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## Maximal Multiplicative Properties of Partitions

### Annals of Combinatorics (2016-03-01) 20: 59-64 , March 01, 2016

Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any *n* ≠ 7. The basis for this is an inequality for the partition function which seems not to have been noticed before.

## Some connections between ergodic theory and the iteration of polynomials

### Arkiv för Matematik (1969-11-01) 8: 25-32 , November 01, 1969

## S-Ringe und verallgemeinerte Charaktere auf endlichen Gruppen

### Mathematische Zeitschrift (1964-06-01) 84: 101-119 , June 01, 1964

## Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments

### Journal of Optimization Theory and Applications (2012-04-01) 153: 195-224 , April 01, 2012

A cell-population-based model for tumor growth under anti-angiogenic treatment, with the tumor volume and its variable carrying capacity as variables, is combined with the linear-quadratic model for damage done by radiation ionization. The resulting multi-input system is analyzed as an optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric constraints that limit the overall amounts of anti-angiogenic agents, respectively, the damage done to healthy tissue by radiotherapy. For various model formulations, explicit expressions for singular controls are derived for both the dosage of the anti-angiogenic therapeutic agent and the radiation dose schedule. Their role in the structure of optimal protocols is discussed.

## Biological Applications

### Mathematical Aspects of Pattern Formation in Biological Systems (2014-01-01) 189: 287-295 , January 01, 2014

We discuss a number of biological, chemical and ecological applications of pattern formation in reaction-diffusion systems. These include the head development and regeneration in *Hydra*, embryology for newt and *Drosophila*, pigmentation patterns on sea shells, fish and mammals and, finally, patterns on growing domains for angelfish body patterns and alligator tooth formation.

## Countable inductive limits of frechet algebras

### Journal d’Analyse Mathématique (1997-12-01) 71: 195-204 , December 01, 1997

We show that the Gelfand-Mazur theorem holds for countable inductive limits of Frechet algebras (we do not assume that the homomorphisms which define the inductive limit are continuous, or one-to-one). This question is motivated by the fact that the spectrum of some elements of such an algebra may be empty. We also discuss in detail a countable inductive limit of Frechet algebras of holomorphic functions, which provides an elementary, but seminal, counterexample to the biinvariant subspace problem for complete, reflexive, locally convex spaces.

## Three Substitution Groups. Illustrations of the Symmetric Group S4

### Studies in Structure (1972-01-01): 187-198 , January 01, 1972

In section 8.5 we constructed a field G.F.2^{3} consisting of eight polynomials of degree 2 over the field Z_{2} using an indeterminate R which satisfied the irreducible cubic equation *R*^{3} = *R* + 1. The seven non-zero elements form a cyclic group under multiplication. This enables us to set out a table of reciprocals among its elements as follows:

## Comment ecrire les nombres entiers dans une base qui n'est pas entiere

### Acta Mathematica Hungarica (1989-09-01) 54: 237-241 , September 01, 1989

## Reduced unitary Whitehead groups of skew fields of noncommutative rational functions

### Journal of Soviet Mathematics (1982-05-01) 19: 1067-1071 , May 01, 1982

We calculate the reduced unitary Whitehead groups of skew fields of quotients of noncommutative polynomial rings. We prove a stability theorem in the case where the noncommutative polynomial ring is related to an inner automorphism of the original skew field.

## Brand Preferences and Simple Markov Processes

### Mathematical Models in Marketing (1976-01-01): 132 , January 01, 1976

### Summary

Brand preference information combined with a simple two-dimensional Markov process is used to study characteristics of market dynamics. Advertising alters temporarily the brand preference structure of the consuming public. Discussions of time relations, period-to-period changes in market shares, gains and losses resulting from promotional activity and rapidity of convergence to new steady-state values are considered. Sensitivity characteristics of the relations are commented upon.