Time-dependent source identification problem for a fractional Schrodinger equation with the Riemann-Liouville derivative

The Schr\"odinger equation $i \partial_t^\rho u(x,t)-u_{xx}(x,t) = p(t)q(x) + f(x,t)$ ( $0<t\leq T, \, 0<\rho<1$), with the Riemann-Liouville derivative is considered. An inverse problem is investigated in which, along with $u(x,t)$, also a time-dependent factor $p(t)$ of the source function is unknown. To solve this inverse problem, we take the additional condition $B [u (\cdot,t)] = \psi (t)$ with an arbitrary bounded linear functional $B$. Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained. The applied method allows us to study a similar problem by taking instead of $d^2/dx^2$ an arbitrary elliptic differential operator $A(x, D)$, having a compact inverse.Comment: Schrodinger type equation

A derivation of boundary conditions for the space-fractional operator with order 0<α<10<\alpha<1 at the vertices of metric graphs

We consider the space-fractional operator with order $0<\alpha<1$ on the metric star graph. The boundary conditions at the vertices of the metric star graph providing the self-adjointness of the operator are derived. The obtained result is extended to the other topologies of the metric graphs

Polyethylene/Layered Aluminosilicate Nanocomposites: Investigation of Thermal Stability under Static and Dynamic Conditions

Based on linear low-density polyethylene and maleated polyethylene a polymer nanocomposites containing modified montmorillonite have been obtained, structure is investigated by XRD analysis. In turn, by the methods of thermal analysis in static and dynamic modes, the resistance of polymer nanocomposites to oxidative destruction it was investigated. In parallel with this, a comparative analysis of the thermal stability of polymer nanocomposites and polymer compositions containing commercially available organic antioxidants for stabilization of materials based on polyolefins. By results of the analysis carried out in a dynamic mode, for a series of polymer composites the activation energy of thermooxidative destruction was calculated. It is shown that the nanocomposites based on polyethylene, containing the modified montmorillonite not only not concede to polymer compositions with antioxidants in to thermal stability, but also exceed their. Accelerated tests, carried out at relatively high temperatures allowed evaluate the durability of polymer nanocomposites to thermooxidative destruction. Received results allow approve about a long-term thermal stability of these materials in the processing, and in the exploitation conditions

Role of Fractals in Perovskite Solar Cells

The interface engineering plays important role in fabrication of the tandem and perovskite based solar cells. Recent experiments show that the interface effects caused by the coupling of the electron bands and the pairing of geometry of contacting surfaces. In particular, it has been experimentally revealed that the transition from planar to the rough interface improves many photoelectric parameters of the device. It means that the value of the fractal dimension of the interface may be key factor in device performance. It is possible to formulate two problems: firstly, the understanding on simple models why the electrical properties at fractal interfaces are improved, and, secondly, to discuss one of the most promising approaches in modern electronics, namely technology of radiation applications in the creation of rough interfaces. Thirdly, the problem of photodegradation is analyzed in detail in the structures containing the fractal interfaces. On the basis of the constructed models, it was found: i) increase of roughness (fractal) of interface structure can enhance the role of total internal light reflection effect, thereby increasing the effective light path, and therefore, the number of generated e-h-pairs; ii) the curvature of the surface leads to the shift of Tamm levels both to the borders of allowed bands, and to the middle of the band gap; it opens the way of the control of carrier recombination on the interface; iii) surface Tamm orbitals interact differently each with other on the convex and concave areas; it leads to the different probability of defect formation and, consequently, reduces the fractal interface, inhibiting the effect of increasing of the photocurrent associated with the fractal interface (new channel of photodegradation)

Airborne hyperspectral discrimination of tree species with different ages using discrete wavelet transform

In this article, the capability of discrete wavelet transform (DWT) to discriminate tree species with different ages using airborne hyperspectral remote sensing is investigated. The performance of DWT is compared against commonly used traditional methods, i.e. original reflectance and first and second derivatives. The hyperspectral data are obtained from Thetford forest of the UK, which contains Corsican and Scots pines with different ages and broadleaved tree species. The discrimination is performed by employing three different spectral measurement techniques (SMTs) including Spectral Angle Mapper (SAM), Spectral Information Divergence (SID), and a combination of SAM and SID. Five different mother wavelets with a total of 50 different orders are tested. The wavelet detail coefficient (CD) from each decomposition level and combination of all CDs plus the approximation coefficient from the final decomposition level (C-All) are extracted from each mother wavelet. The results show the superiority of DWT against the reflectance and derivatives for all the three SMTs. In DWT, C-All provided the highest discrimination accuracy compared to other coefficients. An over- all accuracy difference of about 20 – 30% is observed between the finest coefficient and C-All. Amongst the SMTs, SID provided the highest accuracy, while SAM showed the lowest accuracy. Using DWT in combination with SID, an overall accuracy up to around 71.4% is obtained, which is around 13.5%, 14.7%, and 27% higher than the accuracies achieved with reflectance and first and second derivatives, respectively

A review of applying second-generation wavelets for noise removal from remote sensing data.

The processing of remotely sensed data includes compression, noise reduction, classification, feature extraction, change detection and any improvement associated with the problems at hand. In the literature, wavelet methods have been widely used for analysing remote sensing images and signals. The second-generation of wavelets, which is designed based on a method called the lifting scheme, is almost a new version of wavelets, and its application in the remote sensing field is fresh. Although first-generation wavelets have been proven to offer effective techniques for processing remotely sensed data, second-generation wavelets are more efficient in some respects, as will be discussed later. The aim of this review paper is to examine all existing studies in the literature related to applying second-generation wavelets for denoising remote sensing data. However, to make a better understanding of the application of wavelet-based denoising methods for remote sensing data, some studies that apply first-generation wavelets are also presented. In the part of hyperspectral data, there is a focus on noise removal from vegetation spectrum