trivial subsequence. The existence of a finite invariant measure is not required in these results.  相似文献   

20.
We investigate the category mod of finite length modules over the ring =A k , where is a V-ring, i.e. a ring for which every simple module is injective, k a subfield of its centre and A an elementary k-algebra. Each simple module E j gives rise to a quasiprogenerator P j = A E j . By a result of K. Fuller, P j induces a category equivalence from which we deduce that mod j mod EndP j . As a consequence we can(1) construct for each elementary k-algebra A over a finite field k a nonartinian noetherian ring such that modA mod(2) find twisted versions of algebras of wild representation type such that itself is of finite or tame representation type (in mod)(3) describe for certain rings the minimal almost split morphisms in mod and observe that almost all of these maps are not almost split in Mod.  相似文献   

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