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Full-Text Articles in Physical Sciences and Mathematics
A Note On K-Commutative Matrices, D. W. Robinson
A Note On K-Commutative Matrices, D. W. Robinson
Faculty Publications
Let A and B be square matrices over a field in which the minimum polynomial of A is completely reducible. It is shown that A is k commutative with respect to B for some non-negative integer k if and only if B commutes with every principal idempotent of A. The proof is brief, simplifying much of the previous study of k-commutative matrices. The result is also used to generalize some well-known theorems on finite matrix commutators that involve a complex matrix and its transposed complex conjugate.
A Thermodynamic Study Of Step-Wise Complex Formation In Several Aqueous Copper (Ii)-Amino Acid Systems, Vipin M. Kothari
A Thermodynamic Study Of Step-Wise Complex Formation In Several Aqueous Copper (Ii)-Amino Acid Systems, Vipin M. Kothari
Theses and Dissertations
pK_n values for step-wise dissociation of protons from the protonated ligands (glycine, α-amino isobutyric acid, sarcosine and theonine) were determined potentiometrically with a Beckman Model GS pH meter in aqueous solution at 10, 20, 30 and 40° C. Log K values for step-wise interaction of glycine, α-amino isobutyric acid, sarcosine and threonine with copper(II) ion were also determined potentiometrically with a pH meter at 10, 20, 30 and 40° C. The standard free energy of formation for the step-wise interaction of copper(II) with each of the above ligands was calculated from the values of log K. Enthalpy and entropy changes …
A Thermodynamic Study Of Complex Formation In Aqueous Solution.|Ni.|Pthe Hg(Ii)-, Zn(Ii)-, Cd(Ii)-, Ag(I)-Serine Systems.|Nii.|Pthe Hg(Ii)-, Zn(Ii)-, Cd(Ii)-, In(Iii)- Thioglycollic Acid System :|Ba Study Of The Effect Of D[Pi]-D[Pi] Bonding On These Complexes, Marriner Lee Morrell
Theses and Dissertations
Thermodynamic equilibrium constants were obtained potentiometrically using a Beckman pH meter for metal-serine and metal-thioglycolloc acid complexes to study the thermodynamic properties of the complexes and the effect of dπ - dπ bonding on the equilibrium constants. The following calculations were made: 1. The stepwise dissociation of protons from serine at 10, 20, 30, and 40°C and the stepwise dissociation of protons from thioglycollic acid at 20, 30, and 40°C. 2. The thermodynamic formation constants for Zn(II), Cd(II), Hg(II), and Ag(I) with serine at 10, 20, 30, and 40°C and at two ionic strengths. 3. The thermodynamic formation constants for …
The Influence Of Temperature And Some Other Factors On The Biological And Nonbiological Oxidation Of Chalcopyrite, Pyrite And Copper Sulfide, Ezra Revier Palmer
The Influence Of Temperature And Some Other Factors On The Biological And Nonbiological Oxidation Of Chalcopyrite, Pyrite And Copper Sulfide, Ezra Revier Palmer
Theses and Dissertations
The purpose of this study was: (1) to find the effect of temperature on the wet oxidation of chalcopyrite, pyrite, and copper sulfide over the biological and nonbiological range; (2) to determine the influence of ferrous and ferric iron and free oxygen(air) on the oxidation. The sulfide minerals studied were oxidized over a range of temperatures between 25° to 75° C. The optimum biological oxidation occurred near 35° C. The nonbiological oxidation was very slow at low temperatures but increased with increasing temperature. The effect of solutions used in leaching the various sulfides over the temperature range differred. A synthetic …