scholarly journals Relaxed Multibang Regularization for the Combinatorial Integral Approximation

2021 ◽  
Vol 59 (4) ◽  
pp. 2645-2668
Author(s):  
Paul Manns
Keyword(s):  
Integral Approximation

scholarly journals Comments on ’’Higher order modified potentials for the effective phase integral approximation’’

1981 ◽  
Vol 22 (6) ◽  
pp. 1190-1191 ◽  
Author(s):  
Nanny Fröman ◽  
Per Olof Fröman
Keyword(s):  
Higher Order ◽  
Integral Approximation ◽  
Phase Integral ◽  
Effective Phase

scholarly journals Line integral approximation of double integrals

1953 ◽  
Vol 4 (2) ◽  
pp. 287-287
Author(s):  
H. D. Brunk ◽  
G. M. Ewing
Keyword(s):  
Line Integral ◽  
Integral Approximation ◽  
Double Integrals

Phase‐Integral Approximation in Momentum Space and the Bound States of an Atom. II

1969 ◽  
Vol 10 (6) ◽  
pp. 1004-1020 ◽  
Author(s):  
Martin C. Gutzwiller
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Integral Approximation ◽  
Phase Integral

scholarly journals Integral approximation of simplicial volume of graph manifolds

2019 ◽  
Vol 51 (4) ◽  
pp. 715-731 ◽  
Author(s):  
Daniel Fauser ◽  
Stefan Friedl ◽  
Clara Löh
Keyword(s):  
Simplicial Volume ◽  
Integral Approximation ◽  
Graph Manifolds

scholarly journals Pyrolysis Kinetic Parameters of Omari Oil Shale Using Thermogravimetric Analysis

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4060
Author(s):  
Ziad Abu El-Rub ◽  
Joanna Kujawa ◽  
Samer Al-Gharabli
Keyword(s):  
Activation Energy ◽  
Thermogravimetric Analysis ◽  
Kinetic Parameters ◽  
Oil Shale ◽  
Arrhenius Plot ◽  
Frequency Factor ◽  
Coefficient Of Determination ◽  
Assay Method ◽  
Temperature Integral ◽  
Integral Approximation

Oil shale is one of the alternative energies and fuel solutions in Jordan because of the scarcity of conventional sources, such as petroleum, coal, and gas. Oil from oil shale reservoirs can be produced commercially by pyrolysis technology. To optimize the process, mechanisms and rates of reactions need to be investigated. Omari oil shale formation in Jordan was selected as a case study, for which no kinetic models are available in the literature. Oil shale was analyzed using the Fischer assay method, proximate analysis (moisture, volatile, and ash), gross calorific value, elemental analysis (CHNS), and X-ray fluorescence (XRF) measurements. Non-isothermal thermogravimetric analysis was applied to study the kinetic parameters (activation energy and frequency factor) at four selected heating rates (5, 10, 15, and 20 °C/min). When oil shale was heated from room temperature to 1100 °C, the weight loss profile exhibited three different zones: drying (devolatilization), pyrolysis, and mineral decomposition. For each zone, the kinetic parameters were calculated using three selected methods: integral, temperature integral approximation, and direct Arrhenius plot. Furthermore, the activation energy in the pyrolysis zone was 112–116 kJ/mol, while the frequency factor was 2.0 × 107 − 1.5 × 109 min−1. Moreover, the heating rate has a directly proportional relationship with the rate constant at each zone. The three different methods gave comparable results for the kinetic parameters with a higher coefficient of determination (R2) for the integral and temperature integral approximation compared with the direct Arrhenius plot. The determined kinetic parameters for Omari formation can be employed in developing pyrolysis reactor models.

Two classes of special functions for the phase-integral approximation

1979 ◽  
Vol 12 (8) ◽  
pp. 1149-1154 ◽  
Author(s):  
J A Campbell
Keyword(s):  
Special Functions ◽  
Integral Approximation ◽  
Phase Integral
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