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Upper trace bounds for the product of two n × n complex matrices are presented. The real component of the trace inequality is tighter than von Neumann's inequality, and the imaginary component is new.
We consider a Markov chain in continuous time with one absorbing state and a finite set S of transient states. When S is irreducible the limiting distribution of the chain as t→∞, conditional on survival up to time t, is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which S may be reducible, and show that it remains valid if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on S has geometric (but not, necessarily, algebraic) multiplicity one. The result is then applied to pure death processes and, more generally, to quasi-death processes. We also show that the result holds true even when the geometric multiplicity is larger than one, provided the irreducible subsets of S satisfy an accessibility constraint. ...
1. 1. In artificial heart stimulation, the essential quantity is the density of current, , in the intramyocardial wall. Dosage of the pulse amplitude in volts can have serious consequences for the patient. Curve indications in volts on pacemakers and in publications and records must, therefore, be rejected. 2. 2. Hence, the pacemaker should supply stabilized current pulses even while the load impedance is increasing. 3. 3. The distortion of the voltage curve at stabilized current is an electrode effect. 4. 4. Separate measurement and registration of the physical quantities involved in stimulation is advisable. The values obtained in every individual patient warrant conclusions as to the method of choice. It is recommended that one start with the Furman and Schwedel method, i.e., with one electrode in the right ventricle and the other p...
Report describing the design, feasibility, and economic concerns of a small-scale reprocessing plant.
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