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31.
Summary Forf ( C n() and 0 t x letJ n (f, t, x) = (–1)n f(–x)f (n)(t) +f(x)f (n) (–t). We prove that the only real-analytic functions satisfyingJ n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ 0 (f, x, x) 0 and 0 x (x – t)n – 1Jn(f, t, x)dt 0 (n 1).  相似文献   
32.
When the follower's optimality conditions are both necessary and sufficient, the nonlinear bilevel program can be solved as a global optimization problem. The complementary slackness condition is usually the complicating constraint in such problems. We show how this constraint can be replaced by an equivalent system of convex and separable quadratic constraints. In this paper, we propose different methods for finding the global minimum of a concave function subject to quadratic separable constraints. The first method is of the branch and bound type, and is based on rectangular partitions to obtain upper and lower bounds. Convergence of the proposed algorithm is also proved. For computational purposes, different procedures that accelerate the convergence of the proposed algorithm are analysed. The second method is based on piecewise linear approximations of the constraint functions. When the constraints are convex, the problem is reduced to global concave minimization subject to linear constraints. In the case of non-convex constraints, we use zero-one integer variables to linearize the constraints. The number of integer variables depends only on the concave parts of the constraint functions.Parts of the present paper were prepared while the second author was visiting Georgia Tech and the University of Florida.  相似文献   
33.
Let t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M n , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d t and, for each x M, we define a smooth real function x (t) : (1 + i (t)), where the i(t) are the eigenvalues of AA T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t , restricted to v at the point x -t M n.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that x ' (t) 0 for all x M and real t; then, if x t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.  相似文献   
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The Doss trick is employed to find solutions of Schrüdinger equations on symmetric spaces of compact type. The potentials and initial conditions are taken from an algebra of functions which admit an holomorphic extension to the complexification of the considered symmetric spaces.  相似文献   
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Areas of single-layer MoS2 film can be prepared in a tube furnace without the need for temperature control. The films were characterized by means of Raman spectroscopy, photoluminescence, low-energy electron diffraction and microscopy, and X-ray photoelectron spectroscopy and mapping. Transport measurements show n-doped material with a mobility of 0.26 cm2 V-1 s-1.  相似文献   
38.
On spanning tree problems with multiple objectives   总被引:4,自引:0,他引:4  
We investigate two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights. First, we want to minimize the maximum ofQ linear objective functions taken over the set of all spanning trees (max-linear spanning tree problem, ML-ST). Secondly, we look for efficient spanning trees (multi-criteria spanning tree problem, MC-ST).Problem ML-ST is shown to be NP-complete. An exact algorithm which is based on ranking is presented. The procedure can also be used as an approximation scheme. For solving the bicriterion MC-ST, which in the worst case may have an exponential number of efficient trees, a two-phase procedure is presented. Based on the computation of extremal efficient spanning trees we use neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.Partially supported by Deutsche Forschungsgemeinschaft and HCº Contract no. ERBCHRXCT 930087.Partially supported by Alexander von Humboldt-Stiftung.  相似文献   
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The application of a semiconductor-laser amplifier with reduced facet reflectivity as all-optical switch is described. An optical data signal is switched on and off with an extinction ratio of 10 dB when an optical control signal is turned on and off. The two optical signals are polarized perpendicularly to each other. The device was operated up to 100 MHz.Nanjing Institute of Posts and Telecommunication Nanjing, PR China  相似文献   
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