Determination of stoichiometric coefficients by the matrix method

The problem of calculating stoichiometric coefficients in a chemical equation can be solved by standard methods and the method of multidimensional vector space, but good knowledge of vector algebra is required. In this paper, the authors proposed a matrix method and other treatment of the problem was given as the authors' own interpretation. A matrix was formed in the form of base using all the elements which take place in a chemical reaction, after which the matrixes of all the chemical compounds were determined based on numerical indexes and element symbols. This approach enables the setting of a principal matrix equation based on a mathematical approach. The solutions of this matrix equation are the desired stoichiometric coefficients that form a balanced equation. A new approach to tabular solving is presented. This method, compared to existing standard methods, is faster, simpler, and more effective, especially for complex chemical equations. The method was tasted on examples from inorganic chemistry and metallurgy.

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Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

Zeitschrift für Naturforschung A ◽

10.1515/zna-2004-0913 ◽

2004 ◽

Vol 59 (9) ◽

pp. 621-622 ◽

Cited By ~ 1

Author(s):

Fatih Ucun ◽

Vesile Gūçlü

Keyword(s):

Gas Phase ◽

Condensed Phase ◽

Matrix Method ◽

Solid Phase ◽

Force Constants ◽

Matrix Solution ◽

The Matrix ◽

Newton Raphson ◽

Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

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New Computational Methods for Solving Problems of the Astronomical Vessel Position

Journal of Navigation ◽

10.1017/s0373463305003188 ◽

2005 ◽

Vol 58 (2) ◽

pp. 315-335 ◽

Cited By ~ 4

Author(s):

Tien-Pen Hsu ◽

Chih-Li Chen ◽

Jiang-Ren Chang

Keyword(s):

Coordinate System ◽

Computational Methods ◽

Matrix Method ◽

Iteration Scheme ◽

Computation Method ◽

Direct Computation ◽

Celestial Navigation ◽

Vector Algebra ◽

The Matrix ◽

Triangle Method

In this paper, a simplified and direct computation method formulated by the fixed coordinate system and relative meridian concept in conjunction with vector algebra is developed to deal with the classical problems of celestial navigation. It is found that the proposed approach, the Simultaneous Equal-altitude Equation Method (SEEM), can directly calculate the Astronomical Vessel Position (AVP) without an additional graphical procedure. The SEEM is not only simpler than the matrix method but is also more straightforward than the Spherical Triangle Method (STM). Due to tedious computation procedures existing in the commonly used methods for determining the AVP, a set of optimal computation procedures for the STM is also suggested. In addition, aimed at drawbacks of the intercept method, an improved approach with a new computation procedure is also presented to plot the celestial line of position without the intercept. The improved approach with iteration scheme is used to solve the AVP and validate the SEEM successfully. Methods of solving AVP problems are also discussed in detail. Finally, a benchmark example is included to demonstrate these proposed methods.

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SOME EXPERIMENTAL DIFFICULTIES ENCOUNTERED IN THE APPLICATION OF X-RAY DIFFRACTOMETER MEASUREMENTS TO THE MATRIX METHOD OF R. DIAMOND FOR THE DETERMINATION OF CRYSTALLITE SIZE DISTRIBUTIONS IN TURBOSTRATIC CARBONS

Proceedings of the Fifth Conference on Carbon ◽

10.1016/b978-0-08-009708-4.50048-1 ◽

1963 ◽

pp. 507-515

Author(s):

H.A. MCKINSTRY ◽

M.A. SHORT

Keyword(s):

Crystallite Size ◽

Matrix Method ◽

Size Distributions ◽

X Ray ◽

The Matrix

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A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis

Biochemical Journal ◽

10.1042/bj2920351 ◽

1993 ◽

Vol 292 (2) ◽

pp. 351-360 ◽

Cited By ~ 7

Author(s):

S Thomas ◽

D A Fell

Keyword(s):

