Multivariable polynomial injections on rational numbers

For each number field k, the Bombieri-Lang conjecture for k-rational points on surfaces of general type implies the existence of a polynomial f(x,y) in k[x,y] inducing an injection k x k --> k.Comment: 4 page

On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ($P$) or with delay ($D$) to the transmitter. Denoting by $S_1$, $S_2$, and $S_3$ the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_1,S_2,S_3) \in \{P,D\}^3$. We denote by $\lambda_{S_1 S_2 S_3}$ the fraction of time during which the state $S_1S_2S_3$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$, $PDP$, and $DDP$. We then focus our attention on the symmetric case in which $\lambda_{PDD}=\lambda_{DPD}$. For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that, the synergistic gains in terms of SDoF by alternating CSIT is not restricted to multi-receiver wiretap channels; and, can also be harnessed under broadcast setting.Comment: To Appear in IEEE Transactions on Information Forensics and Securit

Heuristics for the Brauer-Manin obstruction for curves

We conjecture that if C is a curve of genus >1 over a number field k such that C(k) is empty, then a method of Scharaschkin (equivalent to the Brauer-Manin obstruction in the context of curves) supplies a proof that C(k) is empty. As evidence, we prove a corresponding statement in which C(F_v) is replaced by a random subset of the same size in J(F_v) for each residue field F_v at a place v of good reduction for C, and the orders of Jacobians over finite fields are assumed to be smooth (in the sense of having only small prime divisors) as often as random integers of the same size. If our conjecture holds, and if Shafarevich-Tate groups are finite, then there exists an algorithm to decide whether a curve over k has a k-point, and the Brauer-Manin obstruction to the Hasse principle for curves over the number fields is the only one.Comment: 7 page

Self-organized patterns of macroscopic quantum tunneling in molecular magnets

We study low temperature resonant spin tunneling in molecular magnets induced by a field sweep with account of dipole-dipole interactions. Numerical simulations uncovered formation of self-organized patterns of the magnetization and of the ensuing dipolar field that provide resonant condition inside a finite volume of the crystal. This effect is robust with respect to disorder and should be relevant to the dynamics of the magnetization steps observed in molecular magnets.Comment: 4 Phys. Rev. pages, 5 figure

Kernchemische Untersuchungen zur Produktion einiger medizinisch relevanter Strontium und Rubidium-Isotope

In palliative pain therapy of cancer patients with bone metastases the longer-lived $\beta^{-}$-emitter$^{89}$Sr (T$_{1/2}$ = 50.5 d) is often used. However, since corpuscular radiation cannot be measuredfrom outside the body, there is a lack of biodistribution data. The radiation dose caused to thepatient is therefore estimated rather empirically. The shorter-lived positron-emitter $^{83}$Sr($_{T1/2}$ = 32.4 h, I$_{\beta^+}$ = 24 %) offers the possibility of quantitative investigation of the biokinetics viaPET studier, allowing thereby a better estimation of the dose. In this work, the possibility ofproduction of $^{83}$Sr by proton induced reaction an highly enriched $^{85}$Rb was investigated andcompared with the known production method $^{82}$Kr($^{3}$He,2n) $^{83}$Sr. For this purpose, extensivenuclear data measurements an the $^{85}$Rb(p,p' xn)- and $^{85}$Rb(p,xn)-reactions, leading to theformation of the isotopes $^{84m, g}$Rb, $^{83}$Rb, $^{82}$Rb, $^{81}$Rb and $^{85m, g}$Sr, $^{83}$Sr, $^{82}$Sr, $^{81}$Sr, were done.From the measured excitation functions the expected theoretical yields could be calculatedand the optimum conditions for the production of $^{83}$Sr were deduced. The optimum energyrange was found to be E$_{p}$ = 35 $\rightarrow$ 30 MeV, with $^{83}$Sr thick target yield of > 90 MBq/$\mu$Ah andthe isotopic impurity of 10 %. This impurity is much lower inthe energy range of 18 $\rightarrow$ 10 MeV (< 1 %), however, the yield of $^{83}$Sr is reduced to5 MBq/$\mu$Ah. The chemical separation of radioisotopes was performed using HPLC in the caseof data measurements and liquid chromatography in production irradiations. The chemicalyields were $\approx$ 100%. The experimentally determined cross section data were compared withtheoretical calculations, using the hybrid model code ALICE-IPPE 1996. They were in goodagreement. The determination of the isomeric cross section ratios of the isomer pairs $^{85m,g}$Srand $^{84m, g}$Rb confirmed the previous observation that with the increasing energy of theprojectile the isomeric state with the higher spin ($^{85g}$Sr with spin 9/2$^{+}$ and $^{84g}$Rb with spin 6$^{-}$)is favoured as compared to the state with the lower spin ($^{85m}$Sr with Spin 1/2$^{-}$ and $^{84m}$Rb withSpin 2$^{-}$)