Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

‎in this article we discuss examples of fractal $omega$-operads‎. ‎thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{globular sets are also called $omega$-graphs by the french school.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma of...

For simplicity, we follow the rules: x, y are sets, N is an element of N, c, i, j, k, m, n are natural numbers, D is a non empty set, s is an element of 2Set Seg(n + 2), p is an element of the permutations of n-element set, p1, q1 are elements of the permutations of (n+ 1)-element set, p2 is an element of the permutations of (n+ 2)-element set, K is a field, a, b are elements of K, f is a finit...

This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building previous in this field, the $p$-Laplace operator is utilized to approximate a descent method shapes. In particular, it shown how geometric constraints are algorithmically incorporated avoiding penalty terms by assigning them subproblem of finding suitable direction. A special focu...

The differential equation is an that involves the derivative (derivatives) of dependent variable with respect to independent (variables). represents nothing but a rate change, and helps us present relationship between changing quantity change in another quantity. Adomian decomposition method one iterative methods can be used solve equations, both integer fractional order, linear or nonlinear, o...

The differential-geometric and topological structure of Delsarte transmutation operators and associated with them Gelfand-Levitan-Marchenko type eqautions are studied making use of the De Rham-Hodge-Skrypnik differential complex. The relationships with spectral theory and special Berezansky type congruence properties of Delsarte transmuted operators are stated. Some applications to multidimensi...

In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...