Trend/Cycle decomposition

Author(s):  
Charles R. Nelson
Keyword(s):  
2012 ◽  
Author(s):  
Mardi H. Dungey ◽  
Jan P. A. M. Jacobs ◽  
Jing Tian ◽  
Simon van Norden

Author(s):  
Jiami Yang ◽  
Yong Zeng ◽  
Stephen Ekwaro-Osire ◽  
Abraham Nispel ◽  
Hua Ge

As sustainability becomes increasingly important, product design is taking a proactive role in producing products that are both useful and sustainable. This paper introduces and discusses a tool named Environment-based life cycle decomposition (eLCD) to adapt the Environment-based Design (EBD) methodology to sustainable design. The eLCD brings to EBD three major features: 1) a holistic environment structure for sustainable conceptual design, 2) an effective and efficient tool for collecting information for sustainability decision-making, and 3) an analysis tool that takes sustainability as an integral part of the design rather than as a burden. The environment of a product is everything except the product itself, which can be defined in three dimensions, namely, environment types, life cycle events, and life cycle time. The environment types are designated as natural, built (including physical artifact and digital artifact), economic, and social environment. The eLCD provides an effective template for information collection to support the design decision-making process. The effectiveness of eLCD is demonstrated by its application to the upscaling of a wind turbine, where an energy storage system is introduced to make full use of wind energy with the least waste in serving the electricity demand.


2014 ◽  
Vol 19 (4) ◽  
pp. 776-790 ◽  
Author(s):  
Mardi Dungey ◽  
Jan P.A.M. Jacobs ◽  
Jing Tian ◽  
Simon van Norden

A well-documented property of the Beveridge–Nelson trend–cycle decomposition is the perfect negative correlation between trend and cycle innovations. We show how this may be consistent with a structural model where permanent innovations enter the cycle or transitory innovations enter the trend, and that identification restrictions are necessary to make this structural distinction. A reduced-form unrestricted version is compatible with either option, but cannot distinguish which is relevant. We discuss economic interpretations and implications using U.S. real GDP data.


Author(s):  
FRANCO FAGNOLA ◽  
VERONICA UMANITÀ

A generic quantum Markov semigroup [Formula: see text] of a d-level quantum open system with a faithful normal invariant state ρ admits a dual semigroup [Formula: see text] with respect to the scalar product induced by ρ. We show that the difference of the generators [Formula: see text] can be written as the sum of a derivation 2i[H, ⋅] and a weighted difference of automorphisms [Formula: see text] where [Formula: see text] is a family of cycles on the d levels of the system, wc are positive weights and [Formula: see text] are unitaries. This formula allows us to represent the deviation from equilibrium (in a "small" time interval) as the superposition of cycles of the system where the difference between the forward and backward evolution is written as the difference of a reversible evolution and its time reversal. Moreover, it generalises cycle decomposition of Markov jump processes. We also find a similar formula with partial isometries instead of unitaries.


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