Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Singular values of some modular functions

We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.Comment: 19 pages,corrected typo

Beta-decay of nuclei around Se-90. Search for signatures of a N=56 sub-shell closure relevant the r-process

Nuclear structure plays a significant role on the rapid neutron capture process (r-process) since shapes evolve with the emergence of shells and sub-shells. There was some indication in neighboring nuclei that we might find examples of a new N=56 sub-shell, which may give rise to a doubly magic Se-90 nucleus. Beta-decay half lives of nuclei around Se-90 have been measured to determine if this nucleus has in fact a doubly-magic character. The fragmentation of Xe-136 beam at the National Superconducting Cyclotron Laboratory at Michigan State University was used to create a cocktail of nuclei in the A=90 region. We have measured the half lives of twenty-two nuclei near the r-process path in the A=90 region. The half lives of As-88 and Se-90 have been measured for the first time. The values were compared with theoretical predictions in the search for nuclear-deformation signatures of a N=56 sub-shell, and its possible role in the emergence of a potential doubly-magic Se-90. The impact of such hypothesis on the synthesis of heavy nuclei, particularly in the production of Sr, Y and Zr elements was investigated with a weak r-process network. The new half lives agree with results obtained from a standard global QRPA model used in r-process calculations, indicating that Se-90 has a quadrupole shape incompatible with a closed N=56 sub-shell in this region. The impact of the measured Se-90 half-life in comparison with a former theoretical predication associated with a spherical half-life on the weak-r-process is shown to be strong

Determination of optimal drug dose and light dose index to achieve minimally invasive focal ablation of localised prostate cancer using WST11-vascular-targeted photodynamic (VTP) therapy

Objective: To determine the optimal drug and light dose for prostate ablation using WST11 (TOOKAD® Soluble) for vascular-targeted photodynamic (VTP) therapy in men with low-risk prostate cancer. Patients and Methods: In all, 42 men with low-risk prostate cancer were enrolled in the study but two who underwent anaesthesia for the procedure did not receive the drug or light dose. Thus, 40 men received a single dose of 2, 4 or 6 mg/kg WST11 activated by 200 J/cm light at 753 nm. WST11 was given as a 10-min intravenous infusion. The light dose was delivered using cylindrical diffusing fibres within hollow plastic needles positioned in the prostate using transrectal ultrasonography (TRUS) guidance and a brachytherapy template. Magnetic resonance imaging (MRI) was used to assess treatment effect at 7 days, with assessment of urinary function (International Prostate Symptom Score [IPSS]), sexual function (International Index of Erectile Function [IIEF]) and adverse events at 7 days, 1, 3 and 6 months after VTP. TRUS-guided biopsies were taken at 6 months. Results: In all, 39 of the 40 treated men completed the follow-up. The Day-7 MRI showed maximal treatment effect (95% of the planned treatment volume) in men who had a WST11 dose of 4 mg/kg, light dose of 200 J/cm and light density index (LDI) of >1. In the 12 men treated with these parameters, the negative biopsy rate was 10/12 (83%) at 6 months, compared with 10/26 (45%) for the men who had either a different drug dose (10 men) or an LDI of <1 (16). Transient urinary symptoms were seen in most of the men, with no significant difference in IPSS score between baseline and 6 months after VTP. IIEF scores were not significantly different between baseline and 6 months after VTP. Conclusion: Treatment with 4 mg/kg TOOKAD Soluble activated by 753 nm light at a dose of 200 J/cm and an LDI of >1 resulted in treatment effect in 95% of the planned treatment volume and a negative biopsy rate at 6 months of 10/12 men (83%)

Beta-decay half-lives and beta-delayed neutron emission probabilities of nuclei in the region below A=110, relevant for the r-process

Measurements of the beta-decay properties of r-process nuclei below A=110 have been completed at the National Superconducting Cyclotron Laboratory, at Michigan State University. Beta-decay half-lives for Y-105, Zr-106,107 and Mo-111, along with beta-delayed neutron emission probabilities of Y-104, Mo-109,110 and upper limits for Y-105, Zr-103,104,105,106,107 and Mo-108,111 have been measured for the first time. Studies on the basis of the quasi-random phase approximation are used to analyze the ground-state deformation of these nuclei.Comment: 21 pages, 10 figures, article accepted for publication in Physical Review

Atomic-scale confinement of optical fields

In the presence of matter there is no fundamental limit preventing confinement of visible light even down to atomic scales. Achieving such confinement and the corresponding intensity enhancement inevitably requires simultaneous control over atomic-scale details of material structures and over the optical modes that such structures support. By means of self-assembly we have obtained side-by-side aligned gold nanorod dimers with robust atomically-defined gaps reaching below 0.5 nm. The existence of atomically-confined light fields in these gaps is demonstrated by observing extreme Coulomb splitting of corresponding symmetric and anti-symmetric dimer eigenmodes of more than 800 meV in white-light scattering experiments. Our results open new perspectives for atomically-resolved spectroscopic imaging, deeply nonlinear optics, ultra-sensing, cavity optomechanics as well as for the realization of novel quantum-optical devices