This paper presents a new numerical model for computing the current density, field distributions and AC losses in superconductors. The model, based on the direct magnetic field H formulation without the use of vector and scalar potentials (which are used in conventional formulations), relies on first-order edge finite elements. These elements are by construction curl conforming and therefore suitable to satisfy the continuity of the tangential component of magnetic field across adjacent elements, with no need for explicitly imposing the condition . This allows the overcoming of one of the major problems of standard nodal elements with potential formulation: in the case of strong discontinuities or nonlinearities of the physical properties of the materials and/or in presence of sharp corners in the conductors’ geometry, the discontinuities of the potentials’ derivatives are unnatural and without smoothing artifices the convergence of the algorithm is put at risk. In this work we present in detail the model for two-dimensional geometries and we test it by comparing the numerical results with the predictions of analytical solutions for simple geometries. We use it successively for investigating cases of practical interest involving more complex configurations, where the interaction between adjacent tapes is important. In particular we discuss the results of AC losses in superconducting windings.

The crucial role of pituitary GnRH receptors (GnRH-R) in the control of reproductive functions is well established. These receptors are the target of GnRH agonists (through receptor desensitization) and antagonists (through receptor blockade) for the treatment of steroid-dependent pathologies, including hormone-dependent tumors. It has also become increasingly clear that GnRH-R are expressed in cancer tissues, either related (i.e. prostate, breast, endometrial, and ovarian cancers) or unrelated (i.e. melanoma, glioblastoma, lung, and pancreatic cancers) to the reproductive system. In hormone-related tumors, GnRH-R appear to be expressed even when the tumor has escaped steroid dependence (such as castration-resistant prostate cancer). These receptors are coupled to a G(αi)-mediated intracellular signaling pathway. Activation of tumor GnRH-R by means of GnRH agonists elicits a strong antiproliferative, antimetastatic, and antiangiogenic (more recently demonstrated) activity. Interestingly, GnRH antagonists have also been shown to elicit a direct antitumor effect; thus, these compounds behave as antagonists of GnRH-R at the pituitary level and as agonists of the same receptors expressed in tumors. According to the ligand-induced selective-signaling theory, GnRH-R might assume various conformations, endowed with different activities for GnRH analogs and with different intracellular signaling pathways, according to the cell context. Based on these consistent experimental observations, tumor GnRH-R are now considered a very interesting candidate for novel molecular, GnRH analog-based, targeted strategies for the treatment of tumors expressing these receptors. These agents include GnRH agonists and antagonists, GnRH analog-based cytotoxic (i.e. doxorubicin) or nutraceutic (i.e. curcumin) hybrids, and GnRH-R-targeted nanoparticles delivering anticancer compounds.

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Prostate cancer growth depends, in its earlier stages, on androgens and is usually pharmacologically modulated with androgen blockade. However, androgen-ablation therapy may generate androgen-independent prostate cancer, often characterized by an increased invasiveness. We have found that the 5A-reduced testosterone derivative, dihydrotestosterone (the most potent natural androgen) inhibits cell migration with an androgen receptor-independent mechanism. We have shown that the dihydrotestosterone metabolite 5A-androstane-3B,17B-diol (3B-Adiol), a steroid which does not bind androgen receptors, but efficiently binds the estrogen receptor B (ERB), exerts a potent inhibition of prostate cancer cell migration through the activation of the ERB signaling. Very surprisingly, estradiol is not active, suggesting the existence of different pathways for ERB activation in prostate cancer cells. Moreover, 3B-Adiol, through ERB, induces the expression of E-cadherin, a protein known to be capable of blocking metastasis formation in breast and prostate cancer cells. The inhibitory effects of 3B-Adiol on prostate cancer cell migration is counteracted by short interfering RNA against E-cadherin. Altogether, the data showed that (a) circulating testosterone may act with estrogenic effects downstream in the catabolic process present in the prostate, and (b) that the estrogenic effect of testosterone derivatives (ERB-dependent) results in the inhibition of cell migration, although it is apparently different from that linked to estradiol on the same receptor and may be protective against prostate cancer invasion and metastasis. These results also shed some light on clinical observations suggesting that alterations in genes coding for 3B-hydroxysteroid dehydrogenases (the enzymes responsible for 3B-Adiol formation) are strongly correlated with hereditary prostate cancer. (Cancer Res 2005; 65(12): 5445-53)

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