Sensitivity of convergent matrices and polynomials

A matrix A is said to be convergent if and only if all its characteristic roots have modulus less than unity. When A is real an explicit expression is given for real matrices B such that A + B is also convergent, this expression depending upon the solution of a quadratic matrix equation of Riccati type. If A and A + B are taken to be in companion form, then the result becomes one of convergent polynomials (i.e., polynomials whose roots have modulus less then unity), and is much easier to apply. A generalization is given for the case when A and A + B are complex and have the same number of roots inside and outside a general circle.     

Observation of a direct low-mass e+e− continuum in π-p interactions at 16 GeV/c

The production of prompt electron-positron pairs in 16 GeV/c π^-p collisions has been measured using the LASS spectrometer at SLAC. An excess of events is observed above the estimated contribution of direct and Dalitz decays of known resonances in the kinematic range defined by $\text{0.1?χ?0.45, 0?p}{}_{\mathrm{T}}\text{?0.8}\text{GeV}\text{c}$ and $\text{0.2?M(e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)?0.7}\text{GeV}\text{c}{}^2$. The excess signal decreases slowly with increasing M, but exhibits very steep χ and p_T² dependence.     

On a system of non-linear differential equations

Summary E. Kasner(1925) considered a system of non-linear differential equations in three variables. The authors of this paper have extended this system to n variables by means of a linear transformation with complex coefficients. The formulas obtained for the solutions of the differential equations give a simplification of Kasner’s solutions. Entrata in Redazione il 26 agosto 1968.     

The atomic absorption determination of antimony,arsenic, bismuth, cadmium, lead, and tin in iron, copper,and zinc alloys with the graphite furnace

Antimony, arsenic, bismuth, cadmium, lead, and tin can be determined in metallurgical samples by flame atomic absorption spectrometry at levels of 0.005 wt%, but lower concentrations frequently necessitate preconcentration. The graphite furnace allows determination of these elements at concentrations 1–2 orders of magnitude lower than is possible with flame techniques. All six elements have detection limits at or below 1μg g⁻¹ in a variety of alloys. Calibration for antimony and load was done with standards containing the principal component of the alloy as a synthetic matrix. Bismuth, cadmium, and tin could be determined accurately only by the standard addition method. Arsenic could be determined in iron alloys with synthetic standards, but standard additions were required for copper alloys.     

The Itô-Clifford integral III. The Markov property of solutions to stochastic differential equations

It is shown that the solution to the Itô-Clifford stochastic differential equationdX _t =F(X _t ,t)dΨ _t +dΨ _t G(X _t ,t)+H(X _t ,t)dt, whereF, G, H are suitable Lipschitz functions andΨ _t is the fermion martingale, satisfies a Markov property.