Point sources identification problems with pointwise overdetermination

This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination conditions. We present conditions for existence and uniqueness of solutions to the problem, display non-uniqueness examples, and, in model situations, we give estimates on the number of measurements that allow completely identify sources and their locations. The results rely on asymptotic representations of Green functions of the corresponding elliptic problems with a parameter. They can be used in constructing new numerical algorithms for determining a solution.Comment: This article is actually a survey of the results obtained in the previous articles of the authors. In some model cases, we discuss the uniqueness and existence results for some classes of inverse problems. The results uses a new approach based on asymptotic representations of the Green function of the corresponding elliptic proble

Molecular dissection of Penelope transposable element regulatory machinery

© 2008 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. The definitive version was published in Nucleic Acids Research 36 (2008): 2522-2529, doi:10.1093/nar/gkm1166Penelope-like elements (PLEs) represent a new class of retroelements identified in more than 80 species belonging to at least 10 animal phyla. Penelope isolated from Drosophila virilis is the only known transpositionally active representative of this class. Although the size and structure of the Penelope major transcript has been previously described in both D. virilis and D. melanogaster transgenic strains, the architecture of the Penelope regulatory region remains unknown. In order to determine the localization of presumptive Penelope promoter and enhancer-like elements, segments of the putative Penelope regulatory region were linked to a CAT reporter gene and introduced into D. melanogaster by P-element-mediated transformation. The results obtained using ELISA to measure CAT expression levels and RNA studies, including RT–PCR, suggest that the active Penelope transposon contains an internal promoter similar to the TATA-less promoters of LINEs. The results also suggest that some of the Penelope regulatory sequences control the preferential expression in the ovaries of the adult flies by enhancing expression in the ovary and reducing expression in the carcass. The possible significance of the intron within Penelope for the function and evolution of PLEs, and the effect of Penelope insertions on adjacent genes, are discussed.This work was supported by grants from Russian Academy of Sciences (Cell and Molecular Biology to M.E.), and Welcome Trust Grant (075698) to M.E and D.J.F

Waveguide-Integrated Electrically Driven Light-Emitting Carbon Nanotubes

In this work proof-of-concept devices with light-emitting electrically driven carbon nanotubes (CNTs) integrated in nanophotonic environments are presented. Electroluminescent and incandescent CNTs can be envisioned as waveguide-integrated light sources for future on-chip data communication due to their unique structural, electrical and optical properties. The challenge thereby is to integrate and electrically contact solution processed CNTs across CMOS compatible waveguide structures and to enforce efficient coupling of light from the CNT into the waveguide. Various nanophotonic devices with versatile functionalities were fabricated and equipped with CNTs by means of site-selective dielectrophoresis. The realized electrically driven CNT-based light emitters integrated with nanophotonic circuits allow for efficient coupling and propagation of light in waveguides over centimeter distances. Furthermore, in scope of the thesis it was demonstrated how spectral properties of a CNT emitter can be controlled directly on a chip with passive devices using grating structures, Mach-Zehnder interferometers and directional couplers. Moreover, it was observed that in combination with a one-dimensional photonic crystal cavity CNT becomes an emitter with exceptionally narrow linewidths at desired adjustable wavelength. Finally, the usage of electrically driven CNTs as fast waveguide-integrated light emitters with Gbit/s response speed was shown. Therefore direct, near-field coupling of electrically generated CNT-emitted light into a waveguide, opposed to far-field fiber coupling of external light sources, opens new avenues for scalable nanoscale optoelectronic systems in a CMOS compatible framework

On the nature of ill-posedness of the forward-backward heat equation

We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by the J-self-adjoint linear operator L depending on a small parameter. The problem has been originated from the lubrication approximation of a viscous fluid film on the inner surface of the rotating cylinder. For a certain range of the parameter we rigorously prove the conjecture, based on the numerical evidence, that the set of eigenvectors of the operator $L$ does not form a Riesz basis in \L^2 (-\pi,\pi). Our method can be applied to a wide range of the evolutional problems given by $PT-$symmetric operators.Comment: 21 pages; Remark 5.2 added, acknowledgements added, several typos fixe

The similarity problem for indefinite Sturm-Liouville operators and the HELP inequality

