Background: In this research, the decomposition of Aroclor 1254, including 20 kinds of poly chlorinated biphenyls (PCBs), in real waste transformer oil in the presence of PEG1000, NaOH, zero valent iron and H2O by microwave (MW) irradiation was studied. Methods: Central composites design (CCD) method was carried out for experimental design. The effects of microwave power levels (200- 1000 W), ...

In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the LDU decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition...

We extend, in the context of a connected real semisimple Lie group, some results on the QR iteration and the Cholesky iteration of a nonsingular matrix. A group theoretic understanding of the abstract mechanisms of the iterations is obtained.

The Iwasawa decomposition of a connected semisimple complex Lie group or a connected semisimple split real Lie group is one of the most fundamental observations of classical Lie theory. It implies that the geometry of a connected semisimple complex resp. split real Lie group G is controlled by any maximal compact subgroup K. Examples are Weyl’s unitarian trick in the representation theory of Li...

We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm.

In this paper we consider the question how the set of inversions of a permutation π ∈ Sn can be partitioned into two subsets, which are themselves inversion sets of permutations in Sn. Our method is to study the modular decomposition of the inversion graph of π. A correspondence to the substitution decomposition of π is also given. Moreover, we consider the special case of multiplicative decomp...

An algorithm for the efficient computation of the CUR decomposition is presented. The method is based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for its implementation. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations.