scholarly journals A new method for determining stoichiometric coefficients using minors of a matrix

2022 ◽  
Author(s):  
Rainier Lombaard
Keyword(s):  
Linear Algebra ◽  
Chemical Reactions ◽  
Inverse Method ◽  
Reduction Reaction ◽  
New Method ◽  
Complex Structures ◽  
Traditional Methods ◽  
Matrix Inverse ◽  
Spinel Materials

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

scholarly journals A method for determining stoichiometric coefficients using minors of a matrix

2022 ◽  
Author(s):  
Rainier Lombaard
Keyword(s):  
Linear Algebra ◽  
Chemical Reactions ◽  
Inverse Method ◽  
Reduction Reaction ◽  
Complex Structures ◽  
Traditional Methods ◽  
Matrix Inverse ◽  
Spinel Materials

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

scholarly journals A METHOD FOR DETERMINING STOICHIOMETRIC COEFFICIENTS USING MINORS OF A MATRIX

2022 ◽  
Author(s):  
Rainier Lombaard
Keyword(s):  
Linear Algebra ◽  
Chemical Reactions ◽  
Inverse Method ◽  
Reduction Reaction ◽  
Complex Structures ◽  
Traditional Methods ◽  
Matrix Inverse ◽  
Spinel Materials

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

scholarly journals A new method for determining stoichiometric coefficients using minors of a matrix

2021 ◽  
Author(s):  
Rainier Lombaard
Keyword(s):  
Chemical Reactions ◽  
Matrix Algebra ◽  
Inverse Method ◽  
Reduction Reaction ◽  
New Method ◽  
Complex Structures ◽  
Metallothermic Reduction ◽  
Mathematical Basis ◽  
Matrix Inverse ◽  
Spinel Materials

The motivation of this study was the investigation into the metallothermic reduction of chromite ores. Spinel materials have complex structures and as a result, balancing of the reduction reactions by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then a new optimised method is proposed. The mathematical basis of both methods is explored using matrix algebra and then demonstrated using a typical chromite reduction reaction.

scholarly journals A New Method for Analysis of Complex Structures Based on FRF’s of Substructures

2004 ◽  
Vol 11 (1) ◽  
pp. 1-7 ◽  
Author(s):  
C.Q. Liu ◽  
Xiaobo Liu
Keyword(s):  
Frequency Response ◽  
Equations Of Motion ◽  
Complex Structure ◽  
Dynamic Responses ◽  
New Method ◽  
Total System ◽  
Complex Structures ◽  
Response Functions ◽  
Traditional Methods ◽  
Generic Class

A new method is presented for synthesizing the dynamic responses of a complex structure based upon the frequency response functions of the substructures. This method is shown to be superior to traditional methods for several reasons: (i) It can be applied to a generic class of systems. (ii) The analyst is spared the responsibilities of eliminating the coupling forces and rearranging the equations of motion. (iii) The coupling forces and the responses of the total system can be obtained simultaneously and efficiently.

Binaural speech-to-noise loudness ratio at the speech reception threshold in vehicles

2021 ◽  
Vol 69 (2) ◽  
pp. 173-179
Author(s):  
Nilolina Samardzic ◽  
Brian C.J. Moore
Keyword(s):  
Speech Intelligibility ◽  
New Method ◽  
Traditional Methods ◽  
Speech Reception ◽  
Typical Error ◽  
Transmission Index ◽  
Speech Transmission ◽  
Articulation Index ◽  
Speech Intelligibility Index ◽  
Binaural Listening

Traditional methods for predicting the intelligibility of speech in the presence of noise inside a vehicle, such as the Articulation Index (AI), the Speech Intelligibility Index (SII), and the Speech Transmission Index (STI), are not accurate, probably because they do not take binaural listening into account; the signals reaching the two ears can differ markedly depending on the positions of the talker and listener. We propose a new method for predicting the intelligibility of speech in a vehicle, based on the ratio of the binaural loudness of the speech to the binaural loudness of the noise, each calculated using the method specified in ISO 532-2 (2017). The method was found to give accurate predictions of the speech reception threshold (SRT) measured under a variety of conditions and for different positions of the talker and listener in a car. The typical error in the predicted SRT was 1.3 dB, which is markedly smaller than estimated using the SII and STI (2.0 dB and 2.1 dB, respectively).

