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相似文献
32.
Bjorn Poonen 《Journal of the American Mathematical Society》1996,9(3):783-812
Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing
which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module. 33.
A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units to=h/moc2 for a particle at rest, and of similar interval unit so when in relative motion, with conventional relativistic corrections.
For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. to and so are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept. 相似文献 34.
N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1991,68(2):305-320
In this paper, we consider a sequence of abstract optimal control problems by allowing the cost integrand, the partial differential operator, and the control constraint set all to vary simultaneously. Using the notions of -convergence of functions,G-convergence of operators, and Kuratowski-Mosco convergence of sets, we show that the values of the approximating problems converge to that of the limit problem. Also we show that a convergent sequence of optimal pairs for the approximating problems has a limit which is optimal for the limit problem. A concrete example of parabolic optimal control problems is worked out in detail.This research was supported by NSF Grant No. DMS-88-02688. 相似文献
35.
In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g
1,g
2) andS = S
1 ×S
2,S
i
are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg
i
are, respectively, convex andS
i
-convex,i = 1, 2. In particular, we consider the special case whenS
2 is in afinite dimensional space,g
2 is affine andS
2 is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g
2 is affine andS = S
2 is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong
2 and the finite dimensionality assumption onS
2, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones. 相似文献
36.
Improved estimation of duality gap in binary quadratic programming using a weighted distance measure
We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations. 相似文献
37.
The classical Discrete Fourier Transform (DFT) satisfies a duality property that transforms a discrete time signal to the frequency domain and back to the original domain. In doing so, the original signal is reversed to within a multiplicative factor, namely the dimension of the transformation matrix. In this paper, we prove that the DFT based on Simpson's method satisfies a similar property and illustrate its effect on a real discrete signal. The duality property is particularly useful in determining the components of the transformation matrix as well as components of its positive integral powers. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
38.
Martin Forde 《Stochastic Processes and their Applications》2019,129(3):799-821
We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability where can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.1 相似文献
39.
40.
Pham Duy Khanh Tran Hong Mo Trinh T. T. Tran 《Numerical Functional Analysis & Optimization》2019,40(8):924-943
Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example. 相似文献
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