Conflicts of Interest: CDB, HBM, EEM, and MBY have patents pending related to both coagulation/fibrinolysis diagnostics and therapeutic fibrinolytics, and are passive co-founders and holds stock options in Thrombo Therapeutics, Inc. HBM and EEM have received grant support from Haemonetics and Instrumentation Laboratories. MBY has previously received a gift of Alteplase (tPA) from Genentech, and owns stock options as a co-founder of Merrimack Pharmaceuticals. All other authors have nothing to disclose.

In this paper, we consider a small polynomial perturbation of the Hamiltonian vector field with the Hamiltonian F (x, y) = x[y 2 − (x − 3) 2 ] having a center bounded by a triangle. The main result of this work is that the principal Poincaré-Pontryagin function associated with such a perturbation and with the family of ovals surrounding the center belongs to the C[t, 1/t] module generated by Abelian integrals I 0 (t) and I 2 (t) and by I * (t), where I * (t) is not an Abelian integral. We show that, in general, the principal Poincaré-Pontryagin function of order two of a polynomial perturbation of the degree at least five is not an Abelian integral.

In this paper, we study small polynomial perturbations of a Hamiltonian vector field with Hamiltonian F formed by a product of (d + 1) real linear functions in two variables. We assume that the corresponding lines are in a general position in R 2 . That is, the lines are distinct, non-parallel, no three of them have a common point and all critical values not corresponding to intersections of lines are distinct. We prove in this paper that the principal Poincaré-Pontryagin function M k (t), associated to such a perturbation and to any family of ovals surrounding a singular point of center type, belongs to the C[t, 1/t]-module generated by Abelian integrals and some integrals I * i, j (t), with 1 i < j d defined in the paper. Moreover, I * i, j (t) are not Abelian integrals.They are iterated integrals of length two.

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It is known that the Principal Poincaré Pontryagin Function is generically an Abelian integral. We give a sufficient condition on monodromy to ensure that it is an Abelian integral also in non generic cases.In non generic cases it is an iterated integral. Uribe [17,18] gives in a special case a precise description of the Principal Poincaré Pontryagin Function, an iterated integral of length at most 2, involving logarithmic functions with only one ramification at a point at infinity. We extend this result to some non isodromic families of real Morse polynomials.

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Objective: The genital mycoplasmas (Mycoplasma hominis and Ureaplasma urealyticum) and Chlamydia trachomatis have been implicated as possible etiologic factors in infertility. Their role in patients with infertility needs to be further defined. Methods: Seventy-nine infertile patients underwent laparoscopy with cultures obtained for aerobic and anaerobic bacteria, Chlamydia, Mycoplasma, and Ureaplasma from the peritoneal fluid, fallopian tube, endometrium, and endocervix. Cultures for similar organisms were taken from the endocervix of 80 fertile women in their first trimester. Culture results were also compared according to ovulatory status and laparoscopic findings in the infertile group. Results: There were no differences in the recovery of Ureaplasma (29% vs. 28%) or Chlamydia (4% vs. 0%) positive cervical cultures in the fertile and infertile groups, respectively. However, a significantly higher number of Mycoplasma positive cervical cultures (14% vs. 5%, P = 0.05) were found in the fertile group. Only two upper genital tract cultures were found to be positive (Ureaplasma). Conclusions: Therefore, if these organisms play a role in infertility, they are present and eradicated prior to infertility work-up and thus do not supports the use of a routine trial of antibiotics prior to laparoscopy.

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