A modified apparatus for determination of carbon in metals by the low pressure method

The low pressure method of determination of carbon in metals and alloys was modified to include certain new techniques. An isopentane slush bath dispensed with the use of liquid oxygen and the usual McLeod gauge was replaced by a differential oil manometer, which increased the sensitivity. As little as 5 μg of carbon in CaCO₃-quartz standards could be determined with a coefficient of variation of 16.0% which improved to 3.3% at the 100-μg level. The apparatus was used for the determination of carbon in metals such as uranium, zirconium and iron and in steels and cupronickel alloy.     

A potentiometric study of the oxidation of cobalt(II) with gold(III) chloride in presence of 1,10 phenanthroline or 2,2'-bipyridine : A new titration of cobalt (II) and its application to nickel-base alloys

The redox reaction between cobalt(II) and gold(III) chloride in the presence of 1.10-phenanthroline or 2,2'-bipyridine was studied, and a titration of the cobalt(II) complex with a gold(III) chloride solution was developed. A 4-fold amount of 1,10-phenanthroline or 2,2'-bipyridine was necessary for rapid quantitative reaction; the permissible pH range was 1.5–5. The oxidation of the cobalt(II) complex proceeds rapidly at 40–50°C, and a direct potentiometric titration was possible. The following maximum errors were obtained: 3.3% for 0.2–1.0 mg Co, 2.0% for 1–5 mg Co, and 0.70% for 10–40 mg Co. The following ions did not interfere: Ni(II), Zn(II), Pb(II), Cd(II), Mn(II), Fe(II), Cr(III), Al(III), Th(IV), Se(IV), Ti(IV), U(VI), Mo(VI), SO^2-₄ and PO^3-₄. Even small quantities of silver(I), copper(II), palladium(II), mercury(II)and iron(III) interfered. The method was applied to the determination of high cobalt contents in high-temperature nickel-base alloys.     

Alternatingly Hyperexpansive Operator Tuples

The notion of an alternatingly hyperexpansive operator on a Hilbert space is generalized to that of an alternatingly hyperexpansive operator tuple, which necessitates exploring the theory of absolutely monotone functions as defined on the m-fold product N ^m of the semi-group N of non-negative integers and as defined on semi-open cubes in the m-dimensional real Euclidean space R ^m. The multi-variable Laplace transform and the Stieltjes Moment Problem make a natural appearance in the development of the relevant theory, which also highlights the close connections of alternatingly hyperexpansive operator tuples with completely hyperexpansive and subnormal ones. In particular, if T is subnormal and the joint (Taylor) spectrum of its minimal normal extension is contained in a certain subset of the Hermitian space C ^m, then T turns out to be alternatingly hyperexpansive. In the context of multi-variable weighted shifts, the last assertion can be related to the notion of a Stieltjes Moment Net. The general characterization of an alternatingly hyperexpansive m-variable weighted shift T, however, requires a certain net of (positive) numbers associated with T to be absolutely monotone on N ^m and allows for such a T to be non-subnormal.     

On the duals of subnormal tuples

A notion of the dual of a subnormal tuple of operators is discussed.     

On completely hyperexpansive operators

We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.

     

On the Unital C*-Algebras Generated by Certain Subnormal Tuples

We consider an important class of subnormal operator m-tuples M _p (p = m,m + 1, . . .) that is associated with a class of reproducing kernel Hilbert spaces H_p{{\mathcal H}_p} (with M _m being the multiplication tuple on the Hardy space of the open unit ball \mathbb B^2m{{\mathbb B}^{2m}} in \mathbb C^m{{\mathbb C}^m} and M _m+1 being the multiplication tuple on the Bergman space of \mathbb B^2m{{\mathbb B}^{2m}}). Given any two C*-algebras A{\mathcal A} and B{\mathcal B} from the collection {C^*(M_p), C^*([(M)\tilde]_p): p 3 m}{\{C^*({M}_p), C^*({\tilde M}_p): p \geq m\}} , where C*(M _p ) is the unital C*-algebra generated by M _p and C^*([(M)\tilde]_p){C^*({\tilde M}_p)} the unital C*-algebra generated by the dual [(M)\tilde]_p{{\tilde M}_p} of M _p , we verify that A{\mathcal A} and B{\mathcal B} are either *-isomorphic or that there is no homotopy equivalence between A{\mathcal A} and B{\mathcal B} . For example, while C*(M _m ) and C*(M _m+1) are well-known to be *-isomorphic, we find that C^*([(M)\tilde]_m){C^*({\tilde M}_m)} and C^*([(M)\tilde]_m+1){C^*({\tilde M}_{m+1})} are not even homotopy equivalent; on the other hand, C*(M _m ) and C^*([(M)\tilde]_m){C^*({\tilde M}_{m})} are indeed *-isomorphic. Our arguments rely on the BDF-theory and K-theory.     

Completely Hyperexpansive Operator Tuples

The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy–Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several–variable generalization allows for a stimulating interaction with the multiparameter spectral theory.