A model with closed form analytic solution for steady-state, closed-circuit comminution processes

1975 ◽  
Vol 11 (1) ◽  
pp. 87-88 ◽  
Author(s):  
R.P. Gardner ◽  
K. Verghese
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Analytic Solution ◽  
Closed Circuit

An investment model with entry and exit decisions

2000 ◽  
Vol 37 (2) ◽  
pp. 547-559 ◽  
Author(s):  
J. Kate Duckworth ◽  
Mihail Zervos
Keyword(s):  
Dynamic Programming ◽  
Closed Form ◽  
Production Scheduling ◽  
Analytic Solution ◽  
Investment Model ◽  
Programming Approach ◽  
Entry And Exit ◽  
Dynamic Programming Approach ◽  
Exit Decisions ◽  
Parameter Values

We consider an investment model which generalizes a number of models that have been studied in the literature. The model involves entry and exit decisions as well as decisions relating to production scheduling. We then address the problem of its valuation from the standpoint of the dynamic programming approach. Our analysis results in a closed form analytic solution that can take qualitatively different forms depending on parameter values.

scholarly journals Quantum Calcium-Ion Interactions with EEG

Sci ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Stochastic Systems ◽  
Analytic Solution ◽  
Short Term Memory ◽  
Mathematical Physics ◽  
Modest Improvement ◽  
Classical Physics ◽  
Arbitrary Time ◽  
Eeg Data

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

Some Properties of R. G. D. Allen's Treatment of Kalecki's 1935 Model of Business Cycles

2002 ◽  
Vol 24 (4) ◽  
pp. 463-474
Author(s):  
John V. Baxley ◽  
John C. Moorhouse
Keyword(s):  
Business Cycles ◽  
Business Cycle ◽  
Mathematical Models ◽  
Closed Form ◽  
Analytic Solution ◽  
John Maynard Keynes

More than sixty-five years have passed since Michal Kalecki (1935) published one of the first formal mathematical models of business cycles. His paper presents a closed-form analytic solution. This characteristic, among others, sets Kalecki's work apart from that of contemporary literary business cycle theorists such as Friedrich A. Hayek (1935) and John Maynard Keynes (1936).

scholarly journals Boundary Effects in Solution of Boltzmann's Equation for Electron Swarms

1981 ◽  
Vol 34 (3) ◽  
pp. 223 ◽  
Author(s):  
RE Robson
Keyword(s):  
Steady State ◽  
Analytic Solution ◽  
Full Range ◽  
Mean Free Path ◽  
Path Model ◽  
Zero Field ◽  
Frequency Model ◽  
Molecule Interactions ◽  
Boltzmann's Equation ◽  
Boltzmann’S Equation

The combined effect of interaction of electrons with walls, neutral molecules and an electrostatic field is considered through analytic solution of Boltzmann's equation. In the first instance, we discuss a half-range decomposition in velocity space, corresponding to electrons moving to and from the walls, which is valid for all types of electron-molecule interactions. The half-range equations are solved in the steady state for zero field and the constant mean free path model, and it is shown that the familiar full-range 'two-term' approximation equations are adequate in this case, as far as estimating bulk properties of the electrons is concerned. For the nonzero field, again in the steady state, the full-range equations are solved for the constant collision frequency model.

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