scholarly journals The Integration of Radiocarbon Dating in Archaeology

Radiocarbon ◽  
1983 ◽  
Vol 25 (2) ◽  
pp. 639-644 ◽  
Author(s):  
H T Waterbolk
Keyword(s):  
Radiocarbon Dating ◽  
The Other ◽  
New Method ◽  
Time Range ◽  
Traditional Methods ◽  
Radiocarbon Dates ◽  
Fully Integrated ◽  
Expected Time ◽  
The Past

In the past 30 years many hundreds of archaeologic samples have been dated by radiocarbon laboratories. Yet, one cannot say that 14C dating is fully integrated into archaeology. For many archaeologists, a 14C date is an outside expertise, for which they are grateful, when it provides the answer to an otherwise insoluble chronologic problem and when it falls within the expected time range. But if a 14C date contradicts other chronologic evidence, they often find the ‘solution’ inexplicable. Some archaeologists are so impressed by the new method, that they neglect the other evidence; others simply reject problematic 14C dates as archaeologically unacceptable. Frequently, excavation reports are provided with an appendix listing the relevant 14C dates with little or no discussion of their implication. It is rare, indeed, to see in archaeologic reports a careful weighing of the various types of chronologic evidence. Yet, this is precisely what the archaeologist is accustomed to do with the evidence from his traditional methods for building up a chronology: typology and stratigraphy. Why should he not be able to include radiocarbon dates in the same way in his considerations?

scholarly journals The Energy Change of the Complete Multipartite Graph

2020 ◽  
Vol 36 (36) ◽  
pp. 309-317
Author(s):  
Haiying Shan ◽  
Changxiang He ◽  
Zhensheng Yu
Keyword(s):  
Linear Algebra ◽  
Singular Values ◽  
New Method ◽  
Energy Change ◽  
Natural Question ◽  
Complete Multipartite Graph ◽  
Multipartite Graph ◽  
Energy Of Graph ◽  
Complete Multipartite ◽  
Edge Addition

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. [S. Akbari, E. Ghorbani, and M. Oboudi. Edge addition, singular values, and energy of graphs and matrices. {\em Linear Algebra Appl.}, 430:2192--2199, 2009.] proved that for a complete multipartite graph $K_{t_1 ,\ldots,t_k}$, if $t_i\geq 2 \ (i=1,\ldots,k)$, then deleting any edge will increase the energy. A natural question is how the energy changes when $\min\{t_1 ,\ldots,t_k\}=1$. In this paper, a new method to study the energy of graph is explored. As an application of this new method, the above natural question is answered and it is completely determined how the energy of a complete multipartite graph changes when one edge is removed.

Joint Parameters Identification of a Structure With Large Number of Discrete Joints

2003 ◽  
Author(s):  
J. H. Wang ◽  
S. C. Chuang
Keyword(s):  
Frequency Response ◽  
Dynamic Behavior ◽  
Error Function ◽  
Parameters Identification ◽  
New Method ◽  
Response Functions ◽  
Traditional Methods ◽  
Measured Frequency Response ◽  
Joint Parameters ◽  
Better Than

The joint parameters of a structure with a large number of discrete joints generally are very difficult to identify accurately. The difficulty is due to the fact that the dynamic behavior of a structure becomes more complex with more number of joints. A new identification method which uses the measured frequency response functions (FRFs) to identify the joint parameters is proposed in this work to overcome this difficulty. The new method uses an error function to select different best data to identify different joints so that the accuracy of the identification can be improved. The accuracy of the new method and other two traditional methods is compared in this work. The results show that the accuracy of the proposed new method is far better than other two previous methods. The proposed new method has special advantage when (1) the number of joints is large, (2) the orders of magnitude of the joint parameters are different significantly.

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