In vivo and in vitro testing of microelectronically fabricated planar sensors designed for applications in cardiology

Summary Ion-sensitive, planar micro-electrode arrays were fabricated by photolithographic microelectronics technology on a flexible polyimide substrate. The steps of the microelectronics processing are summarized. The electrodes were tested in blood serum, whole blood and in the hamstring muscle of anesthetized rabbits. The performance characteristics of planar pH-sensors are compared with commercial glass electrodes. The close correlation of the data are encouraging for further acute and later chronic applications.Dedicated to Professor Dr. Wilhelm Fresenius     

Galerkin solutions of stiff two-point boundary-value problems

Through the example of Conte (Ref. 6), the Galerkin procedure with a small number (N6) of low-degree polynomial modes is illustrated as a computationally rapid and effective technique for solving extremely stiff linear two-point boundary-value problems. Numerical solutions are provided for eigenvalue spreads ranging from 20 through 10⁶. They agree with the exact solution to at least 2N decimal places. The errors are insensitive to the eigenvalue spread. Comparisons are made with the continuation technique of Roberts and Shipman (Ref. 1), who did not succeed in solving this example for =(36,000).This work was supported in part by the National Science Foundation under Grant No. GJ-1075.     

Uniform approximation by some Hermite interpolating splines

In this paper some upper bound for the error ∥ s-f ∥_∞ is given, where f ε C¹[a,b], but s is a so-called Hermite spline interpolant (HSI) of degree 2q ?1 such that f(x_i) = s(x_i), f′(rmx_i) = s′(x_i), s^(j) (x_i) = 0 (i = 0, 1, …, n; j = 2, 3, …, q ?1; n > 0, q > 0) and the knots x_i are such that a = x₀ < x₁ < … < x_n = b. Necessary and sufficient conditions for the existence of convex HSI are given and upper error bound for approximation of the function fε C¹[a, b] by convex HSI is also given.     

An explicit form of the differential equationsy″=q(t)y with periodic solutions

Summary This paper contains an explicit form of a differential equation of the type y″=q(t)y, all solutions of which are periodic or half-periodic. Entrata in Redazione il 30 giugno 1969.     

Sur les équations différentielles linéaires du second ordre dont les solutions ont des racines formant une suite convexe

Sans résumé Présenté par P. Turán     

Some inequalities for the gamma function

Several inequalities involving gamma function are obtained. They are established using elementary properties of logarithmically convex functions.     

On generalized Seiffert means

Generalizations of two Seiffert means, usually denoted by P and T, are defined and investigated. The means under discussion are symmetric and homogeneous of degree one in each variable. Computable lower and upper bounds for the new means are also established. Several inequalities involving means discussed in this paper are obtained. In particular, two Wilker’s type inequalities involving those means are derived.