Problemas de palabra en Rusia y América

Puesto que este texto es sobre problemas de palabra, necesitamos primero definir el tema. Para mantenernos tan cerca como sea posible del significado exacto de las palabras, sugiero que un problema de no palabra es un problema formulado usando únicamente símbolos matemáticos y palabras técnicas como “resuelva la ecuación...” De igual forma, el problema de palabra usa palabras no matemáticas. Ubicándonos en un contexto matemático, estas palabras deben ser interpretadas matemáticamente lo que es una gran contribución al valor, entusiasmo y riesgo de los problemas de palabra

Andrei Toom Interview

NOTE: to view these items please visit http://dynkincollection.library.cornell.eduInterview conducted by Eugene Dynkin with Andrei Toom on February 23, 1990 in Ithaca, New York

A Critical Phenomenon in Growth Systems

The paper treats of interacting infinite or finite systems whose components' states are in the set f0; 1; 2; 3; : : :g . All components' initial states are zeroes. Components interact with each other in a local deterministic way, in addition to which every component's state grows by one with a constant probability ` at every moment of the discrete time. Our main question about infinite systems is whether the average value of components tends to infinity or remains bounded as t ! 1 . The analogous question about finite systems is how long the system's average remains less than a constant: this time may be bounded or tend to infinity as the system' size tends to infinity. Both in the infinite and finite cases sufficient conditions for both ways of behavior are given here. It is shown that the different ways of behavior may occur with one and the same deterministic interaction depending on the value of ` . The combinatorial method applied here to growth systems, was developed [7, 8, 9] fo..