Inverse medium problem for a singular contrast

We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.Peer reviewe

Group classification of heat conductivity equations with a nonlinear source

We suggest a systematic procedure for classifying partial differential equations invariant with respect to low dimensional Lie algebras. This procedure is a proper synthesis of the infinitesimal Lie's method, technique of equivalence transformations and theory of classification of abstract low dimensional Lie algebras. As an application, we consider the problem of classifying heat conductivity equations in one variable with nonlinear convection and source terms. We have derived a complete classification of nonlinear equations of this type admitting nontrivial symmetry. It is shown that there are three, seven, twenty eight and twelve inequivalent classes of partial differential equations of the considered type that are invariant under the one-, two-, three- and four-dimensional Lie algebras, correspondingly. Furthermore, we prove that any partial differential equation belonging to the class under study and admitting symmetry group of the dimension higher than four is locally equivalent to a linear equation. This classification is compared to existing group classifications of nonlinear heat conductivity equations and one of the conclusions is that all of them can be obtained within the framework of our approach. Furthermore, a number of new invariant equations are constructed which have rich symmetry properties and, therefore, may be used for mathematical modeling of, say, nonlinear heat transfer processes.Comment: LaTeX, 51 page

New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found

A quantitative theory-versus-experiment comparison for the intense laser dissociation of H2+

A detailed theory-versus-experiment comparison is worked out for H$_2^+$ intense laser dissociation, based on angularly resolved photodissociation spectra recently recorded in H.Figger's group. As opposite to other experimental setups, it is an electric discharge (and not an optical excitation) that prepares the molecular ion, with the advantage for the theoretical approach, to neglect without lost of accuracy, the otherwise important ionization-dissociation competition. Abel transformation relates the dissociation probability starting from a single ro-vibrational state, to the probability of observing a hydrogen atom at a given pixel of the detector plate. Some statistics on initial ro-vibrational distributions, together with a spatial averaging over laser focus area, lead to photofragments kinetic spectra, with well separated peaks attributed to single vibrational levels. An excellent theory-versus-experiment agreement is reached not only for the kinetic spectra, but also for the angular distributions of fragments originating from two different vibrational levels resulting into more or less alignment. Some characteristic features can be interpreted in terms of basic mechanisms such as bond softening or vibrational trapping.Comment: submitted to PRA on 21.05.200

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations

Comparative morphological characteristics of the uteroplacental area in abnormal placentation

The aim. To carry out a comparative morphological characteristic of the uteroplacental area with abnormal placentation – pl. accreta, pl. increta, pl. percreta. Materials and methods. The study included 47 patients with atypical placentation; the comparison group included 10 healthy pregnant women with uterine scar after a previous caesarean section. A histological study of uteroplacental area samples was performed with hematoxylin and eosin, methylene blue staining. An immunohistochemical study with primary antibodies to cytokeratin 7 (CK7), Hif2a, vascular endothelial growth factor, α-SMA was carried out. The differences between the compared values were considered to be statistically significant at p < 0.05. The results of the study. Pl. accreta was determined in 12 (25.5 %), pl. increta – in 30 (63.9 %), pl. percreta – in 5 (10.6 %) patients. In all patients of the main group, the decidua was completely or partially absent in the area of abnormal placentation or was replaced by an uneven layer of fetal fibrinoid. Cases when placental villi unevenly penetrated into the thickness of myometrium in the form of “tongues” or “coves” bordered by fetal fibrinoid and often located intermuscularly were defined as pl. increta (n = 26). Cases with the placental villi ingrowth to the serous membrane were considered as pl.  percreta (n  =  5). In cases with deep variants of  ingrowth (pl. increta and pl. percreta) (n = 31), the villi were visualized in the lumen of the vessels and the thinning of the lower uterine segment with the presence of stretched muscle bundles was revealed. Aseptic necrosis of  the myometrium was  found: in 2 (16.7 %) of 12 women with pl. accreta, in 26 (86.7 %) of 30 women with pl. increta and in 5 (100 %) women with pl. percreta. There were no areas of necrosis in the myometrium of the women of comparison group. Conclusion. The appearance and increase of myometrial necrosis zones in response to an increase in the depth of placental villus ingrowth were detected. Myometrial necrosis zones could be the cause of activation of angiogenic factors and an important stimulus for the development of abnormal vascularization in placenta accreta spectrum

Imaging the square of the correlated two-electron wave function of a hydrogen molecule

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H2two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sourcesThis work was funded by the Deutsche Forschungsgemeinschaft, the BMBF, the European Research Council under the European Union Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 290853 XCHEM, the MINECO projects FIS2013-42002-R and FIS2016-77889-R, and the European COST Action XLIC CM1204. All calculations were performed at the CCC-UAM and Mare Nostrum Supercomputer Centers. We are grateful to the staff of PETRA III for excellent support during the beam time. K.M. and M.M. would like to thank the DFG for support via SFB925/A3. A.K. and V.S. thank the Wilhelm und Else Heraeus-Foundation for support. J.L. would like to thank the DFG for support. S.K. acknowledges support from the European Cluster of Advanced Laser Light Sources (EUCALL) project which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 654220. T.W. was supported by the U.S. Department of Energy Basic Energy Sciences under Contract No. DE-AC02-05CH11231. A.P. acknowledges a Ramón y Cajal contract from the Ministerio de Economa y Competitivida

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

Reproductive parameters and the use of MOET in transgenic founder goat carrying the human granulocyte colony-stimulating factor (hG-CSF) gene.

Abstract: This study aimed to monitor estrous cycle parameters of a human granulocyte colony-stimulating factor (hG-CSF)-transgenic founder female goat and to perform superovulation and embryo recovery (surgical or transcervical method) for further transfer to recipients to quickly obtain offspring. Two experiments were performed using a transgenic (TF) and a non-transgenic (NTF) female. In experiment 1, three estrous cycles were monitored for the following parameters: estrus behavior, progesterone concentration and ovarian activity. In experiment 2, two superovulation/embryo recovery sessions were performed and the recovered embryos were transferred to previously prepared recipients. Data were compared by either t test or Fisher's exact test. The mean interval between natural estrus was 20.7 ± 0.6 and 19.7 ± 0.6 (P > 0.05) days for the TF and NTF, respectively. Progesterone concentrations and ovarian activity were normal and similar between goats. The ovulation rate was similar between TF and NTF (12.0 ± 1.4 vs. 18.0 ± 4.2 CL; P > 0.05). No significant differences in embryo recovery rate (P > 0.05) were observed between the surgical and transcervical methods for TF (69.2 vs. 72.7%) or NTF (100.0 vs. 86.7%). Sixteen embryos from the TF were transferred to recipients, and eight kids were born. Among these kids, the transgene was identified in three (two males and one female), resulting in a transgenesis rate of 37.5%. In summary, the TF is a true founder, since she proved fertility and capacity of transmitting the hG-CSF transgene to progeny, suggesting that the analyzed reproductive traits were not compromised by the presence of the transgene