## SEARCH

#### Institution

##### ( see all 1263)

- Mathematisches Institut der Universität 91 (%)
- University of California 65 (%)
- Universität Innsbruck 64 (%)
- Universität Wien 62 (%)
- University of Illinois 50 (%)

#### Author

##### ( see all 4548)

- Gröbner, Wolfgang 62 (%)
- Hofreiter, Nikolaus 62 (%)
- Weil, André 32 (%)
- Takeuti, Gaisi 28 (%)
- Zaring, Wilson M. 28 (%)

#### Publication

##### ( see all 182)

- Mathematical notes of the Academy of Sciences of the USSR 210 (%)
- Mathematische Annalen 194 (%)
- Cybernetics 160 (%)
- Mathematische Zeitschrift 156 (%)
- Siberian Mathematical Journal 126 (%)

#### Subject

##### ( see all 72)

- Mathematics [x] 4757 (%)
- Mathematics, general 2518 (%)
- Algebra 717 (%)
- Analysis 590 (%)
- Applications of Mathematics 417 (%)

## CURRENTLY DISPLAYING:

Most articles

Fewest articles

Showing 1 to 10 of 4757 matching Articles
Results per page:

## Back Matter - Invariant Subspaces

### Invariant Subspaces (1973-01-01): 77 , January 01, 1973

## Diffusion Limited Reactions

### Variational Methods Applied to Problems of Diffusion and Reaction (1973-01-01) 24: 42-58 , January 01, 1973

A diffusion limited reaction rate is one which depends solely on the rate at which solute molecules diffuse to the site of reaction such as the surface of a reactant particle. When all reaction processes at the surface of the reactant particle are so fast that surface equilibrium conditions are maintained, the effective (or net) reaction rate does not depend on the nature of the process at the site of reaction, but rather upon the rate of transport by diffusion.

## The graph of an abstract polytope

### Mathematical Programming (1973-12-01) 4: 336-346 , December 01, 1973

Recently a generalization of simple convex polytopes to combinatorial entities known as abstract polytopes has been proposed. The graph of an abstract polytope of dimension*d* is a regular connected graph of degree*d.* Given a connected regular graph Г of degree*d*, it is interesting to find out whether it is the graph of some abstract polytope*P.* We obtain necessary and sufficient conditions for this, in terms of the existence of a class of simple cycles in Г satisfying certain properties. The main result in this paper is that if a pair of simple convex polytopes or abstract polytopes have the same two-dimensional skeleton, then they are isomorphic. Every two-dimensional face of a simple convex polytope or an abstract polytope is a simple cycle in its graph. Given the graph of a simple convex polytope or an abstract polytope and the simple cycles in this graph corresponding to all its two-dimensional faces, then we show how to construct all its remaining faces. Given a regular connected graph Г and a class of simple cyles*D* in it, we provide necessary and sufficient conditions under which*D* is the class of two-dimensional faces of some abstract polytope which has Г as its graph.

## Back Matter - Spectral Analysis of Nonlinear Operators

### Spectral Analysis of Nonlinear Operators (1973-01-01): 346 , January 01, 1973

## Effect of field theoretical corrections on X-ray spectra

### Proceedings of the Indian Academy of Sciences - Section A (1973-01-01) 77: 26-41 , January 01, 1973

The wavelengths of
$$K_{\alpha _1 } , K_{\alpha _2 } , K_{\beta _1 } , K_{\beta _2 } , K_{\beta _2 } I and K_{\beta _2 } II$$
lines of heavy elements of atomic number 70–92 and the associated energy levels, K, L_{II}, L_{III}, M_{II}, M_{III}, N_{II} and N_{III} have been calculated using a modified form of the relativistic energy formula of Sommerfeld, incorporating in it both the total and internal screening constants in a closed form. All the field theoretical corrections in the second and the fourth order as well as the finite nuclear size correction have been included.

The relative intensities $$K_{\alpha _2 } /K_{\alpha _1 } , K_{\beta _2 } / K_{\beta _1 } , and K_{\beta _2 } II/K_{\beta _2 } I$$ have been calculated with relativistic wavefunctions. In addition to the retradation and screening, field theoretical corrections have also been used. A logical extension of the one electron-model with application of the field theoretical corrections improves the calculated results of not only the energy levels but also the relative intensities of X-ray lines.

## On some Hasse Principles over formally real fields

### Mathematische Zeitschrift (1973-12-01) 134: 291-301 , December 01, 1973

## Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren

### Mathematische Zeitschrift (1973-09-01) 134: 255-274 , September 01, 1973

## La formalizzazione della nozione di prova e una nuova definizione dell'indipendenza. II

### Annali dell’Università di Ferrara (1973-12-01) 18: 15-53 , December 01, 1973

### Riassunto

La prima parte di questo lavoro è stata pubblicata sul Vol. XVII, N. 9 di questa rivista. In essa si è compiuta un'analisi delle trattazioni dell'indipendenza nella teoria delle probabilità, analisi che ha consentito di individuare tre approcci fondamentali al problema della definizione dell'indipendenza. Ciascuno dei suddetti approcci è stato ampiamente analizzato sia nelle sue trattazioni intuitive sia, quando ciò si verifichi, nelle sue trattazioni formalizzate. Questo articolo consta della seconda, terza e quarta parte del lavoro. Nella seconda parte si espongono intuitivamente le idee di fondo relative alla nozione di «prova» che si intende introdurre tra i concetti primitivi della teoria delle probabilità. La terza parte è dedicata all'analisi, operata sempre a livello intuitivo, di una nuova definizione d'indipendenza non coinvolgente la nozione di «probabilità», definizione che diviene formulabile grazie alla nozione di «prova». La quarta parte è infine dedicata alla formalizzazione degli argomenti trattati nella seconda e nella terza parte.

## Modular Forms and ℓ-Adic Representations

### Modular Functions of One Variable II (1973-01-01) 349: 361-500 , January 01, 1973

This report is another attempt on the part of its author to come to terms with the circumstance that L-functions can be introduced not only in the context of automorphic forms, with which he has had some experience, but also in the context of diophantine geometry. That this circumstance can be the source of deep problems was, I believe, first perceived by E. Artin. He was, to be sure, concerned with forms on GL(1) and with varieties of dimension 0. This remains the only case in which results of any profundity have been obtained. These have been hard won. Their mathematical germ is the theory of cyclotomic fields; itself easy-only in comparison to the general theory.