Computer Program ◽

Metabolic Control ◽

Matrix Method ◽

Metabolic Control Analysis ◽

Control Analysis ◽

Point Distribution ◽

Algebraic Expressions ◽

The Matrix ◽

Control Coefficients

A computer program (MetaCon) is described for the evaluation of flux control, concentration control and branch-point distribution control coefficients of a metabolic pathway. Requiring only the reaction scheme as input, the program produces algebraic expressions for the control coefficients in terms of elasticity coefficients, metabolite concentrations and pathway fluxes. Any of these variables can be substituted by numeric or simple algebraic expressions; the expressions will then be automatically rearranged in terms of the remaining unknown variables. When all variables have been substituted, numeric values will be obtained for the control coefficients. The program is a computerized implementation of the matrix method for the determination of control coefficients. The features of MetaCon are compared with those of other programs available to workers in Metabolic Control Analysis. Potential benefits of, and methods of using, MetaCon are discussed. The mathematical background and validity of the matrix method rules are discussed, and the algorithm used by MetaCon is described. The matrix method is shown to be a specific case of a previously described general formalism for calculating control coefficients.

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Determination of Force Constants of Planar XY3 and Tetrahedral XY4 Molecules by the GF Matrix Method

Zeitschrift für Naturforschung A ◽

10.1515/zna-2005-0309 ◽

2005 ◽

Vol 60 (3) ◽

pp. 183-186 ◽

Cited By ~ 1

Author(s):

Vesile Güçlü ◽

Fatih Ucun

Keyword(s):

Computer Program ◽

Matrix Method ◽

Force Constants ◽

Internal Coordinates ◽

The Matrix ◽

Newton Raphson ◽

Raphson Method

The force constants of the internal coordinates of planar XY3 and tetrahedral XY4 molecules were calculated using the GF matrix method. The matrix solutions were carried out by means of a computer program built relative to the Newton-Raphson method, and the calculations were listed in tables. For tetrahedral XY4 molecules having the same Y atom it was found that the force constants decrease with the increasing mass of the X atom, and this was attributed to the slowing of the molecule with increasing mass of the centre X atom.

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A New Approach for Determination of the Attenuation Bandwidth of a Resonating Metamaterial

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.846.264 ◽

2016 ◽

Vol 846 ◽

pp. 264-269 ◽

Cited By ~ 6

Author(s):

Arnab Banerjee ◽

Raj Das ◽

Emilio P. Calius

Keyword(s):

Wave Interaction ◽

Electromagnetic Properties ◽

Governing Equations ◽

New Approach ◽

New Class ◽

Artificial Materials ◽

Internal Structures ◽

The Matrix ◽

Bloch’S Theorem

Due to the presence of internal structures, metamaterials, a new class of artificial materials, can be engineered to have various unconventional properties during wave interaction. They can be rationally designed to offer controlled mechanical, acoustic or electromagnetic properties through resonant electromagnetic, acoustic or mechanical structures inside the metamaterial. Due to these properties, metamaterials have been effectively used for cloaking, wave guiding and designing filters in the field of optics, electromagnetics, acoustics and elastodynamics. In this paper, a Fourier transfer based methodology is proposed to determine the attenuation bandwidth of a metamaterial instead of using conventional Bloch’s theorem. The applicability of this method is wider than that of Bloch’s theorem, because this method allows analysis beyond the necessary periodicity of the metamaterial. All the governing equations are non-dimensionalised to effectively quantify the attenuation bandwidth at the lower and higher frequency range of the resonating frequency of the internal structures present in the matrix of the material. The attenuation bandwidth is characterized into low and high frequency parts to determine the effect of the variation of the mass ratio and the number of the repeating units on the attenuation bandwidth of the 1D metamaterial chain.