We study two problems. The first one is the similarity problem for the indefinite Sturm-Liouville operator A=-(\sgn\, x)\frac{d}{wdx}\frac{d}{rdx} acting in $L^2_{w}(-b,b)$. It is assumed that w,r\in L^1_{\loc}(-b,b) are even and positive a.e. on $(-b,b)$. The second object is the so-called HELP inequality $$(\int_{0}^b\frac{1}{\tilde{r}}|f'|\, dx)^2 \le K^2 \int_{0}^b|f|^2\tilde{w}\,dx\int_{0}^b\Big|\frac{1}{\tilde{w}}\big(\frac{1}{\tilde{r}}f'\big)'\Big|^2\tilde{w}\, dx,$$ where the coefficients \tilde{w},\tilde{r}\in L^1_{\loc}[0,b) are positive a.e. on $(0,b)$. Both problems are well understood when the corresponding Sturm-Liouville differential expression is regular. The main objective of the present paper is to give criteria for both the validity of the HELP inequality and the similarity to a self-adjoint operator in the singular case. Namely, we establish new criteria formulated in terms of the behavior of the corresponding Weyl-Titchmarsh $m$-functions at 0 and at $\infty$. As a biproduct of this result we show that both problems are closely connected. Namely, the operator $A$ is similar to a self-adjoint one precisely if the HELP inequality with $\tilde{w}=r$ and $\tilde{r}=w$ is valid. Next we characterize the behavior of $m$-functions in terms of coefficients and then these results enable us to reformulate the obtained criteria in terms of coefficients. Finally, we apply these results for the study of the two-way diffusion equation, also known as the time-independent Fokker-Plank equation.Comment: 42 page

Comportamiento ruidoso de los residentes de un edificio de apartamentos como una cuestión de ley de vecindad (el caso de la relación entre dueños de perros y vecinos)

The aim of this study is to examine in detail such a segment of neighborhood law as the silence related relations of neighbors in an apartment building. Neighborhood law, despite its long existence in the legal systems of foreign countries, remains unspecific in the regulation of relations between apartment owners, while in Russia neighborhood law has not received due attention from the federal legislator. We believe that competition between public and private law on this issue should be resolved in favor of private law. Civil law in the current state contains a great potential for the regulation of neighborhood relations and protection of neighborhood rights. The possibilities of civil law in this area should be expanded in the course of the forthcoming reform of property legislation. It is necessary to continue the development of neighborhood law in Russia.El objetivo de este estudio es examinar en detalle un segmento de la ley del vecindario como las relaciones de vecinos relacionadas con el silencio en un edificio de apartamentos. La ley de vecindad, a pesar de su larga existencia en los sistemas legales de países extranjeros, sigue siendo inespecífica en la regulación de las relaciones entre los propietarios de apartamentos, mientras que en Rusia la ley de vecindad no ha recibido la debida atención del legislador federal. Creemos que la competencia entre el derecho público y privado en este tema debe resolverse a favor del derecho privado. La ley civil en el estado actual tiene un gran potencial para la regulación de las relaciones vecinales y la protección de los derechos vecinales. Las posibilidades del derecho civil en esta área deberían ampliarse en el curso de la próxima reforma de la legislación de propiedad. Es necesario continuar el desarrollo de la ley de vecindad en Rusia

Collinear cluster tripartition as sequential binary fission in the 235^{235}U(nth_{\rm th},f) reaction

The mechanism leading to the formation of the observed products of the collinear cluster tripartition is carried out within the framework of the model based on the dinuclear system concept. The yield of fission products is calculated using the statistical model based on the driving potentials for the fissionable system. The minima of potential energy of the decaying system correspond to the charge numbers of the products which are produced with large probabilities in the sequential fission (partial case of the collinear cluster tripartition) of the compound nucleus. The realization of this mechanism supposes the asymmetric fission channel as the first stage of sequential mechanism. It is shown that only the use of the driving potential calculated by the binding energies with the shell correction allows us to explain the yield of the true ternary fission products. The theoretical model is applied to research collinear cluster tripartition in the reaction $^{235}$U(n$_{\rm th}$,f). Calculations showed that in the first stage of this fission reaction, the isotopes $^{82}$Ge and $^{154}$Nd are formed with relatively large probabilities and in the second stage of sequential fission of the isotope Nd mainly Ni and Ge are formed. This is in agreement with the yield of the isotope $^{68}$Ni which is observed as the product of the collinear cluster tripartition in the experiment.Comment: 20 pages, 9 figure

On a necessary aspect for the Riesz basis property for indefinite Sturm-Liouville problems

In 1996, H. Volkmer observed that the inequality $$(\int_{-1}^1\frac{1}{|r|}|f'|dx)^2 \le K^2 \int_{-1}^1|f|^2dx\int_{-1}^1\Big|\Big(\frac{1}{r}f'\Big)'\Big|^2dx$$ is satisfied with some positive constant $K>0$ for a certain class of functions $f$ on $[-1,1]$ if the eigenfunctions of the problem $$-y"=\lambda\, r(x)y,\quad y(-1)=y(1)=0$$ form a Riesz basis of the Hilbert space $L^2_{|r|}(-1,1)$. Here the weight $r\in L^1(-1,1)$ is assumed to satisfy $xr(x)>0$ a.e. on $[-1,1]$. We present two criteria in terms of Weyl-Titchmarsh $m$-functions for the Volkmer inequality to be valid. Using these results we show that this inequality is valid if the operator associated with the spectral problem satisfies the linear resolvent growth condition. In particular, we show that the Riesz basis property of eigenfunctions is equivalent to the linear resolvent growth if $r$ is odd.Comment: 26 page