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31.
Let B be the open unit ball of a complex Banach space X and let B be homogeneous. We prove distortion results for normalized convex mappings f:B→X which generalize various finite dimensional distortion theorems and improve some infinite dimensional ones. In particular, our results are valid for the open unit balls of complex Hilbert spaces and the Cartan domains. 相似文献
32.
In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ1 and ℓ2 norms. These inverse optimization problems are either linear programming when ℓ1 norm is used in the formulation, or convex quadratic separable programming when ℓ2 norm is used. 相似文献
33.
Zhipeng Qiu 《Applied mathematics and computation》2010,216(5):1553-1565
In this paper, a 3(n+1) dimensional sexually transmitted disease model is studied. The model involves two competing strains 1 and 2, where females are divided into n different groups based on their susceptibility to two distinct pathogenic strains. The first and second reproduction numbers , which have their biological meaning, are defined for strain , respectively. With the non-degeneracy assumption (H), a complete classification for dynamics of this model in terms of is presented, which is based on the theory of type-K monotone dynamical systems. 相似文献
34.
To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First
we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then,
to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results
are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale
problems. 相似文献
35.
The spatial inhomogeneity of pulsed atmospheric pressure discharge in argon is investigated using the electron number density Ne diagnostics procedure applied to asymmetrically broadened Ar I lines. A dedicated fitting procedure is used for describing Ar I 703.0 nm line shape recorded from argon gas discharge and H I (at 486.13 and 656.28 nm) lines recorded from Ar-H2 gas mixture discharge. The results revealed the change in Ne in both axial and radial directions. The additional Ar I lines at 614.5, 710.7, 731.2, and 731.6 nm, recorded from integral spatial radiation, are analysed as well to confirm the results from the plasma column region. The possibility of using AlO (B2∑+–X2∑+) and CN (B2∑+–X2∑+) molecular bands for gas temperature Tg measurements in this type of gas discharge source is demonstrated and Tg used as an input parameter for the Ne diagnostics procedure. For the proper identification of molecular band spectral lines, the Fortrat parabolas are constructed. The results obtained from Ar I 703.0 nm line indicate three different Ne values, with Ne1 ≈ 0.6 × 1016 cm−3, Ne2 ≈ 3.6 × 1016 cm−3, and Ne3 ≈ 19 × 1016 cm−3 measured from the plasma column. These Ne values increase in the cathode and anode region. 相似文献
36.
Elmor L. Peterson 《Mathematical Programming》1977,12(1):392-405
F.E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A.C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied.We also show that the regularity condition is so weak that it is automatically satisfied in linear programming (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints),l
p
-regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-73-2516. 相似文献
37.
Gur Huberman 《Mathematical Programming》1983,26(1):100-108
Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate
an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating
program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between
the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear
programming. Also, we apply our bounds to a convex transportation problem.
Thanks are due to Ron Dembo, Paul Zipkin and the referees for valuable comments. This research was supported by NSF Grant
ENG-76-15599. 相似文献
38.
To investigate the structure of number sense and then to assess its uses in fifth‐grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and substantially valid. It can be reliably used as a screening measure for a quick check of students' number sense development via online self‐assessment. Compared with our previous study, both qualitative and quantitative changes were detected in students' number sense development at different grades. The qualitative change in number sense development is manifested in different numbers of factor components produced at different grades. The quantitative change is manifested in different amounts of factor variance explained at different grades. Furthermore, among the four aspects of number sense, Taiwanese students perform best on recognizing the relative number size yet relatively worse on judging the reasonableness of computational results. 相似文献
39.
Characteristic Numbers of Matrix Lie Algebras 总被引:1,自引:0,他引:1
ZHANG Yu-Feng FAN En-Gui 《理论物理通讯》2008,49(4):845-850
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras. 相似文献
40.
Gerd Niestegge 《Foundations of Physics》2008,38(9):783-795
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach
is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as
a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces
with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces
become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras. 相似文献