scholarly journals Erratum to: General equilibrium second-order hydrodynamic coefficients for free quantum fields

2018 ◽  
Vol 2018 (7) ◽  
Author(s):  
M. Buzzegoli ◽  
E. Grossi ◽  
F. Becattini
Keyword(s):  
General Equilibrium ◽  
Second Order ◽  
Hydrodynamic Coefficients ◽  
Quantum Fields

JEEA-FBBVA Lecture 2018: The Microeconomic Foundations of Aggregate Production Functions

2019 ◽  
Vol 17 (5) ◽  
pp. 1337-1392
Author(s):  
David Rezza Baqaee ◽  
Emmanuel Farhi
Keyword(s):  
General Equilibrium ◽  
Technical Change ◽  
Second Order ◽  
Production Functions ◽  
Reduced Form ◽  
Input Output ◽  
Aggregate Production ◽  
General Methodology ◽  
Microeconomic Foundations

Abstract Aggregate production functions are reduced-form relationships that emerge endogenously from input–output interactions between heterogeneous producers and factors in general equilibrium. We provide a general methodology for analyzing such aggregate production functions by deriving their first- and second-order properties. Our aggregation formulas provide nonparametric characterizations of the macroelasticities of substitution between factors and of the macrobias of technical change in terms of microsufficient statistics. They allow us to generalize existing aggregation theorems and to derive new ones. We relate our results to the famous Cambridge–Cambridge controversy.

OCTONIC FIRST-ORDER EQUATIONS OF RELATIVISTIC QUANTUM MECHANICS

2009 ◽  
Vol 24 (22) ◽  
pp. 4157-4167 ◽  
Author(s):  
VICTOR L. MIRONOV ◽  
SERGEY V. MIRONOV
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Maxwell Equations ◽  
Relativistic Quantum ◽  
Order Equation ◽  
Second Order ◽  
Relativistic Quantum Mechanics ◽  
Quantum Fields ◽  
First Order ◽  
Spatial Operators

We demonstrate a generalization of relativistic quantum mechanics using eight-component octonic wave function and octonic spatial operators. It is shown that the second-order equation for octonic wave function describing particles with spin 1/2 can be reformulated in the form of a system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special types of wave functions the second-order equation can be reduced to the single first-order equation analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not have quantum fields.

Optimal Expectations

2005 ◽  
Vol 95 (4) ◽  
pp. 1092-1118 ◽  
Author(s):  
Markus K Brunnermeier ◽  
Jonathan A Parker
Keyword(s):  
Decision Making ◽  
General Equilibrium ◽  
Portfolio Choice ◽  
Second Order ◽  
Optimistic Bias ◽  
Prior Beliefs ◽  
First Order ◽  
Future Utility ◽  
Consumption Saving ◽  
Forward Looking

Forward-looking agents care about expected future utility flows, and hence have higher current felicity if they are optimistic. This paper studies utility-based biases in beliefs by supposing that beliefs maximize average felicity, optimally balancing this benefit of optimism against the costs of worse decision making. A small optimistic bias in beliefs typically leads to first-order gains in anticipatory utility and only second-order costs in realized outcomes. In a portfolio choice example, investors overestimate their return and exhibit a preference for skewness; in general equilibrium, investors' prior beliefs are endogenously heterogeneous. In a consumption-saving example, consumers are both overconfident and overoptimistic.

scholarly journals Peculiarities of Zigzag Behaviour in Linear Models of Ship Yaw Motion

2016 ◽  
Vol 23 (1) ◽  
pp. 23-38
Author(s):  
Jarosław Artyszuk
Keyword(s):  
Linear Models ◽  
Nonlinear Models ◽  
Second Order ◽  
Hydrodynamic Coefficients ◽  
Quality Indices ◽  
Order Model ◽  
Present Survey ◽  
Time Constants ◽  
First Order ◽  
Ship Steering

Abstract The present survey, as part of larger project, is devoted to properties of pure linear models of yaw motion for directionally stable ships, of the first- and second-order, sometimes referred to as the Nomoto models. In rather exhaustive way, it exactly compares and explains both models in that what is being lost in the zigzag behaviour, if the reduction to the simpler, first-order dynamics (K-T model) is attempted with the very famous [Nomoto et al., 1957] approximation: T = T1 + T2 - T3. The latter three time constants of the second-order model, more physically sound, are strictly dependent on the hydrodynamic coefficients of an essential part of the background full-mission manoeuvring model. The approximation of real ship behaviour in either of the mentioned linearity orders, and the corresponding complex parameters may facilitate designing and evaluating ship steering, and identifying some regions of advanced nonlinear models, where linearisation is valid.As a novel outcome of the conducted investigation, a huge inadequacy of such a first- -order model for zigzag simulation is reported. If this procedure is used for determining steering quality indices, those would be of course inadequate, and the process of utilizing them (e.g. autopilot) inefficient.

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