Steklov problem of the first class for a fractional order delay differential equation

Методом функции Грина получено решение задачи Стеклова первого класса для линейного уравнения с дробной производной Герасимова-Капуто с запаздывающим аргументом. Доказана теорема существования и единственности задачи. The solution to the Steklov problem with conditions of the first class for a linear delay differential equation with a Gerasimov-Caputo fractional derivative is obtained by Green function method. The existence and uniqueness theorem to the problem is proved.

Graphene on SiC Substrate as Biosensor: Theoretical Background, Preparation, and Characterization

This work is devoted to the development and optimization of the parameters of graphene-based sensors. The graphene films used in the present study were grown on semi-insulating 6H-SiC substrates by thermal decomposition of SiC at the temperature of ~1700 °C. The results of measurements by Auger and Raman spectroscopies confirmed the presence of single-layer graphene on the silicon carbide surface. Model approach to the theory of adsorption on epitaxial graphene is presented. It is demonstrated that the Green-function method in conjunction with the simple substrate models permit one to obtain analytical results for the charge transfer between adsorbed molecules and substrate. The sensor structure was formed on the graphene film by laser. Initially, a simpler gas sensor was made. The sensors developed in this study demonstrated sensitivity to the NO2 concentration at the level of 1–0.01 ppb. The results obtained in the course of development and the results of testing of the graphene-based sensor for detection of protein molecules are also presented. The biosensor was fabricated by the technology previously developed for the gas sensor. The working capacity of the biosensor was tested with an immunochemical system constituted by fluorescein and monoclonal antibodies (mAbs) binding this dye.

Quantum transport in a chain of quantum dots with inhomogeneous size distribution and manifestation of 1D Anderson localization

The effect of inhomogeneous quantum dot (QD) size distribution on the electronic transport of one-dimensional (1D) QD chains (QDCs) is theoretically investigated. The non-equilibrium Green function method is employed to compute the electron transmission probabilities of QDCs. The ensemble averaged transmission probability shows a close agreement with the conductivity equation predicted by Anderson et al. for a disordered electronic system. The fidelity of quantum transport is defined as the transmission performance of an ensemble of QDCs of length N (N-QDCs) to assess the robustness of QDCs as a practical electronic device. We found that the fidelity of inhomogeneous N-QDCs with the standard deviation of energy level distribution σε is a Lorentzian function of variable Nσε2. With these analytical expressions, we can predict the conductance and fidelity of any QDC characterized by (N, σε). Our results can provide a guideline for combining the chain length and QD size distributions for high-mobility electron transport in 1D QDCs.

An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene

A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.