Flags in zero dimensional complete intersections and indices of real vector fields

We introduce bilinear forms in a flag in a complete intersection local $\mathbb R$-algebra of dimension 0, related to the Eisenbud-Levine, Khimshiashvili bilinear form. We give a variational interpretation of these forms in terms of Jantzen's filtration and bilinear forms. We use the signatures of these forms to compute in the real case the constant relating the GSV-index with the signature function of vector fields tangent to an even dimensional hypersurface singularity, one being topologically defined and the other computable by finite dimensional commutative algebra methods.Comment: 17 pages. v2: Some changes in the introduction. A few typos corrected. To appear in Mathematische Zeitschrif

Reply to the comment on the letter "Geometric Origin of the Tennis Racket Effect"

The author of the comment~[arXiv:2302.04190] criticizes our published results in Phys. Rev. Lett. \textbf{125}, 064301 (2020) about the Tennis Racket Effect (TRE). The TRE is a geometric effect which occurs in the free rotation of any asymmetric rigid body. We explain why the criticism of this comment is not valid.Comment: 3 page

Signatures of physical constraints in rotating rigid bodies

We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery Phase and in the Tennis Racket Effect.Comment: 28 pages, 8 figure

Socio-demographic and fertility related characteristics and motivations of oocyte donors in eleven European countries

Do the socio-demographic and fertility-related characteristics and motivations of oocyte donors differ in European countries? The socio-demographic and fertility-related characteristics and motivations of oocyte donors differ considerably across countries. There have been no other international studies comparing the characteristics of oocyte donors. Regarding their motivations, most studies indicate mixed motives. The proposed study was a transversal epidemiological study. Data were collected from 63 voluntarily participating assisted reproduction technology centres practising oocyte donation in 11 European countries (Belgium, Czech Republic, Finland, France, Greece, Poland, Portugal, Russia, Spain, UK and Ukraine). The survey was conducted between September 2011 and June 2012 and ran for 16 calendar months depending on the number of cycles of oocyte donation performed at the centre. The sample size was computed in order to allow an estimate of the percentage of a relatively rare characteristic (2) with a precision (95 confidence interval) of 1. The calculation gave 1118 donors. In total, 1423 forms were obtained from oocyte donors. All consecutive donors in these centres filled out an anonymous questionnaire when they started their hormonal stimulation, asking for their socio-demographic and fertility-related characteristics, their motivations and compensation. Population characteristics were described and compared by country of donation. Motives for donation and mean amount of money were compared between countries and according to the donors characteristics. The socio-demographic and fertility-related characteristics and motivations of oocyte donors varied enormously across European countries. The number of received forms corresponded with a participation rate of 61.9 of the cycles performed by the participating centres. Mean age was 27.4 years. About 49 of donors were fully employed, 16 unemployed and 15 student. The motivation in the total group of donors was 47.8 pure altruism, 33.9 altruism and financial, 10.8 pure financial, 5.9 altruism and own treatment and finally 2 own treatment only. About 15 of the donors were egg sharers (patient donors), mainly from the UK and Poland. Women were donating for the first time in 55.4 of cases, for the second time in 20.3 and for the third time in 12.8. The motivation to donate was significantly related to being of foreign origin (P 0.01), age (P 0.001), living in couple or not (P 0.01), level of education (P 0.001) and number of donations (P 0.001). The amount of compensation differed considerably between centres and/or countries. The general donor profile in this study was a well-educated, 27-year-old woman living with her partner and child who mainly donated to help others. The selection of clinics in some countries and the limited participation rate may have led to a bias in donor characteristics. A possible effect of social desirability in the answers by the donors should be taken into account. The diversity of the donor population reflects the differences in European legislation (for example, on anonymity and payment) and economic circumstances. The differences in systems of reimbursement/payment demonstrate the need to have a thorough discussion on the specific meaning of these terms. The study was funded by the European Society for Human Reproduction and Embryology. The authors declare no conflicting interests

Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.Comment: 33 page

Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively