scholarly journals NNLO logarithmic expansions and exact solutions of the DGLAP equations from x-space: New algorithms for precision studies at the LHC

2006 ◽  
Vol 748 (1-2) ◽  
pp. 253-308 ◽  
Author(s):  
Alessandro Cafarella ◽  
Claudio Corianò ◽  
Marco Guzzi
Keyword(s):  
Exact Solutions ◽  
New Algorithms ◽  
Logarithmic Expansions

scholarly journals Fixed point method and its improvement for the system of Volterra-Fredholm integral equations of the second kind

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 191
Author(s):  
Talaat Ismahel Hasan ◽  
Shaharuddin Salleh
Keyword(s):  
Fixed Point ◽  
Exact Solutions ◽  
Integral Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Fredholm Integral Equations ◽  
Numerical Examples ◽  
New Algorithms

In this paper, we consider the system of Volterra-Fredholm integral equations of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition, a few theorems and two new algorithms are introduced.  They are supported by numerical examples and simulations using Matlab. The results are reasonably good when compared with the exact solutions.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

mmpdb: An Open Source Matched Molecular Pair Platform for Large Multi-Property Datasets

2018 ◽  
Author(s):  
Andrew Dalke ◽  
Jerome Hert ◽  
Christian Kramer
Keyword(s):  
Open Source ◽  
Large Datasets ◽  
Molecular Pair ◽  
New Algorithms

We present mmpdb, an open source Matched Molecular Pair (MMP) platform to create, compile, store, retrieve, and use MMP rules. mmpdb is suitable for the large datasets typically found in pharmaceutical and agrochemical companies and provides new algorithms for fragment canonicalization and stereochemistry handling. The platform is written in Python and based on the RDKit toolkit. mmpdb is freely available.

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