Complements on Duality: Economic Interpretation of Dual Variables

1983 ◽  
pp. 142-155
Author(s):  
Michel Sakarovitch
Keyword(s):  
Economic Interpretation ◽  
Dual Variables

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

AN ECONOMIC INTERPRETATION OF VOTING BEHAVIOUR ON PUBLIC FINANCE ISSUES

Kyklos ◽  
1970 ◽  
Vol 23 (4) ◽  
pp. 792-805 ◽  
Author(s):  
RenÉ L. Frey ◽  
Leopold Kohn
Keyword(s):  
Public Finance ◽  
Voting Behaviour ◽  
Economic Interpretation

Mexico's Pre-Revolutionary Reckoning with Railroads

1985 ◽  
Vol 42 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Robert W. Randall
Keyword(s):  
Economic Growth ◽  
Economic Theory ◽  
Transportation Network ◽  
Underdeveloped Country ◽  
Role Of The State ◽  
Economic Interpretation ◽  
Short Run ◽  
Railway System ◽  
Economic Considerations

Economic considerations all but dominate recent historical writing in this country about the railroads of Mexico. Technical matters of construction and operation, as well as the role of the state in both, are touched upon, but economic interpretation, whether of the development of a railway system or of its impact on the nation, is the watchword if not catchword of most writing. Probably the leading example of the dominant approach is Growth against Development: The Economic Impact of Railroads in Porfirian Mexico (Northern Illinois University Press, 1981), by John H. Coatsworth, in which the author concludes that, while “the short run contribution of railroads to economic growth was large,” their longrun impact helped “to create the underdeveloped country Mexico has become.” Applying economic theory and measuring, Coatsworth in essence proves with numbers a case argued more elegantly in straight prose early in this century: that the application of a modern transportation network to a staple producing economy will do little more than extend and intensify the production system so as to increase the staple output.

scholarly journals A HYBRID COLUMN GENERATION ALGORITHM BASED ON METAHEURISTIC OPTIMIZATION

Transport ◽  
2013 ◽  
Vol 31 (4) ◽  
pp. 389-407 ◽  
Author(s):  
Wenbin Hu ◽  
Bo Du ◽  
Ye Wu ◽  
Huangle Liang ◽  
Chao Peng ◽  
...  
Keyword(s):  
Column Generation ◽  
Time Windows ◽  
Path Selection ◽  
Optimization Strategy ◽  
Heuristic Solution ◽  
Generation Algorithm ◽  
Metaheuristic Optimization ◽  
Selection Strategies ◽  
Dual Variables ◽  
Labelling Algorithm

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid Column Generation Algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling Algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two pathkeeping conditions in the main problem.

PREDICTING RETURNS IN US TREASURIES: DO TENTS MATTER?

2018 ◽  
Vol 21 (07) ◽  
pp. 1850047
Author(s):  
R. REBONATO
Keyword(s):  
Economic Significance ◽  
Predicting Factors ◽  
Economic Interpretation ◽  
High Predictability ◽  
New Generation

We look at the economic significance and at the robustness of the new-generation, tent-shaped return-predicting factors in US Treasuries. We find that, in itself, the precise tent shape is neither robust nor important for predictability. However, we explain why the high number of regressors needed to build a tent factor are required for high predictability, and we provide an economic interpretation for the finding.

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