Given bounded positive invertible operators A and B on a Hilbert space H, it is shown that the inequality AXA -1 + B -1 XB 2 X holds for all bounded operators X of rank 1 if and only if B = f (A) for some increasing function f satisfying a certain simple inequality, which in the case when the spectr
Stirred pots, tubular reactors, and self-adjoint operators
β Scribed by D. Ramkrishna; N.R. Amundson
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 626 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0009-2509
No coin nor oath required. For personal study only.
β¦ Synopsis
Boundary value problems involving continuous flow reactors have been considered in which tubular and well-stirred tank reactors have been considered together with an axial dispersion model for the tubular reactor. This formulation does away with the customary but non-physical discontinuity in the state of the feed stream at the inlet to the stirred tank reactor. The problems, restricted to isothermal reactors entertaining first order reaction systems, have been solved by means of an elegant formalism in tune with the general theory of self-adjoint operators in abstract Hilbert space and consistent with the elementary treatment.
π SIMILAR VOLUMES
This paper deals with Volterra perturbations of normal operators in a separable Hilbert space. Invertibility conditions and estimates for the norm of the inverse operators are established. In addition, bounds for the spectrum are suggested. Applications to integral, integro-differential, and matrix
In this contribution we investigate oscillation and spectral properties of self-adjoint differential operators of the form r~ M(y ## ' + L~o~(I). where t C I := [a, co), r~ > 0 and r0 .... ,m-l, 77 Oscillation and nonoscillation of (1.1) are defined using the concept of conjugate points. Two