Narrow Results

We prove the preservation theorems for NATP; many of them extend the previously established preservation results for other model-theoretic tree properties. Using them, we also furnish proper examples of NATP theories which are simultaneously TP₂ and SOP.

First, we show that NATP is preserved by the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property.

Second, the preservation of NATP for two kinds of dense/co-dense expansions, i.e. the theories of lovely pairs and of $H$-structures for geometric theories, and dense/co-dense expansion on vector spaces is proved.

Next, we prove the preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also the preservation of NTP₁ and NTP₂ is considered.

Finally, we present some proper examples of NATP theories using the results proved in this paper, including the parametrization of DLO and the expansion of an algebraically closed field by adding a generic linear order. In particular, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP.

Some small fragments of rag paper - made more than a thousand and a few hundred years ago, and excavated at Turfan, west of China by the Otani-expedition dispatched there during the late Meiji and the Taisho eras - were measured by PIXE. Bromine was highly Detected in all these ancient fragments and modern paper samples that had been placed together with these Turfan manuscripts. In other paper samples, bromine could not be detected (H⁺, 4MeV, 50μC and H⁺, 2MeV, 100μC) and their average concentration was about 1.1ppm (S.D.=1.11ppm, N=15, 0.3~3.4ppm). The bromine contamination of ancient sutras is mainly caused by larvicide of methyl bromide, and the observation suggests that the ancient manuscripts might be spoiled gradually by agricultural chemicals for protecting them from vermin.

In this work we present some moment preserving finite volume schemes (FVS) for solving population balance equations. We are considering unified numerical methods to simultaneous aggregation, breakage, growth and source terms, e.g. for nucleation. The criteria for the preservation of different moments are given. The property of conservation is a special case of preservation. First we present a FVS which shows the preservation with respect to one-moment depending upon the processes under consideration. In case of the aggregation and breakage it satisfies first-moment preservation whereas for the growth and nucleation we observe zeroth-moment preservation. This is due to the well-known property of conservativity of FVS. However, coupling of all the processes shows no preservation for any moments. To overcome this issue, we reformulate the cell average technique into a conservative formulation which is coupled together with a modified upwind scheme to give moment preservation with respect to the first two-moments for all four processes under consideration. This allows for easy coupling of these processes. The preservation is proven mathematically and verified numerically. The numerical results for the first two-moments are verified for various coupled processes where analytical solutions are available.

Background: Oocyte Cryopreservation has become an important part of infertility treatment for various reasons such as fertility preservation in women going for oncological treatment; in oocyte donation cycles; in eliminating several religious, ethical, and legal concerns of embryo freezing and in women who wish to delay childbirth. The newer ”vitrification” technique for freezing has further improved the success rates for actual conception than the earlier method of slow freezing. A successful oocyte freezing program can help in establishment of oocyte banks, which would help to provide compatible oocytes immediately, thus would eliminate the several problems of fresh donor cycles.

Methods: In this retrospective observational study, total 60 oocyte donation cycles were included (38 were fresh and 22 were vitrified oocytes cycle, respectively). After a thorough screening, controlled ovarian hyperstimulation for donors was performed using flexible antagonist protocol. All mature oocytes were allocated into “vitrified oocytes” and “fresh oocytes” groups. Vitrification technique using Cryotop method was used for oocyte freezing. Both clinical and laboratory outcomes of vitrified and fresh oocytes in donor cycles were compared.

Results: A total of 600 oocytes (226 “vitrified oocytes” and 374 fresh oocytes), were studied. After warming 218 oocytes survived resulting in survival rate of 96.4%. Fertilization rate and embryo formation rate was 86.2% and 93.6%, respectively. Results of frozen-thawed oocyte donor cycles were compared with fresh donation cycles. For fresh oocyte group, fertilization rate and embryo formation rate was 83.4% and 92.6%, respectively. On comparing clinical outcomes, clinical pregnancy rate was 60.5% in fresh group and 63.6% in vitrified group.

Conclusions: Both clinical and laboratory results obtained in the study suggest that oocyte cryopreservation can be performed with reproducible success, thus vitrification technique can be provided as a useful tool for achieving highly successful outcomes in an oocyte donor program.

The quantum operators generated by a random variable X, having finite moments of all orders, are expressed as a sum of compositions of powers of the multiplication operator by X and differentiation operator D = d/dX. The multiplication by X operator is located to the left of the differentiation operator.

A simple method of recovering the moments of a probability measure, on ℝ, from the commutator between its annihilation and creation operators, the commutator between the annihilation and preservation operator, and the first moment is presented.