Use of generalized exponential function to build three-dimensional reactive surfaces

2010 ◽  
Vol 389 (17) ◽  
pp. 3604-3612 ◽  
Author(s):  
Lucas R. Salviano ◽  
Cristiano S. Esteves ◽  
Heibbe C.B. de Oliveira ◽  
Kleber C. Mundim ◽  
Luciano Ribeiro ◽  
...  
Keyword(s):  
Exponential Function ◽  
Three Dimensional ◽  
Generalized Exponential Function ◽  
Reactive Surfaces

Modeling diatomic potential energy curves through the generalized exponential function

2006 ◽  
Vol 427 (1-3) ◽  
pp. 10-13 ◽  
Author(s):  
C.S. Esteves ◽  
H.C.B. de Oliveira ◽  
L. Ribeiro ◽  
R. Gargano ◽  
K.C. Mundim
Keyword(s):  
Potential Energy ◽  
Exponential Function ◽  
Potential Energy Curves ◽  
Generalized Exponential Function

scholarly journals Generalized Probability Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alexandre Souto Martinez ◽  
Rodrigo Silva González ◽  
César Augusto Sangaletti Terçariol
Keyword(s):  
Exponential Function ◽  
Error Function ◽  
Generalized Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
Logarithmic Function ◽  
Rank Distribution ◽  
Exponential Functions ◽  
Generalized Exponential Function ◽  
Generalized Probability

From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs). A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.

scholarly journals A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 309-316
Author(s):  
Gülnur Yel ◽  
Tolga Aktürk
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Periodic Functions ◽  
New Approach ◽  
Wave Solutions ◽  
Exponential Function Method

AbstractIn this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

Three-dimensional reactive surfaces for the LiH2+ system: an analysis of accurate ab initio results

2003 ◽  
Vol 287 (3) ◽  
pp. 335-348 ◽  
Author(s):  
R. Martinazzo ◽  
E. Bodo ◽  
F.A. Gianturco ◽  
M. Raimondi
Keyword(s):  
Ab Initio ◽  
Three Dimensional ◽  
Reactive Surfaces

scholarly journals Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hongling Ye ◽  
Ning Chen ◽  
Yunkang Sui ◽  
Jun Tie
Keyword(s):  
Topology Optimization ◽  
Exponential Function ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Taylor Series Expansion ◽  
Optimal Model ◽  
Filter Function ◽  
Frequency Constraints ◽  
Design Variables ◽  
Dynamic Topology

The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM) design variable fields. The composite exponential function (CEF) is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP) algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

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