A link of stochastic differential equations to nonlinear parabolic equations

Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.     

Measurement of kaonic X-rays from Li,LiH AND Be

We have observed X-rays from kaons stopping in targets of Li, LiH and Be. The strong interaction widths, shifts and relative yield of the last observed X-ray have been measured. There is evidence for a difference in the yield of the n = 3 → 2 Li X-rays in Li metal and LiH. There is no evidence in the spectra for X-rays from kaonic hydrogen formed in LiH.     

Random creation and dispersion of mass

Consider evolution of density of a mass or a population, geographically situated in a compact region of space, assuming random creation-annihilation and migration, or dispersion of mass, so the evolution is a random measure. When the creation-annihilation and dispersion are diffusions the situation is described formally by a stochastic partial differential equation; ignoring dispersion make approximations to the initial density by atomic measures and if the corresponding discrete random measures converge “in law” to a unique random measure call it a solution. To account for dispersion Trotter's product formula is applied to semiflows corresponding to dispersion and creation-annihilation. Existence of solutions has been a conjecture for several years despite a claim in ([2], J. Multivariate Anal. 5, 1–52). We show that solutions exist and that non-deterministic solutions are “smeared” continuous-state branching diffusions.     

A completely bounded characterization of operator algebras

Supported by a grant from the NSF     

Polymerization of n-octadecene-1 with catalysts derived from titanium tetrachloride and triethylaluminum

The effects of variation in Al/Ti mole ratio, catalyst concentration, reaction time, and temperature on the yield and some physical properties of polymers of n-octadecene-1 obtained with the use of Ziegler catalyst systems derived from titanium tetrachloride and triethylaluminum have been investigated. Results show many features similar to those obtained by other workers with lower olefins. In general, the yield of polymer shows a distinct maximum at an Al:Ti mole ratio of 2.8:1 and total catalyst concentration (at the stated mole ratio) of 4%, based on monomer; the yield increases sharply with polymerization temperature to a maximum at about 40°C. and with time up to about 12 hr. at 25°C. Polymer intrinsic viscosity also shows a strong dependence on Al:Ti mole ratio and catalyst concentration, increasing between Al:Ti mole ratios of 2.0–3.4, and showing a maximum at catalyst concentration of 3.5% on monomer. Polymer intrinsic viscosity shows a decrease with increasing reaction temperature and an increase with time of polymerization. The polymer densities, melting points, and fraction soluble in hexane (at 25°C.) appear to show much less dependence on the variables under consideration, and no firm conclusions are drawn. An important reaction concurrent with polymerization is the formation of a trans nonterminal isomer of octadecene. This certainly affects the yield (the nonterminal isomer not being polymerizable under the same conditions); the effect of the presence during polymerization of isomerized monomer on the physical characteristics of the polymer is less clear, and further work is proceeding.     

A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems

Large classes of data association problems in multiple targettracking applications involving both multiple and single sensorsystems can be formulated as multidimensional assignment problems.These NP-hard problems are large scale and sparse with noisyobjective function values, but must be solved inreal-time. Lagrangian relaxation methods have proven to beparticularly effective in solving these problems to the noise levelin real-time, especially for dense scenarios and for multiple scansof data from multiple sensors. This work presents a new class ofconstructive Lagrangian relaxation algorithms that circumvent some ofthe deficiencies of previous methods. The results of severalnumerical studies demonstrate the efficiency and effectiveness of thenew algorithm class.