Monitoring of water content and water distribution in ischemic hearts

We determined water content and water distribution by fitting dielectric spectra of ischemic canine hearts between 5 MHz and 3 GHz with a newly developed model which describes heart cells and subcellular organelles as rotational ellipsoids filled with electrolyte enclosed by an isolating membrane. The fraction of dry material is modelled by spherical particles with a small dielectric permittivity. Free model parameters were water content, cell volume fraction, and the conductivity of the electrolytes. Resulting model parameters were compared to data from tissue desiccation and to conductivity changes produced by protons and lactate ions. We investigated hearts in two states: during ischemia after interruption of blood flow (pure ischemia, PI, n=5) and during ischemia after resuscitation with Tyrode's solution (IAR, n=14).The difference between water content determined by tissue desiccation and by dielectric spectroscopy was less than 0.5%. During 360 min of ischemia, water content in IAR decreased from 85+/-1.6% to 83+/-2.2% and in PI from 80+/-0.8% to 78+/-1.5%. Cellular volume fraction in IAR increased from 0.47+/-0.045 to 0.63+/-0.031 and in PI from 0.62+/-0.014 to 0.73+/-0.013, which is consistent with published morphometric data. After 180 min of ischemia, the increase of the cytosolic conductivity was 0.14+/-0.02 S/m as calculated from the dielectric spectrum and was similar to the conductivity increase which was roughly estimated on the basis of tissue lactate concentration.In conclusion, dielectric spectroscopy combined with our model analysis facilitates the monitoring of water content and distribution by means of nondestructive surface probes.     

Modeling the competitive dissociation of protonated 2,3-butanedione. The enthalpy of formation of methylhydroxycarbene

The enthalpy of formation of methylhydroxycarbene, CH(3)COH, has been determined from measurements of the threshold energy for collision-induced dissociation of protonated 2,3-butanedione in a flowing afterglow-triple quadrupole mass spectrometer and found to be 16 +/- 4 kcal/mol, 57 +/- 4 kcal/mol higher than that of acetaldehyde. From the measured enthalpy of formation, the difference between the first and second C-H BDEs in ethanol is found to be 17 kcal/mol, which implies a singlet-triplet splitting of 28 kcal/mol in the carbene. The activation energies for loss of ketene and carbon monoxide from protonated butanedione are found to be 60 +/- 4 and 50 +/- 4 kcal/mol, respectively. On the basis of experimental and computational results, the loss of carbon monoxide is proposed to proceed through a tight transition state. Although calculations also suggest a tight transition state for loss of ketene, the experimental data indicate that it occurs via a loose transition state, possibly forming by proton transfer along the direct dissociation pathway.     

Konvexität in halbgeordneten Ebenen

Let (E, (ie63-01),) be a halfordered plane and call convex if M contains for any two points a,bM all pointsx between a and b. It is shown that segments [a,b] are convex if and only if (E, (ie63-02)) is the affine plane of order 3, (E, (ie63-03),) is an ordered plane or is near-trivial.

---

---

Herrn Professor Johannes Böhm zum 70. Geburtstag gewidmet     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.