Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

«Muslim matter» in the mirror of public discussion (XIX - beginning of XX century)

The relevance of the studied problem is determined by the socio-political processes that have embraced the modern Islamic world, connected with the substantial politicization of the Muslim community, religious revival movements and the spread of radical currents. The paper is aimed at studying the public debate in Russia (XIX-early XX century) regarding the future of domestic Muslims. The leading approach to the study of this problem is the concept that modernization attempts in Russia had compensatory nature and were aimed at strengthening the imperial system. Based on the study of the works by the experts of the "Muslim matter”, the authors came to the conclusion that the public discussion arrived at a view that it is necessary to strengthen the spiritual and cultural assimilation of foreigners on the ways of activating both administrative and cultural methods. Reliability of the results of the study is determined by the authors' appeal to a representative sample and analysis of the works by Russian scientists and publicists, who most clearly reflected the position of their socio-political group regarding the future of the Muslim community in Russia. Along with the opinions of academic orientalists and Islamologists, the views of representatives of the scientific missionary circles, Muslim modernists, revolutionary democrats, etc. are presented. The materials of the paper can be useful for further development of scientific problems on the history of Islam and Muslim peoples, as well as the history of culture and public thought of the peoples of Russia.Keywords: history, social studies, Islamic studies, Russian empire, "Muslim matter", publicdiscussion

QSPR modeling aqueous solubility of polychlorinated biphenyls by optimization of correlation weights of local and global graph invariants

Aqueous solubilities of polychlorinated biphenyls have been correlated with topological molecular descriptors which are functions of local and global invariants of labeled hydrogen filled graphs. Morgan extended connectivity and nearest neighboring codes have been used as local graph invariants. The number of chlorine atoms in biphenyls has been employed as a global graph invariant. Present results show that taking into account correlation weights of global invariants gives quite reasonable improvement of statistical characteristics for the prediction of aqueous solubilities of polychlorinated biphenyls.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

QSPR modeling aqueous solubility of polychlorinated biphenyls by optimization of correlation weights of local and global graph invariants

Aqueous solubilities of polychlorinated biphenyls have been correlated with topological molecular descriptors which are functions of local and global invariants of labeled hydrogen filled graphs. Morgan extended connectivity and nearest neighboring codes have been used as local graph invariants. The number of chlorine atoms in biphenyls has been employed as a global graph invariant. Present results show that taking into account correlation weights of global invariants gives quite reasonable improvement of statistical characteristics for the prediction of aqueous solubilities of polychlorinated biphenyls.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

In Vitro Cytotoxicity of CdSe/ZnS Quantum Dots and Their Interaction with Biological Systems

Semiconductor nanocrystals (quantum dots, QDs) have a wide range of potential application in multiplexed tissue and cell imaging, and for in vivo molecular diagnostics and therapy. Therefore studying of the toxicity of QDs and their influence on various cellular processes in vitro is necessary to understand their interaction with living systems.; The paper presents the results of studies on the evaluation of CdSe/ZnS QD cytotoxicity, as well as the results of studying their interaction with freshly prepared human monocytes in vitro. Keywords: Quantum dots, semiconductor nanocrystals, cytotoxicity, in vitro models, monocytes

Gap solitons in a model of a hollow optical fiber

We introduce a models for two coupled waves propagating in a hollow-core fiber: a linear dispersionless core mode, and a dispersive nonlinear quasi-surface one. The linear coupling between them may open a bandgap, through the mechanism of the avoidance of crossing between dispersion curves. The third-order dispersion of the quasi-surface mode is necessary for the existence of the gap. Numerical investigation reveals that the entire bandgap is filled with solitons, and they all are stable in direct simulations. The gap-soliton (GS) family is extended to include pulses moving relative to the given reference frame, up to limit values of the corresponding boost $\delta$, beyond which the solitons do not exists. The limit values are nonsymmetric for $\delta >0$ and $\delta <0$. The extended gap is also entirely filled with the GSs, all of which are stable in simulations. Recently observed solitons in hollow-core photonic-crystal fibers may belong to this GS family.Comment: 5 pages, 5 figure

Algorithms For Recovery Of Diffusion And Sturm-Liouville Operators With Semi-Separated Boundary Conditions

Diffusion and Sturm-Liouville equations under semi-separated boundary conditions, one of which contains a quadratic function of the spectral parameter are considered in this paper. Some properties of the spectrum of the operators under consideration are given, uniqueness theorems are proved, and algorithms for solving inverse recovery problems for the corresponding boundary value problems are constructed

The Effect of Quantum Dot Shell Structure on Fluorescence Quenching By Acridine Ligand

The current strategy for the development of advanced methods of tumor treatment focuses on targeted drug delivery to tumor cells. Quantum dot (QD) - semiconductor fluorescent nanocrystal, conjugated with a pharmacological ligand, such as acridine, ensures real-time tracking of the delivery process of the active substance. However, the problem of QD fluorescence quenching caused by charge transfer can arise in the case when acridine is bound to the QD. We found that QD shell structure has a defining role on photoinduced electron transfer from QD on acridine ligand which leads to quenching of QD photoluminescence. We have found that multishell CdSe/ZnS/CdS/ZnS QD structure provides minimal reduction of photoluminescence quantum yield at minimal shell thickness compared to classical thin ZnS or “giant” shells. Thus, CdSe/ZnS/CdS/ZnS core/multishell QD could be an optimal choice for engineering of small-sized acridine-based fluorescent labels for tumor diagnosis and treatment systems. Keywords: Quantum dot, photoluminescence quenching, DNA ligand, acridine derivative

Cytotoxicity of Polyelectrolyte Microcapsules Encoded with Semiconductor Nanocrystals

Polyelectrolyte microcapsules are promising carriers of drugs and diagnostic agents for designing targeted and controlled delivery systems design. The use of quantum dots (QDs) as fluorescent labels in bioimaging is a promising approach to bioimaging tool development. The potential toxicity of QDs makes their applicability as fluorescent labels in vivo questionable. Therefore, the cytotoxicity of polyelectrolyte microcapsules encoded with semiconductor nanocrystals has been investigated. Keywords: Polyelectrolyte microcapsules, semiconductor nanocrystals, cytotoxicity, theranostic agents