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The potentiometric determination of stability constants of sulfite and cobalt(II) in ionic strength 2.0 M (NaClO4). Use of the matrix method

Polyhedron ◽

10.1016/s0277-5387(00)86541-9 ◽

1987 ◽

Vol 6 (9) ◽

pp. 1717-1719 ◽

Cited By ~ 5

Author(s):

Éder Tadeu Gomes Cavalheiro ◽

Ana Maria De Guzzi Plepis ◽

Gilberto Orivaldo Chierice ◽

Eduardo F.A. Neves

Keyword(s):

Ionic Strength ◽

Stability Constants ◽

Matrix Method ◽

Potentiometric Determination ◽

The Matrix

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A new approach to studying the autoxidation of adrenaline: possibility of the determination of superoxide dismutase activity and the antioxidant properties of various preparations by polarography

Biomeditsinskaya Khimiya ◽

10.18097/pbmc20125801077 ◽

2012 ◽

Vol 58 (1) ◽

pp. 77-87 ◽

Cited By ~ 12

Author(s):

T.V. Sirota

Keyword(s):

Reactive Oxygen Species ◽

Superoxide Dismutase ◽

Oxygen Consumption ◽

Antioxidant Properties ◽

Chemical Compounds ◽

The Body ◽

Oxygen Species ◽

New Approach ◽

Rate Of Oxygen Consumption

The reaction of adrenaline autoxidation in an alkaline buffer with the formation of superoxide radicals and the product of its oxidation, adrenochrome, which models the quinoid pathway of adrenaline conversion in the body, is accompanied by oxygen consumption. This reaction is applicable for polarographic determination of the activity of superoxide dismutase and the antioxidant properties of biological and chemical compounds, it is based on evaluation of the latent period and the rate of oxygen consumption, which are measured in the presence of the compounds examined. It was assumed that the neuro- and cardiotoxicity of quinone products of adrenaline oxidation is related not only to their "own" properties and reactive oxygen species formed but also the hypoxia of those regions of the cell and tissue where the quinoid oxidation of adrenaline occurs.

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Displacements induced by different nanoprecipitates: a SAXS and WAXS anomalous study on Cu–Ni–Fe and Cu–Ni–Co single crystals

Journal of Applied Crystallography ◽

10.1107/s0021889805006382 ◽

2005 ◽

Vol 38 (3) ◽

pp. 476-487 ◽

Cited By ~ 3

Author(s):

O. Lyon ◽

I. Guillon ◽

C. Servant ◽

J. P. Simon

Keyword(s):

Single Crystals ◽

New Approach ◽

X Ray Scattering ◽

Local Contraction ◽

Composition Variation ◽

Pile Up ◽

The Matrix ◽

Atomic Scattering ◽

Fe Alloys

Single crystals of different Cu–Ni–Co and Cu–Ni–Fe alloys, forming spheroid or plate-like precipitates during decomposition, have been studied by small-angle (SAXS) and wide-angle X-ray scattering (WAXS). The SAXS patterns gave information on the sizes and the organization of the precipitates, while the scattering near Bragg peaks allowed a determination of the distortions of the lattice created by these precipitates. The variations of the SAXS spectra with the atomic scattering factors of Co (or Fe) and Ni were used to determine the composition variation between matrix and precipitates (i.e. the `chemical' term), while those of the WAXS spectra enabled the determination of the displacements in the matrix and in the precipitates. The precipitates were found to be enriched in respectively Co and Ni, or Fe and Ni, inducing a local contraction of the lattice, while the matrix (mainly Cu) was of course depleted in the same elements, and its lattice was dilated. These precipitates are piled up along one of the three 〈100〉 `soft' directions. The variations of the deformation field with the precipitate sizes (along both directions parallel and orthogonal to the pile-up orientation), and with the distance between precipitates have been determined. From the knowledge of such variations, it was possible to modify the respective deformation fields in such a way that the respective precipitates have the same sizes, but with a different geometry, and then to isolate what was induced solely by the geometry of a precipitate. Moreover, these experiments yielded the determination of the secondary components of the displacement field (displacements orthogonal to the pile-up direction), which were found to be weak compared with the primary one (parallel to the same direction). Finally, from the variation of the aspect ratio of the precipitates with the aging duration, it was possible to estimate the surface energy of the precipitates, and a comparison between SAXS and WAXS results shows the applicability of this new approach to the decomposition process.

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