Spatially homogeneous random evolutions

Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the solution for large times. In particular, conditions for the existence of a stationary random field are established. Furthermore space-time renormalization limit theorems are obtained which lead to either Gaussian or non-Gaussian generalized processes depending on the case under consideration.     

Qualitative behavior of geostochastic systems

Stochastic partial differential equations with polynomial coefficients have many applications in the study of spatially distributed populations in genetics, epidemiology, ecology, and chemical kinetics. The purpose of this paper is to describe some methods for investigating the qualitative behavior of spatially homogenous solutions of nonlinear stochastic partial differential equations. The stability and bifurcation of solutions, as well as the behavior near critical points are discussed. The methods employed are the nonlinear Markov approximation, moment density inequalities for identifying invariant sets of behaviors and rescaling and quasi-linearization around critical points.     

Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.     

A plasma klystron for generating ultra-short electron bunches

A technique for producing ultra-short electron bunches (e.g., ⩽100 fs) from a continuous electron beam using a short plasma wave section and a drift space is explored. The bunches are a fraction of a plasma wavelength long and are spaced by a plasma wavelength, making them of interest for injection into plasma accelerators or for driving a klystron-like structure to produce infrared radiation     

Balanced sets in an independence structure induced by a submodular function

A submodular (and non-decreasing) function on a set induces an independence structure; the notion of a “balanced” set in this situation helps us determine whether a given independence structure is induced by any submodular function other than its own rank function, answering a question of U. S. R. Murty and I. Simon. The notion “balanced” also has a natural meaning when one independence structure is induced from another across a bipartite graph.     

Mapping properties of matrix summability methods

Summary Conditions on a complex matrix A are given which are necessary and sufficient for A to have the property that if x belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative kth differences, then Ax belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative jth differences. Entrata in Redazione il 18 giugno 1970.     

A model for streamer propagation

A model is presented to describe the propagation of positive corona streamers in the low field region of a non-uniform field gap in atmospheric air. It has been assumed that the growth is a property solely of the streamer tip, uninfluenced by the channel conductivity. Calculations from the model indicate that the criterion for propagation of a streamer in zero external field is that the number of ions in the tip be 10⁸ and the radius about 3×10^?3 cm. It is proposed that the streamer ceases to propagate as a result of the loss of energy of the tip due to the formation of ion pairs in the channel. The results of previous experimental observations of streamers are compared with calculations derived from the model, and a prediction from the model of the lifetime of streamers after voltage removal is discussed.