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## A generalized moment problem

### Mathematische Annalen (1962-08-01) 146: 326-330 , August 01, 1962

## Measure preserving functions on locally compact spaces

### Mathematische Zeitschrift (1962-12-01) 80: 194-199 , December 01, 1962

## Structure of formamide and its force constants

### Proceedings of the Indian Academy of Sciences - Section A (1962-09-01) 56: 115-124 , September 01, 1962

### V. Summary

A new procedure has been adopted in subjecting formamide—a molecule which has no symmetry—to normal co-ordinate treatment by the Wilson’s F-G matrix method. The molecule is split into two parts for the purposes of calculation. One part is and the other is where R is the CHO group. Both the parts have C-N bond in common. Assuming the part one to be planar and the part two to be pryamidal as suggested by Costain and Dowling, the normal co-ordinate treatment of both the parts has been carried out and the fundamental frequencies calculated. The close agreement between the observed and the calculated values confirms the non-planar structure of formamide. Among all the fundamental frequencies, the frequency due to C-N stretch alone appears to be mass sensitive. On the basis of all these considerations some of the frequencies have been assigned to the wagging and twisting modes, which are different from those that are assigned by Evans.

## On smoothing of pulp quality characteristics in a flow system

### BIT Numerical Mathematics (1962-12-01) 2: 203-211 , December 01, 1962

In this paper the mixing effect of a new flow system of large pulp reservoirs is investigated. The analogy of the reservoir and an information channel is pointed out. Especially, the transfer function of the channel is derived and the calculation of this function by high-speed computers is given.

The cases where the quality of the stream changes discontinuously (chemical pulp) or continuously (mechanical pulp) are investigated separately. In the former case a quantity for the mixing effect is defined.

## § 88 (89)

### Die Data von Euklid (1962-01-01) : 59 , January 01, 1962

### Zusammenfassung

Zieht man in einem der Größe nach gegebenen Kreise eine der Größe nach gegebene Sehne, so muß sie einen Abschnitt abtrennen, der einen gegebenen Winkel faßt.

## A graph theoretic approach to matrix inversion by partitioning

### Numerische Mathematik (1962-12-01) 4: 128-135 , December 01, 1962

Let*M* be a square matrix whose entries are in some field. Our object is to find a permutation matrix*P* such that*PM P*^{−1} is completely reduced, i.e., is partitioned in block triangular form, so that all submatrices below its diagonal are 0 and all diagonal submatrices are square and irreducible. Let*A* be the binary (0, 1) matrix obtained from*M* by preserving the 0's of*M* and replacing the nonzero entries of*M* by 1's. Then*A* may be regarded as the adjacency matrix of a directed graph*D*. Call*D* strongly connected or*strong* if any two points of*D* are mutually reachable by directed paths. A*strong component* of*D* is a maximal strong subgraph. The*condensation D*^{*} of*D* is that digraph whose points are the strong components of*D* and whose lines are induced by those of*D*. By known methods, we construct*D*^{*} from the digraph,*D* whose adjacency matrix*A* was obtained from the original matrix*M*. Let*A*^{*} be the adjacency matrix of*D*^{*}. It is easy to show that there exists a permutation matrix*Q* such that*QA*^{*}*Q*^{−1} is an upper triangular matrix. The determination of an appropriate permutation matrix*P* from this matrix*Q* is straightforward.

## § 82

### Die Data von Euklid (1962-01-01): 55-56 , January 01, 1962

### Zusammenfassung

Stehen vier Strecken in Proportion, so muß sich verhalten wie die erste Strecke zu einer, zu der die zweite gegebenes Verhältnis hat, so die dritte Strecke zu einer, zu der die vierte gegebenes Verhältnis hat.

## Einstein-Maxwell field equations. Third class

### Rendiconti del Circolo Matematico di Palermo (1962-05-01) 11: 157-177 , May 01, 1962

### Summary

In this paper it has been shown that all the quantities excepting a parameter σ and charge can be determined from the field equations of general relativity, when the electromagnetic tensor field is of the third class. The parameter σ and the charge can be determined from Maxwell equations. The electromagnetic tensor, stress tensor, pressure, mass and charge have been obtained as concomitants of gravitational tensor*h*_{λμ}.

## Sulla riducibilità delle curve algebriche sghembe ottenute per «piccola variazione» sopra superficie algebriche irriducibili

### Annali dell’Università di Ferrara (1962-12-01) 11: 107-113 , December 01, 1962

### Riassunto

In questa Nota viene data una condizione per stabilire se, partendo da una curva algebrica sghemba riducibile situata sopra una superficie algebrica irriducibile di ordine qualunque ed operando per «piccola variazione» sulla superficie stessa, sia possibile ottenere una curva algebrica sghemba irriducibile o, se irriducibile, abbia a contenere una o più componenti della curva data.