Relaxation behaviour at the spin-flop phase transition in the quasi-1D antiferromagnet CsMnCl3·2H2O

The low-frequency relaxation behaviour of the linear-chain antiferromagnet CsMnCl3·2H2O at the spin-flop transition has been determined from dynamic susceptibility measurements on a single crystal placed in direct contact with liquid helium. The experiments were performed between 1.4 and 4.2 K in the frequency range 0.1 Hz–3.0 kHz with a frequency-sweeping SQUID susceptometer. Below Tλ = 2.17 K, the relaxation rate τ−1 manifests an exponential temperature dependence, τ−1 = ω0e−E/kT, where E/k = 3.19±0.04 K is approximately equal to the magnitude of the intrachain exchange interaction constant Ja/k. Above Tλ the apparent deviation from the exponential behaviour has been explained satisfactorily by using the thermal conduction model of relaxation. The field-dependent factor ω0 is directly proportional to the ratio of the adiabatic χs to the isothermal χT susceptibilities

Adding semantics to tabular agrifood data

Tabular data are abundant in the agrifood domain, as in many other fields. Tables in databases, spreadsheets and reports are common in business applications, research papers, policy documents, etc. They contain data with a repetitive structure, containing multiple rows of similar data. The header of each ..

On the Equation Y2=(X+p)(X2+p2)

In this paper the family of elliptic curves over Q given by the equation y(2) = (x + p)(x(2) + p(2)) is studied. It is shown that for p a prime number = +/-3 mod 8, the only rational solution to the equation given here is the one with y = 0. The same is true for p = 2. Standard conjectures predict that the rank of the group of rational points is odd for all other primes p. A lot of numerical evidence in support of this is given. We show that the rank is bounded by 3 in general for prime numbers p. Moreover, this bound can only be attained for certain special prime numbers p = 1 mod 16. Examples of such rank 3 curves are given. Lastly, for certain primes p = 9 mod 16 nontrivial elements in the Shafarevich group of the elliptic curve are constructed. In the literature one finds similar investigations of elliptic curves with complex multiplication. It may be interesting to note that the curves considered here do not admit complex multiplication.</p