scholarly journals 6. Matrix series and additional properties of matrices

2017 ◽  
pp. 417-446
Keyword(s):  
Matrix Series

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals BIOSORPTION OF METAL IONS Pb(II), Cu(II), AND Cd(II) ON Sargassum duplicatum IMMOBILIZED SILICA GEL MATRIX

2010 ◽  
Vol 6 (3) ◽  
pp. 245-250 ◽  
Author(s):  
Buhani Buhani ◽  
Suharso Suharso ◽  
Zipora Sembiring
Keyword(s):  
Metal Ions ◽  
Silica Gel ◽  
Functional Group ◽  
Adsorption Process ◽  
Liquid Waste ◽  
Batch Method ◽  
Algae Biomass ◽  
Adsorbent Surface ◽  
Physical And Chemical ◽  
Matrix Series

Sargassum duplicatum algae biomass is biological material which has a potency to be used as a biosorbent adsorb metal ions from industrial liquid waste, because it has effective functional group as a ligand. However, the ability of the algae biomass in adsorbing of heavy metal ions has some problem such as; tiny size, low density, and easy to be degradated by other microorganism. In addition, algae biomass can not be used directly in adsorption column for its application as the biosorbent. In order to improve physical and chemical prpperties of algae biomass, it needs to be immobilized on silica gel matrix. Series of experiment have been done, morphology analysis of adsorbent surface was performed by using Scanning Electron Microscopy (SEM) and adsorption process to examine the effectiveness of algae biomass immobilized in adsorbing Pb(II), Cu(II), and Cd(II) was performed using batch method at 27 °C. Concentration of metal was determined by using Atomic Absorption Spectrophotometer (AAS) and identification of functional group was conducted using Spectrophotometer Infrared (IR). Data obtained showed that interacting among metal ions with algae biomass is optimum at a range of 60 minutes. Adsorption energies of metal ions resulted from the interaction of metal ions with the functional group of -C=O group from carboxyl and amide on algae biomass and -Si-OH group from silica were at a range of 21.09-25.05 kJ/mole.   Keywords: biosorption, silica gel, Sargassum duplicatum, immobilization

Symbolic Analysis of High-Dimensional Time Series

2003 ◽  
Vol 13 (09) ◽  
pp. 2657-2668 ◽  
Author(s):  
Karsten Keller ◽  
Heinz Lauffer
Keyword(s):  
Time Series ◽  
Symbolic Dynamics ◽  
Epileptic Activity ◽  
High Dimensional ◽  
Qualitative Information ◽  
Eeg Data ◽  
Ordinal Patterns ◽  
The Given ◽  
Matrix Series ◽  
Qualitative Changes

In order to extract and to visualize qualitative information from a high-dimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and visualize qualitative changes of EEG data related to epileptic activity.

On the matrix versions of q-zeta function, q-digamma function and q-polygamma function

2019 ◽  
Vol 13 (08) ◽  
pp. 2050142
Author(s):  
Ravi Dwivedi ◽  
Vivek Sahai
Keyword(s):  
Zeta Function ◽  
Matrix Function ◽  
Integral Representations ◽  
Digamma Function ◽  
Polygamma Function ◽  
The Matrix ◽  
Matrix Series ◽  
Zeta Matrix

This paper deals with the [Formula: see text]-analogues of generalized zeta matrix function, digamma matrix function and polygamma matrix function. We also discuss their regions of convergence, integral representations and matrix relations obeyed by them. We also give a few identities involving digamma matrix function and [Formula: see text]-hypergeometric matrix series.

scholarly journals On the Convergence of the S-matrix Series

1952 ◽  
Vol 8 (5) ◽  
pp. 569-570 ◽  
Author(s):  
S. Hori
Keyword(s):  
S Matrix ◽  
Matrix Series

The analysis of chaotic regimes in Chua’s circuit with smooth nonlinearity based on the matrix decomposition method

2019 ◽  
Vol 63 (4) ◽  
pp. 501-512
Author(s):  
A. M. Krot ◽  
U. A. Sychou
Keyword(s):  
Simulation Model ◽  
State Space ◽  
Decomposition Method ◽  
Matrix Decomposition ◽  
Chaotic Regime ◽  
Chua’S Circuit ◽  
Electric Circuits ◽  
Chua's Circuit ◽  
The Matrix ◽  
Matrix Series

The scope of this work are electric circuits or electronic devices with chaotic regimes, in particular the Chua’s circuit. A nonlinear analysis of chaotic attractors based on the Krot’s method of matrix decomposition of vector functions in state-space of complex systems has been used to investigate the Chua’s circuit with smooth nonlinearity. It includes an analysis of linear term of the matrix series as well as an estimation of influence of high order terms of this series on stability of complex system under investigation. Here the method of matrix decomposition has been applied to analysis of the Chua’s attractor. The terms of matrix series have been used to create a simulation model and to reconstruct an attractor of chaotic modes. The proposed simulation model makes it possible to separate an influence of nonlinearities on forming a chaotic regime of the Chua’s circuit. Usage of both the matrix decomposition method and computational experiment has allowed us to find out that the initial turbulence model proposed by L. D. Landau is suitable for set-up description of the chaotic regime of the Chua’s circuit. It is shown that a mode of hard self-excitation in the Chua’s circuit leads to its chaotic regime operating with a double-scroll attractor in the state-space. The results might be used to generate of chaotic oscillations or data encryption. 

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